This program was contributed by Roger Fu <rogerfu@fas.harvard.edu>.
It comes without any warranty or support by its authors or the authors of deal.II.
This program is part of the deal.II code gallery and consists of the following files (click to inspect):
Annotated version of Readme.md
Readme file for CeresFE
Motivation for project
This code was made to simulate the evolution of global-scale topography on planetary bodies. Specifically, it is designed to compute the rates of topography relaxation on the dwarf planet Ceres. The NASA Dawn mission, in orbit around Ceres since March, 2015, has produced a high resolution shape model of its surface. As on other planets including the Earth, topography on Ceres is subject to decay over time due to processes such as viscous flow and brittle failure. Because the efficiency of these processes is dependent on the material properties of the body at depth, simulating the decay of topography and comparing it to the observed shape model permits insights into Ceres' internal structure.
Some previous applications of this basic idea- using topography to constrain internal structure- may be found in the following references:
- Takeuchi, H. and Hasegawa, Y. (1965) Viscosity distribution within the Earth. Geophys. J. R. astr. Soc. 9, 503-508.
- Anderson, D. L. and O'Connell, R. (1967) Viscosity of the Earth. Geophys. J. R. astr. Soc. 14, 287-295.
- Solomon, S. C., Comer, R. P., Head, J. W. (1982) The Evolution of impact basins: Viscous relaxation of topographic relief.
- Zuber, M. T. et al. (2000) Internal structure and early thermal evolution of Mars from Mars Global Surveyor topography and gravity. Science 287, 1788-1793.
- Fu, R. R. et al. (2014) Efficient early global relaxation of asteroid Vesta. Icarus 240, 133-145.
The code included here is a development of a simpler code for the asteroid Vesta, published as reference 5 above. Because both versions of the code were written specifically to model long wavelength topography on these small bodies, the code is rather specific. We hope certain components of it may be useful to the reader even if the problem of topographic relaxation on asteroid belt bodies is not on everyone's radar.
Quick facts about the code
Viscoelastoplastic Asymmetric Lagrangian Uses analytical self-gravity One sentence purpose: Simulates evolution of topography due to self-gravity on axisymmetry planetary body.
More detailed properties of the code in CeresFE
Viscoelastoplasticity
The code is viscoelastoplastic: it solves the Stokes equations modified to include elasticity and iteratively uses the stress solution to account for displacement due to brittle failure The implementation of viscoelasticity follows mainly section 2.2.3 of Keller, T. et al. (2013) Numerical modelling of magma dynamics coupled to tectonic deformation of lithosphere and crust. Geophys. J. Int. 195, 1406-1442. At the end of each FE calculation, the principle stresses (in 3D) are computed in all cells. Each cell is evaluated according to either Byerlee's Rule or a damaged rock brittle failure criterion to determine if failure occurred. See Byerlee, J. (1978) Friction of rocks, Pageoph. 116, 615-626. and Schultz, R. A. (1993) Brittle strength of basalitc rock masses with applications to Venus. J. Geophys. Res. 98, 10,883-10,895. If a cell failed, its viscosity is lowered by a computed amount to simulate plastic yielding. The viscosity fields is smoothed and the FE model run again. This is repeated until the number of failed cells falls below a prescribed number. The final viscosity field (i.e., the effective viscosity) is then used to compute velocities and advance the mesh.
Domain and boundary conditions
The domain of the model is 2D, but the Stokes equations are cast in axisymmetric form. The domain consists of approximately a quarter ellipse, with two straight edges corresponding to the rotation axis and equator of the body. No normal flux boundary conditions are applied to these edges. The remaining curved edge that corresponds to the surface of the body is assigned a zero pressure boundary condition With respect to self-gravity, an ellipse is fitted to the outer surface and any internal density surfaces at each time step and a gravity field is computed analytically following Pohanka, V. (2011) Gravitational field of the homogeneous rotational ellipsoidal body: a simple derivation and applications. Contrib. Geophys. Geodesy 41, 117-157.
Description of files in repo
src/ceres.cc Main code support_code/config_in.h Reads config file and initializes system parameters support_code/ellipsoid_fit.h Finds best-fit ellipse for surface and internal density boundaries. Also uses deal.II support_code/ellipsoid_grav.h Analytically computes self gravity of layered ellipsoids structure support_code/local_math.h Defines some constants for convenience meshes/sample_CeresFE_mesh.inp Sample input mesh config/sample_CeresFE_config.cfg ample configurations file with simulation parameters
Other dependencies
Two more code packages are necessary to run CeresFE:
- config++: https://sourceforge.net/projects/config/
- Armadillo: http://arma.sourceforge.net
To run the code
After running cmake and compiling, run the executable with one argument, which is the config file :
\(ceres \){SOURCE_DIR}/config/sample_CeresFE_config.cfg
Annotated version of src/ceres.cc
#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/logstream.h>
#include <deal.II/base/function.h>
#include <deal.II/base/utilities.h>
#include <deal.II/lac/block_vector.h>
#include <deal.II/lac/full_matrix.h>
#include <deal.II/lac/block_sparse_matrix.h>
#include <deal.II/lac/solver_cg.h>
#include <deal.II/lac/precondition.h>
#include <deal.II/lac/affine_constraints.h>
#include <deal.II/grid/tria.h>
#include <deal.II/grid/grid_generator.h>
#include <deal.II/grid/tria_accessor.h>
#include <deal.II/grid/tria_iterator.h>
#include <deal.II/grid/grid_tools.h>
#include <deal.II/grid/manifold_lib.h>
#include <deal.II/grid/grid_refinement.h>
#include <deal.II/grid/grid_in.h>
#include <deal.II/dofs/dof_handler.h>
#include <deal.II/dofs/dof_renumbering.h>
#include <deal.II/dofs/dof_accessor.h>
#include <deal.II/dofs/dof_tools.h>
#include <deal.II/fe/fe_q.h>
#include <deal.II/fe/fe_system.h>
#include <deal.II/fe/fe_values.h>
#include <deal.II/numerics/vector_tools.h>
#include <deal.II/numerics/matrix_tools.h>
#include <deal.II/numerics/data_out.h>
#include <deal.II/numerics/error_estimator.h>
#include <deal.II/numerics/derivative_approximation.h>
#include <deal.II/numerics/fe_field_function.h>
#include <deal.II/lac/sparse_direct.h>
#include <deal.II/lac/sparse_ilu.h>
#include <iostream>
#include <fstream>
#include <sstream>
#include <string>
#include <time.h>
#include <math.h>
#include <armadillo>
#include "../support_code/ellipsoid_grav.h"
#include "../support_code/ellipsoid_fit.h"
#include "../support_code/config_in.h"
#define DEAL_II_DISABLE_EXTRA_DIAGNOSTICS
#define DEAL_II_ENABLE_EXTRA_DIAGNOSTICS
As in all programs, the namespace dealii is included:
namespace Step22
{
using namespace arma;
template<int dim>
struct InnerPreconditioner;
template<>
struct InnerPreconditioner<2>
{
};
template<>
struct InnerPreconditioner<3>
{
};
Auxiliary functions
template<int dim>
class AuxFunctions
{
public:
};
template<int dim>
{
const double curl = (grad_u[1][0] - grad_u[0][1]);
const double t[2][2] = { { cos(angle), sin(angle) }, {
angle)
}
};
}
::VectorizedArray< Number, width > cos(const ::VectorizedArray< Number, width > &)
::VectorizedArray< Number, width > sin(const ::VectorizedArray< Number, width > &)
inline ::VectorizedArray< Number, width > atan(const ::VectorizedArray< Number, width > &x)
Class for remembering material state/properties at each quadrature point
template<int dim>
struct PointHistory
{
double old_phiphi_stress;
double first_eta;
double new_eta;
double G;
};
Primary class of this problem
template<int dim>
class StokesProblem
{
public:
StokesProblem(const unsigned int degree);
void run();
private:
void setup_dofs();
void assemble_system();
void solve();
void output_results() const;
void refine_mesh();
void solution_stesses();
void smooth_eta_field(std::vector<bool> failing_cells);
void setup_initial_mesh();
void do_elastic_steps();
void do_flow_step();
void update_time_interval();
void initialize_eta_and_G();
void move_mesh();
void do_ellipse_fits();
void append_physical_times(int max_plastic);
void write_vertices(unsigned char);
void write_mesh();
void setup_quadrature_point_history();
void update_quadrature_point_history();
const unsigned int degree;
unsigned int n_u = 0, n_p = 0;
unsigned int plastic_iteration = 0;
unsigned int last_max_plasticity = 0;
std::vector< std::vector <Vector<double> > > quad_viscosities;
std::vector<double> cell_viscosities;
std::vector<PointHistory<dim> > quadrature_point_history;
std::shared_ptr<typename InnerPreconditioner<dim>::type> A_preconditioner;
ellipsoid_fit<dim> ellipsoid;
};
const ::parallel::distributed::Triangulation< dim, spacedim > * triangulation
Class for boundary conditions and rhs
template<int dim>
class BoundaryValuesP:
public Function<dim>
{
public:
BoundaryValuesP() :
{
}
virtual double value(const
Point<dim> &p,
const unsigned
int component = 0) const override;
};
template<int dim>
double BoundaryValuesP<dim>::value(
const Point<dim> &p,
const unsigned int component) const
{
Assert(component < this->n_components,
ExcIndexRange (component, 0, this->n_components));
(void)p;
(void)component;
Assert(p[0] >= -10.0, ExcLowerRangeType<double>(p[0], -10.0));
return 0;
}
template<int dim>
void BoundaryValuesP<dim>::vector_value(
const Point<dim> &p,
{
for (unsigned int c = 0; c < this->n_components; ++c)
values(c) = BoundaryValuesP<dim>::value(p, c);
}
template<int dim>
class RightHandSide:
public Function<dim>
{
public:
RightHandSide () :
Function<dim>(dim+1) {}
A_Grav_namespace::AnalyticGravity<dim> *aGrav) const;
A_Grav_namespace::AnalyticGravity<dim> *aGrav) const;
A_Grav_namespace::AnalyticGravity<dim> *aGrav) const;
};
template<int dim>
double RightHandSide<dim>::value(
const Point<dim> &p,
const unsigned int component,
A_Grav_namespace::AnalyticGravity<dim> *aGrav) const
{
std::vector<double> temp_vector(2);
aGrav->get_gravity(p, temp_vector);
if (component == 0)
{
return temp_vector[0] + system_parameters::omegasquared * p[0];
}
else
{
if (component == 1)
return temp_vector[1];
else
return 0;
}
}
template<int dim>
void RightHandSide<dim>::vector_value(
const Point<dim> &p,
A_Grav_namespace::AnalyticGravity<dim> *aGrav) const
{
for (unsigned int c = 0; c < this->n_components; ++c)
values(c) = RightHandSide<dim>::value(p, c, aGrav);
}
template<int dim>
void RightHandSide<dim>::vector_value_list(
A_Grav_namespace::AnalyticGravity<dim> *aGrav) const
{
virtual void vector_value_list(const std::vector< Point< dim > > &points, std::vector< Vector< RangeNumberType > > &values) const
virtual RangeNumberType value(const Point< dim > &p, const unsigned int component=0) const
virtual void vector_value(const Point< dim > &p, Vector< RangeNumberType > &values) const
#define Assert(cond, exc)
check whether component is in the valid range is up to the derived class
Assert(values.size() == points.size(),
ExcDimensionMismatch(values.size(), points.size()));
for (unsigned int i = 0; i < points.size(); ++i)
this->vector_value(points[i], values[i], aGrav);
}
Class for linear solvers and preconditioners
template<class Matrix, class Preconditioner>
{
public:
InverseMatrix(const Matrix &m, const Preconditioner &preconditioner);
private:
};
template<class Matrix, class Preconditioner>
InverseMatrix<Matrix, Preconditioner>::InverseMatrix(const Matrix &m,
const Preconditioner &preconditioner) :
matrix(&m), preconditioner(&preconditioner)
{
}
template<class Matrix, class Preconditioner>
void InverseMatrix<Matrix, Preconditioner>::vmult(
Vector<double> &dst,
const
Vector<double> &src) const
{
SolverControl solver_control(1000 * src.size(), 1e-9 * src.l2_norm());
dst = 0;
cg.solve(*matrix, dst, src, *preconditioner);
}
Class for the SchurComplement
template<class Preconditioner>
{
public:
private:
};
template<class Preconditioner>
SchurComplement<Preconditioner>::SchurComplement(
system_matrix(&system_matrix), A_inverse(&A_inverse), tmp1(
system_matrix.block(0, 0).m()), tmp2(
system_matrix.block(0, 0).m())
{
}
template<class Preconditioner>
void SchurComplement<Preconditioner>::vmult(
Vector<double> &dst,
const
Vector<double> &src) const
{
system_matrix->block(0, 1).vmult(tmp1, src);
A_inverse->vmult(tmp2, tmp1);
system_matrix->block(1, 0).vmult(dst, tmp2);
}
StokesProblem::StokesProblem
template<int dim>
StokesProblem<dim>::StokesProblem(const unsigned int degree) :
degree(degree),
mapping(),
fe(
FE_Q<dim>(degree + 1), dim,
FE_Q<dim>(degree), 1),
quadrature_formula(degree + 2),
{}
Set up dofs
template<int dim>
void StokesProblem<dim>::setup_dofs()
{
A_preconditioner.reset();
system_matrix.clear();
dof_handler.distribute_dofs(fe);
std::vector<unsigned int> block_component(dim + 1, 0);
block_component[dim] = 1;
void component_wise(DoFHandler< dim, spacedim > &dof_handler, const std::vector< unsigned int > &target_component=std::vector< unsigned int >())
void Cuthill_McKee(DoFHandler< dim, spacedim > &dof_handler, const bool reversed_numbering=false, const bool use_constraints=false, const std::vector< types::global_dof_index > &starting_indices=std::vector< types::global_dof_index >())
========================================Apply Boundary Conditions=====================================
{
constraints.clear();
std::vector<bool> component_maskP(dim + 1, false);
component_maskP[dim] = true;
BoundaryValuesP<dim>(), constraints, component_maskP);
}
{
std::set<types::boundary_id> no_normal_flux_boundaries;
no_normal_flux_boundaries.insert(99);
no_normal_flux_boundaries, constraints);
}
constraints.close();
n_u = dofs_per_block[0];
n_p = dofs_per_block[1];
<< std::endl << " Number of degrees of freedom: "
<< dof_handler.n_dofs() << " (" << n_u << '+' << n_p << ')'
<< std::endl;
{
csp.block(0, 0).reinit(n_u, n_u);
csp.block(1, 0).reinit(n_p, n_u);
csp.block(0, 1).reinit(n_u, n_p);
csp.block(1, 1).reinit(n_p, n_p);
csp.collect_sizes();
sparsity_pattern.copy_from(csp);
}
system_matrix.reinit(sparsity_pattern);
solution.reinit(2);
solution.block(0).reinit(n_u);
solution.block(1).reinit(n_p);
solution.collect_sizes();
system_rhs.reinit(2);
system_rhs.block(0).reinit(n_u);
system_rhs.block(1).reinit(n_p);
system_rhs.collect_sizes();
}
unsigned int n_active_cells() const
void make_hanging_node_constraints(const DoFHandler< dim, spacedim > &dof_handler, AffineConstraints< number > &constraints)
void make_sparsity_pattern(const DoFHandler< dim, spacedim > &dof_handler, SparsityPatternBase &sparsity_pattern, const AffineConstraints< number > &constraints={}, const bool keep_constrained_dofs=true, const types::subdomain_id subdomain_id=numbers::invalid_subdomain_id)
void compute_no_normal_flux_constraints(const DoFHandler< dim, spacedim > &dof_handler, const unsigned int first_vector_component, const std::set< types::boundary_id > &boundary_ids, AffineConstraints< number > &constraints, const Mapping< dim, spacedim > &mapping=(ReferenceCells::get_hypercube< dim >() .template get_default_linear_mapping< dim, spacedim >()), const bool use_manifold_for_normal=true)
Viscosity and Shear modulus functions
template<int dim>
class Rheology
{
public:
double get_eta(double &r, double &z);
double get_G(unsigned int mat_id);
private:
std::vector<double> get_manual_eta_profile();
};
template<int dim>
std::vector<double> Rheology<dim>::get_manual_eta_profile()
{
vector<double> etas;
for (unsigned int i=0; i < system_parameters::sizeof_depths_eta; ++i)
{
etas.push_back(system_parameters::depths_eta[i]);
etas.push_back(system_parameters::eta_kinks[i]);
}
return etas;
}
template<int dim>
double Rheology<dim>::get_eta(double &r, double &z)
{
compute local depth
double ecc = system_parameters::q_axes[0] / system_parameters::p_axes[0];
double Rminusr = system_parameters::q_axes[0] - system_parameters::p_axes[0];
double approx_a =
std::sqrt(r * r + z * z * ecc * ecc);
double group1 = r * r + z * z - Rminusr * Rminusr;
double a0 = approx_a;
double error = 10000;
::VectorizedArray< Number, width > sqrt(const ::VectorizedArray< Number, width > &)
While loop finds the a axis of the "isodepth" ellipse for which the input point is on the surface. An "isodepth" ellipse is defined as one whose axes a,b are related to the global axes A, B by: A-h = B-h
if ((r > system_parameters::q_axes[0] - system_parameters::depths_eta.back()) ||
(z > system_parameters::p_axes[0] - system_parameters::depths_eta.back()))
{
double eps = 10.0;
while (error >= eps)
{
double a02 = a0 * a0;
double a03 = a0 * a02;
double a04 = a0 * a03;
double fofa = a04 - (2 * Rminusr * a03) - (group1 * a02)
+ (2 * r * r * Rminusr * a0) - (r * r * Rminusr * Rminusr);
double fprimeofa = 4 * a03 - (6 * Rminusr * a02) - (2 * group1 * a0)
+ (2 * r * r * Rminusr);
double deltaa = -fofa / fprimeofa;
a0 += deltaa;
::VectorizedArray< Number, width > abs(const ::VectorizedArray< Number, width > &)
cout << "error = " << error << endl;
}
}
else
{
a0 = 0.0;
}
double local_depth = system_parameters::q_axes[0] - a0;
if (local_depth < 0)
local_depth = 0;
if (local_depth > system_parameters::depths_eta.back())
{
if (system_parameters::eta_kinks.back() < system_parameters::eta_floor)
return system_parameters::eta_floor;
else if (system_parameters::eta_kinks.back() > system_parameters::eta_ceiling)
return system_parameters::eta_ceiling;
else
return system_parameters::eta_kinks.back();
}
std::vector<double> viscosity_function = get_manual_eta_profile();
unsigned int n_visc_kinks = viscosity_function.size() / 2;
find the correct interval to do the interpolation in
int n_minus_one = -1;
for (unsigned int n = 1; n <= n_visc_kinks; ++n)
{
unsigned int ndeep = 2 * n - 2;
unsigned int nshallow = 2 * n;
if (local_depth >= viscosity_function[ndeep] && local_depth <= viscosity_function[nshallow])
n_minus_one = ndeep;
}
find the viscosity interpolation
if (n_minus_one == -1)
return system_parameters::eta_ceiling;
else
{
double visc_exponent =
(viscosity_function[n_minus_one]
- local_depth)
/ (viscosity_function[n_minus_one]
- viscosity_function[n_minus_one + 2]);
double visc_base = viscosity_function[n_minus_one + 3]
/ viscosity_function[n_minus_one + 1];
This is the true viscosity given the thermal profile
double true_eta = viscosity_function[n_minus_one + 1] *
std::pow(visc_base, visc_exponent);
::VectorizedArray< Number, width > pow(const ::VectorizedArray< Number, width > &, const Number p)
Implement latitude-dependence viscosity
if (system_parameters::lat_dependence)
{
if (lat > 80)
lat = 80;
double T_eq = 155;
double taper_depth = 40000;
double surface_taper = (taper_depth - local_depth) / taper_depth;
if (surface_taper < 0)
surface_taper = 0;
double log_eta_contrast = surface_taper * system_parameters::eta_Ea * 52.5365 * (T_eq - T_surf) / T_eq / T_surf;
true_eta *=
std::pow(10, log_eta_contrast);
}
if (true_eta > system_parameters::eta_ceiling)
return system_parameters::eta_ceiling;
else if (true_eta < system_parameters::eta_floor)
return system_parameters::eta_floor;
else
return true_eta;
}
}
template<int dim>
double Rheology<dim>::get_G(unsigned int mat_id)
{
return system_parameters::G[mat_id];
}
Initialize the eta and G parts of the quadrature_point_history object
template<int dim>
void StokesProblem<dim>::initialize_eta_and_G()
{
const unsigned int n_q_points = quadrature_formula.size();
Rheology<dim> rheology;
dof_handler.begin_active(); cell != dof_handler.end(); ++cell)
{
PointHistory<dim> *local_quadrature_points_history =
reinterpret_cast<PointHistory<dim> *>(cell->user_pointer());
local_quadrature_points_history >= &quadrature_point_history.front(),
ExcInternalError());
local_quadrature_points_history < &quadrature_point_history.back(),
ExcInternalError());
fe_values.reinit(cell);
for (unsigned int q = 0; q < n_q_points; ++q)
{
double r_value = fe_values.quadrature_point(q)[0];
double z_value = fe_values.quadrature_point(q)[1];
typename ActiveSelector::active_cell_iterator active_cell_iterator
@ update_quadrature_points
Transformed quadrature points.
defines local viscosity
double local_viscosity = 0;
local_viscosity = rheology.get_eta(r_value, z_value);
local_quadrature_points_history[q].first_eta = local_viscosity;
local_quadrature_points_history[q].new_eta = local_viscosity;
defines local shear modulus
double local_G = 0;
unsigned int mat_id = cell->material_id();
local_G = rheology.get_G(mat_id);
local_quadrature_points_history[q].G = local_G;
initializes the phi-phi stress
local_quadrature_points_history[q].old_phiphi_stress = 0;
}
}
}
====================== ASSEMBLE THE SYSTEM ======================
template<int dim>
void StokesProblem<dim>::assemble_system()
{
system_matrix = 0;
system_rhs = 0;
const unsigned int dofs_per_cell = fe.dofs_per_cell;
const unsigned int n_q_points = quadrature_formula.size();
std::vector<types::global_dof_index> local_dof_indices(dofs_per_cell);
@ update_values
Shape function values.
@ update_JxW_values
Transformed quadrature weights.
@ update_gradients
Shape function gradients.
runs the gravity script function
const RightHandSide<dim> right_hand_side;
A_Grav_namespace::AnalyticGravity<dim> *aGrav =
new A_Grav_namespace::AnalyticGravity<dim>;
std::vector<double> grav_parameters;
grav_parameters.push_back(system_parameters::q_axes[system_parameters::present_timestep * 2 + 0]);
grav_parameters.push_back(system_parameters::p_axes[system_parameters::present_timestep * 2 + 0]);
grav_parameters.push_back(system_parameters::q_axes[system_parameters::present_timestep * 2 + 1]);
grav_parameters.push_back(system_parameters::p_axes[system_parameters::present_timestep * 2 + 1]);
grav_parameters.push_back(system_parameters::rho[0]);
grav_parameters.push_back(system_parameters::rho[1]);
std::cout << "Body parameters are: " ;
for (int i=0; i<6; ++i)
std::cout << grav_parameters[i] << " ";
std::cout << endl;
aGrav->setup_vars(grav_parameters);
std::vector<Vector<double> > rhs_values(n_q_points,
std::vector<SymmetricTensor<2, dim> > phi_grads_u(dofs_per_cell);
std::vector<double> div_phi_u(dofs_per_cell);
std::vector<Tensor<1, dim> > phi_u(dofs_per_cell);
std::vector<double> phi_p(dofs_per_cell);
dof_handler.begin_active(), first_cell = dof_handler.begin_active(),
endc = dof_handler.end();
for (; cell != endc; ++cell)
{
PointHistory<dim> *local_quadrature_points_history =
reinterpret_cast<PointHistory<dim> *>(cell->user_pointer());
local_quadrature_points_history >= &quadrature_point_history.front(),
ExcInternalError());
local_quadrature_points_history < &quadrature_point_history.back(),
ExcInternalError());
double cell_area = cell->measure();
if (cell_area<0)
append_physical_times(-1);
,
ExcInternalError());
unsigned int m_id = cell->material_id();
#define AssertThrow(cond, exc)
initializes the rhs vector to the correct g values
fe_values.reinit(cell);
right_hand_side.vector_value_list(fe_values.get_quadrature_points(),
rhs_values, aGrav);
std::vector<Vector<double> > new_viscosities(quadrature_formula.size(),
Vector<double>(dim + 1));
Finds vertices where the radius is zero DIM
bool is_singular = false;
for (unsigned int f = 0; f < GeometryInfo<dim>::faces_per_cell; ++f)
if (cell->face(f)->center()[0] == 0)
is_singular = true;
if (is_singular == false || system_parameters::cylindrical == false)
{
local_matrix = 0;
local_rhs = 0;
===== outputs the local gravity
std::vector<Point<dim> > quad_points_list(n_q_points);
quad_points_list = fe_values.get_quadrature_points();
if (plastic_iteration
== (system_parameters::max_plastic_iterations - 1))
{
if (cell != first_cell)
{
std::ofstream fout("gravity_field.txt", std::ios::app);
fout << quad_points_list[0] << " " << rhs_values[0];
fout.close();
}
else
{
std::ofstream fout("gravity_field.txt");
fout << quad_points_list[0] << " " << rhs_values[0];
fout.close();
}
}
for (unsigned int q = 0; q < n_q_points; ++q)
{
local_quadrature_points_history[q].old_stress;
double &local_old_phiphi_stress =
local_quadrature_points_history[q].old_phiphi_stress;
double r_value = fe_values.quadrature_point(q)[0];
get local density based on mat id
double local_density = system_parameters::rho[m_id];
defines local viscosities
double local_viscosity = 0;
if (plastic_iteration == 0)
local_viscosity = local_quadrature_points_history[q].first_eta;
else
local_viscosity = local_quadrature_points_history[q].new_eta;
Define the local viscoelastic constants
double local_eta_ve = 2
/ ((1 / local_viscosity)
+ (1 / local_quadrature_points_history[q].G
/ system_parameters::current_time_interval));
double local_chi_ve = 1
/ (1
+ (local_quadrature_points_history[q].G
* system_parameters::current_time_interval
/ local_viscosity));
for (unsigned int k = 0; k < dofs_per_cell; ++k)
{
phi_grads_u[k] = fe_values[velocities].symmetric_gradient(k,
q);
div_phi_u[k] = (fe_values[velocities].divergence(k, q));
phi_u[k] = (fe_values[velocities].value(k, q));
if (system_parameters::cylindrical == true)
{
div_phi_u[k] *= (r_value);
div_phi_u[k] += (phi_u[k][0]);
}
phi_p[k] = fe_values[pressure].value(k, q);
}
for (unsigned int i = 0; i < dofs_per_cell; ++i)
{
for (unsigned int j = 0; j <= i; ++j)
{
if (system_parameters::cylindrical == true)
{
local_matrix(i, j) += (phi_grads_u[i]
* phi_grads_u[j] * 2 * local_eta_ve
* r_value
+ 2 * phi_u[i][0] * phi_u[j][0]
* local_eta_ve / r_value
- div_phi_u[i] * phi_p[j]
* system_parameters::pressure_scale
- phi_p[i] * div_phi_u[j]
* system_parameters::pressure_scale
+ phi_p[i] * phi_p[j] * r_value
* system_parameters::pressure_scale)
* fe_values.JxW(q);
}
else
{
local_matrix(i, j) += (phi_grads_u[i]
* phi_grads_u[j] * 2 * local_eta_ve
- div_phi_u[i] * phi_p[j]
* system_parameters::pressure_scale
- phi_p[i] * div_phi_u[j]
* system_parameters::pressure_scale
+ phi_p[i] * phi_p[j]) * fe_values.JxW(q);
}
}
if (system_parameters::cylindrical == true)
{
const unsigned int component_i =
fe.system_to_component_index(i).first;
local_rhs(i) += (fe_values.shape_value(i, q)
* rhs_values[q](component_i) * r_value
* local_density
- local_chi_ve * phi_grads_u[i] * old_stress
* r_value
- local_chi_ve * phi_u[i][0]
* local_old_phiphi_stress)
* fe_values.JxW(q);
}
else
{
const unsigned int component_i =
fe.system_to_component_index(i).first;
local_rhs(i) += fe_values.shape_value(i, q)
* rhs_values[q](component_i) * fe_values.JxW(q)
* local_density;
}
}
}
}
else
{
local_matrix = 0;
local_rhs = 0;
===== outputs the local gravity
std::vector<Point<dim> > quad_points_list(n_q_points);
quad_points_list = fe_values.get_quadrature_points();
for (unsigned int q = 0; q < n_q_points; ++q)
{
local_quadrature_points_history[q].old_stress;
double &local_old_phiphi_stress =
local_quadrature_points_history[q].old_phiphi_stress;
double r_value = fe_values.quadrature_point(q)[0];
double local_density = system_parameters::rho[m_id];
defines local viscosities
double local_viscosity = 0;
if (plastic_iteration == 0)
{
local_viscosity = local_quadrature_points_history[q].first_eta;
}
else
local_viscosity = local_quadrature_points_history[q].new_eta;
Define the local viscoelastic constants
double local_eta_ve = 2
/ ((1 / local_viscosity)
+ (1 / local_quadrature_points_history[q].G
/ system_parameters::current_time_interval));
double local_chi_ve = 1
/ (1
+ (local_quadrature_points_history[q].G
* system_parameters::current_time_interval
/ local_viscosity));
for (unsigned int k = 0; k < dofs_per_cell; ++k)
{
phi_grads_u[k] = fe_values[velocities].symmetric_gradient(k,
q);
div_phi_u[k] = (fe_values[velocities].divergence(k, q));
phi_u[k] = (fe_values[velocities].value(k, q));
if (system_parameters::cylindrical == true)
{
div_phi_u[k] *= (r_value);
div_phi_u[k] += (phi_u[k][0]);
}
phi_p[k] = fe_values[pressure].value(k, q);
}
for (unsigned int i = 0; i < dofs_per_cell; ++i)
{
for (unsigned int j = 0; j <= i; ++j)
{
if (system_parameters::cylindrical == true)
{
local_matrix(i, j) += (phi_grads_u[i]
* phi_grads_u[j] * 2 * local_eta_ve
* r_value
+ 2 * phi_u[i][0] * phi_u[j][0]
* local_eta_ve / r_value
- div_phi_u[i] * phi_p[j]
* system_parameters::pressure_scale
- phi_p[i] * div_phi_u[j]
* system_parameters::pressure_scale
+ phi_p[i] * phi_p[j] * r_value
* system_parameters::pressure_scale)
* fe_values.JxW(q);
}
else
{
local_matrix(i, j) += (phi_grads_u[i]
* phi_grads_u[j] * 2 * local_eta_ve
- div_phi_u[i] * phi_p[j]
* system_parameters::pressure_scale
- phi_p[i] * div_phi_u[j]
* system_parameters::pressure_scale
+ phi_p[i] * phi_p[j]) * fe_values.JxW(q);
}
}
if (system_parameters::cylindrical == true)
{
const unsigned int component_i =
fe.system_to_component_index(i).first;
local_rhs(i) += (fe_values.shape_value(i, q)
* rhs_values[q](component_i) * r_value
* local_density
- local_chi_ve * phi_grads_u[i] * old_stress
* r_value
- local_chi_ve * phi_u[i][0]
* local_old_phiphi_stress)
* fe_values.JxW(q);
}
else
{
const unsigned int component_i =
fe.system_to_component_index(i).first;
local_rhs(i) += fe_values.shape_value(i, q)
* rhs_values[q](component_i) * fe_values.JxW(q)
* local_density;
}
}
}
}
for (unsigned int i = 0; i < dofs_per_cell; ++i)
for (unsigned int j = i + 1; j < dofs_per_cell; ++j)
local_matrix(i, j) = local_matrix(j, i);
cell->get_dof_indices(local_dof_indices);
constraints.distribute_local_to_global(local_matrix, local_rhs,
local_dof_indices, system_matrix, system_rhs);
}
std::cout << " Computing preconditioner..." << std::endl << std::flush;
A_preconditioner = std::shared_ptr<
typename InnerPreconditioner<dim>::type>(
new typename InnerPreconditioner<dim>::type());
A_preconditioner->initialize(system_matrix.block(0, 0),
typename InnerPreconditioner<dim>::type::AdditionalData());
delete aGrav;
}
====================== SOLVER ======================
template<int dim>
void StokesProblem<dim>::solve()
{
const InverseMatrix<SparseMatrix<double>,
typename InnerPreconditioner<dim>::type> A_inverse(
system_matrix.block(0, 0), *A_preconditioner);
{
A_inverse.vmult(tmp, system_rhs.block(0));
system_matrix.block(1, 0).vmult(schur_rhs, tmp);
schur_rhs -= system_rhs.block(1);
system_matrix, A_inverse);
int n_iterations = system_parameters::iteration_coefficient
* solution.block(1).size();
double tolerance_goal = system_parameters::tolerance_coefficient
* schur_rhs.l2_norm();
std::cout << "\nMax iterations and tolerance are: " << n_iterations
<< " and " << tolerance_goal << std::endl;
preconditioner.
initialize(system_matrix.block(1, 1),
system_matrix.block(1, 1), preconditioner);
constraints.distribute(solution);
std::cout << " " << solver_control.last_step()
<< " outer CG Schur complement iterations for pressure"
<< std::endl;
}
{
system_matrix.block(0, 1).vmult(tmp, solution.block(1));
tmp *= -1;
tmp += system_rhs.block(0);
A_inverse.vmult(solution.block(0), tmp);
constraints.distribute(solution);
solution.block(1) *= (system_parameters::pressure_scale);
}
}
typename SparseLUDecomposition< number >::AdditionalData AdditionalData
void initialize(const SparseMatrix< somenumber > &matrix, const AdditionalData ¶meters=AdditionalData())
LinearOperator< Range_2, Domain_2, Payload > schur_complement(const LinearOperator< Domain_1, Range_1, Payload > &A_inv, const LinearOperator< Range_1, Domain_2, Payload > &B, const LinearOperator< Range_2, Domain_1, Payload > &C, const LinearOperator< Range_2, Domain_2, Payload > &D)
====================== OUTPUT RESULTS ======================
template<int dim>
void StokesProblem<dim>::output_results() const
{
std::vector < std::string > solution_names(dim, "velocity");
solution_names.push_back("pressure");
std::vector<DataComponentInterpretation::DataComponentInterpretation> data_component_interpretation(
data_component_interpretation.push_back(
data_out.add_data_vector(solution, solution_names,
data_out.build_patches();
std::ostringstream filename;
if (system_parameters::present_timestep < system_parameters::initial_elastic_iterations)
{
filename << system_parameters::output_folder << "/time"
<< "_elastic_displacements" << ".txt";
}
else
{
filename << system_parameters::output_folder << "/time"
<< "_flow" <<
Utilities::int_to_string(plastic_iteration, 2) << ".txt";
}
std::ofstream output(filename.str().c_str());
data_out.write_gnuplot(output);
}
void attach_dof_handler(const DoFHandler< dim, spacedim > &)
@ component_is_part_of_vector
std::string int_to_string(const unsigned int value, const unsigned int digits=numbers::invalid_unsigned_int)
====================== FIND AND WRITE TO FILE THE STRESS TENSOR; IMPLEMENT PLASTICITY ======================
template<int dim>
void StokesProblem<dim>::solution_stesses()
{
note most of this section only works with dim=2
name the output text files
std::ostringstream stress_output;
stress_output << system_parameters::output_folder << "/time"
<< "_principalstresses" <<
Utilities::int_to_string(plastic_iteration, 2)
<< ".txt";
std::ofstream fout_snew(stress_output.str().c_str());
fout_snew.close();
std::ostringstream stresstensor_output;
stresstensor_output << system_parameters::output_folder << "/time"
<<
Utilities::int_to_string(system_parameters::present_timestep, 2)
<< "_stresstensor" <<
Utilities::int_to_string(plastic_iteration, 2)
<< ".txt";
std::ofstream fout_sfull(stresstensor_output.str().c_str());
fout_sfull.close();
std::ostringstream failed_cells_output;
failed_cells_output << system_parameters::output_folder << "/time"
<<
Utilities::int_to_string(system_parameters::present_timestep, 2)
<< "_failurelocations" <<
Utilities::int_to_string(plastic_iteration, 2)
<< ".txt";
std::ofstream fout_failed_cells(failed_cells_output.str().c_str());
fout_failed_cells.close();
std::ostringstream plastic_eta_output;
plastic_eta_output << system_parameters::output_folder << "/time"
<<
Utilities::int_to_string(system_parameters::present_timestep, 2)
<< "_viscositiesreg" <<
Utilities::int_to_string(plastic_iteration, 2)
<< ".txt";
std::ofstream fout_vrnew(plastic_eta_output.str().c_str());
fout_vrnew.close();
std::ostringstream initial_eta_output;
if (plastic_iteration == 0)
{
initial_eta_output << system_parameters::output_folder << "/time"
<< "_baseviscosities.txt";
std::ofstream fout_baseeta(initial_eta_output.str().c_str());
fout_baseeta.close();
}
std::cout << "Running stress calculations for plasticity iteration "
<< plastic_iteration << "...\n";
This makes the set of points at which the stress tensor is calculated
std::vector<Point<dim> > points_list(0);
std::vector<unsigned int> material_list(0);
dof_handler.begin_active(), endc = dof_handler.end();
This loop gets the gradients of the velocity field and saves it in the tensor_gradient_? objects DIM
for (; cell != endc; ++cell)
{
points_list.push_back(cell->center());
material_list.push_back(cell->material_id());
}
Make the FEValues object to evaluate values and derivatives at quadrature points
Make the object that will hold the velocities and velocity gradients at the quadrature points
std::vector < std::vector<Tensor<1, dim> >> velocity_grads(quadrature_formula.size(),
std::vector<Vector<double> > velocities(quadrature_formula.size(),
Make the object to find rheology
Write the solution flow velocity and derivative for each cell
std::vector<Vector<double> > vector_values(0);
std::vector < std::vector<Tensor<1, dim> > > gradient_values(0);
std::vector<bool> failing_cells;
Write the stresses from the previous step into vectors
std::vector<SymmetricTensor<2, dim>> old_stress;
std::vector<double> old_phiphi_stress;
std::vector<double> cell_Gs;
dof_handler.begin_active(); cell != dof_handler.end(); ++cell)
{
Makes pointer to data in quadrature_point_history
PointHistory<dim> *local_quadrature_points_history =
reinterpret_cast<PointHistory<dim> *>(cell->user_pointer());
fe_values.reinit(cell);
fe_values.get_function_gradients(solution, velocity_grads);
fe_values.get_function_values(solution, velocities);
std::vector<Tensor<1, dim>> current_cell_grads(dim+1);
current_cell_old_stress = 0;
double current_cell_old_phiphi_stress = 0;
double cell_area = 0;
Averages across each cell to find mean velocities, gradients, and old stresses
for (unsigned int q = 0; q < quadrature_formula.size(); ++q)
{
cell_area += fe_values.JxW(q);
velocities[q] *= fe_values.JxW(q);
current_cell_velocity += velocities[q];
for (unsigned int i = 0; i < (dim+1); ++i)
{
velocity_grads[q][i] *= fe_values.JxW(q);
current_cell_grads[i] += velocity_grads[q][i];
}
current_cell_old_stress += local_quadrature_points_history[q].old_stress * fe_values.JxW(q);
current_cell_old_phiphi_stress += local_quadrature_points_history[q].old_phiphi_stress * fe_values.JxW(q);
}
current_cell_velocity /= cell_area;
for (unsigned int i = 0; i < (dim+1); ++i)
current_cell_grads[i] /= cell_area;
current_cell_old_stress /= cell_area;
current_cell_old_phiphi_stress /= cell_area;
vector_values.push_back(current_cell_velocity);
gradient_values.push_back(current_cell_grads);
old_stress.push_back(current_cell_old_stress);
old_phiphi_stress.push_back(current_cell_old_phiphi_stress);
Get cell shear modulus: assumes it's constant for the cell
unsigned int mat_id = cell->material_id();
double local_G = rheology.get_G(mat_id);
cell_Gs.push_back(local_G);
}
tracks where failure occurred
std::vector<double> reduction_factor;
unsigned int total_fails = 0;
if (plastic_iteration == 0)
cell_viscosities.resize(0);
loop across all the cells to find and adjust eta of failing cells
{
double current_cell_viscosity = 0;
Fill viscosities vector, analytically if plastic_iteration == 0 and from previous viscosities for later iteration
if (plastic_iteration == 0)
{
double local_viscosity;
local_viscosity = rheology.get_eta(points_list[i][0], points_list[i][1]);
current_cell_viscosity = local_viscosity;
cell_viscosities.push_back(current_cell_viscosity);
}
else
{
current_cell_viscosity = cell_viscosities[i];
}
double cell_eta_ve = 2
/ ((1 / current_cell_viscosity)
+ (1 / cell_Gs[i]
/ system_parameters::current_time_interval));
double cell_chi_ve = 1
/ (1
+ (cell_Gs[i]
* system_parameters::current_time_interval
/ current_cell_viscosity));
find local pressure
double cell_p = vector_values[i].operator()(2);
find stresses tensor makes non-diagonalized local matrix A
double sigma13 = 0.5
* (gradient_values[i][0][1] + gradient_values[i][1][0]);
mat A;
A << gradient_values[i][0][0] << 0 << sigma13 << endr
<< 0 << vector_values[i].operator()(0) / points_list[i].operator()(0)<< 0 << endr
<< sigma13 << 0 << gradient_values[i][1][1] << endr;
mat olddevstress;
olddevstress << old_stress[i][0][0] << 0 << old_stress[i][0][1] << endr
<< 0 << old_phiphi_stress[i] << 0 << endr
<< old_stress[i][0][1] << 0 << old_stress[i][1][1] << endr;
vec P;
P << cell_p << cell_p << cell_p;
mat Pmat = diagmat(P);
mat B;
B = (cell_eta_ve * A + cell_chi_ve * olddevstress) - Pmat;
finds principal stresses
vec eigval;
mat eigvec;
eig_sym(eigval, eigvec, B);
double sigma1 = -min(eigval);
double sigma3 = -max(eigval);
Writes text files for principal stresses, full stress tensor, base viscosities
std::ofstream fout_snew(stress_output.str().c_str(), std::ios::app);
fout_snew << " " << sigma1 << " " << sigma3 << "\n";
fout_snew.close();
std::ofstream fout_sfull(stresstensor_output.str().c_str(), std::ios::app);
fout_sfull << A(0,0) << " " << A(1,1) << " " << A(2,2) << " " << A(0,2) << "\n";
fout_sfull.close();
if (plastic_iteration == 0)
{
std::ofstream fout_baseeta(initial_eta_output.str().c_str(), std::ios::app);
fout_baseeta << points_list[i]<< " " << current_cell_viscosity << "\n";
fout_baseeta.close();
}
Finds adjusted effective viscosity
if (system_parameters::plasticity_on)
{
if (system_parameters::failure_criterion == 0)
{
if (sigma1 >= 5 * sigma3)
{
failing_cells.push_back(true);
double temp_reductionfactor = 1;
if (sigma3 < 0)
temp_reductionfactor = 100;
else
temp_reductionfactor = 1.9 * sigma1 / 5 / sigma3;
reduction_factor.push_back(temp_reductionfactor);
total_fails++;
Text file of all failure locations
std::ofstream fout_failed_cells(failed_cells_output.str().c_str(), std::ios::app);
fout_failed_cells << points_list[i] << "\n";
fout_failed_cells.close();
}
else
{
reduction_factor.push_back(1);
failing_cells.push_back(false);
}
}
else
{
if (system_parameters::failure_criterion == 1)
{
double temp_reductionfactor = 1;
if (sigma3 < -114037)
{
std::cout << " ext ";
failing_cells.push_back(true);
temp_reductionfactor = 10;
reduction_factor.push_back(temp_reductionfactor);
total_fails++;
Text file of all failure locations
std::ofstream fout_failed_cells(failed_cells_output.str().c_str(), std::ios::app);
fout_failed_cells << points_list[i] << "\n";
fout_failed_cells.close();
}
else
{
double sigma_c = 160e6;
double yield_sigma1 = sigma3 +
std::sqrt( (3.086 * sigma_c * sigma3) + (0.002 * sigma3 * sigma3) );
if (sigma1 >= yield_sigma1)
{
std::cout << " comp ";
failing_cells.push_back(true);
temp_reductionfactor = 1.0 * sigma1 / 5 / sigma3;
reduction_factor.push_back(temp_reductionfactor);
total_fails++;
Text file of all failure locations
std::ofstream fout_failed_cells(failed_cells_output.str().c_str(), std::ios::app);
fout_failed_cells << points_list[i] << "\n";
fout_failed_cells.close();
}
else
{
reduction_factor.push_back(1);
failing_cells.push_back(false);
}
}
}
else
{
std::cout << "Specified failure criterion not found\n";
}
}
}
else
reduction_factor.push_back(1);
}
If there are enough failed cells, update eta at all quadrature points and perform smoothing
std::cout << " Number of failing cells: " << total_fails << "\n";
double last_max_plasticity_double = last_max_plasticity;
double total_fails_double = total_fails;
double decrease_in_plasticity = ((last_max_plasticity_double - total_fails_double) / last_max_plasticity_double);
if (plastic_iteration == 0)
decrease_in_plasticity = 1;
last_max_plasticity = total_fails;
if (total_fails <= 100 || decrease_in_plasticity <= 0.2)
{
system_parameters::continue_plastic_iterations = false;
{
Writes to file the undisturbed cell viscosities
std::ofstream fout_vrnew(plastic_eta_output.str().c_str(), std::ios::app);
fout_vrnew << " " << cell_viscosities[j] << "\n";
fout_vrnew.close();
}
}
else
{
Decrease the eta at quadrature points in failing cells
unsigned int cell_no = 0;
dof_handler.begin_active(); cell != dof_handler.end(); ++cell)
{
fe_values.reinit(cell);
Make local_quadrature_points_history pointer to the cell data
PointHistory<dim> *local_quadrature_points_history =
reinterpret_cast<PointHistory<dim> *>(cell->user_pointer());
local_quadrature_points_history >= &quadrature_point_history.front(),
ExcInternalError());
local_quadrature_points_history < &quadrature_point_history.back(),
ExcInternalError());
quad_viscosities[cell_no].resize(quadrature_formula.size());
for (unsigned int q = 0; q < quadrature_formula.size(); ++q)
{
if (plastic_iteration == 0)
local_quadrature_points_history[q].new_eta = local_quadrature_points_history[q].first_eta;
local_quadrature_points_history[q].new_eta /= reduction_factor[cell_no];
Prevents viscosities from dropping below the floor necessary for numerical stability
if (local_quadrature_points_history[q].new_eta < system_parameters::eta_floor)
local_quadrature_points_history[q].new_eta = system_parameters::eta_floor;
quad_viscosities[cell_no][q].reinit(dim+1);
for (unsigned int ii=0; ii<dim; ++ii)
quad_viscosities[cell_no][q](ii) = fe_values.quadrature_point(q)[ii];
quad_viscosities[cell_no][q](dim) = local_quadrature_points_history[q].new_eta;
}
cell_no++;
}
smooth_eta_field(failing_cells);
Writes to file the smoothed eta field (which is defined at each quadrature point) for each cell
cell_viscosities.resize(triangulation.n_active_cells(), 0);
dof_handler.begin_active(); cell != dof_handler.end(); ++cell)
{
if (failing_cells[cell_no])
{
fe_values.reinit(cell);
Averages across each cell to find mean eta
double cell_area = 0;
for (unsigned int q = 0; q < quadrature_formula.size(); ++q)
{
cell_area += fe_values.JxW(q);
cell_viscosities[cell_no] += quad_viscosities[cell_no][q][dim] * fe_values.JxW(q);
}
cell_viscosities[cell_no] /= cell_area;
Writes to file
std::ofstream fout_vrnew(plastic_eta_output.str().c_str(), std::ios::app);
fout_vrnew << " " << cell_viscosities[cell_no] << "\n";
fout_vrnew.close();
}
else
{
std::ofstream fout_vrnew(plastic_eta_output.str().c_str(), std::ios::app);
fout_vrnew << " " << cell_viscosities[cell_no] << "\n";
fout_vrnew.close();
}
cell_no++;
}
}
}
====================== SMOOTHES THE VISCOSITY FIELD AT ALL QUADRATURE POINTS ======================
template<int dim>
void StokesProblem<dim>::smooth_eta_field(std::vector<bool> failing_cells)
{
std::cout << " Smoothing viscosity field...\n";
unsigned int cell_no = 0;
dof_handler.begin_active(); cell != dof_handler.end(); ++cell)
{
if (failing_cells[cell_no])
{
PointHistory<dim> *local_quadrature_points_history =
reinterpret_cast<PointHistory<dim> *>(cell->user_pointer());
Currently this algorithm does not permit refinement. To permit refinement, daughter cells of neighbors must be identified Find pointers and indices of all cells within certain radius
bool find_more_cells = true;
std::vector< TriaIterator< CellAccessor<dim> > > neighbor_cells;
std::vector<int> neighbor_indices;
unsigned int start_cell = 0;
int new_cells_found = 0;
neighbor_cells.push_back(cell);
neighbor_indices.push_back(cell_no);
cell_touched[cell_no] = true;
while (find_more_cells)
{
new_cells_found = 0;
for (unsigned int i = start_cell; i<neighbor_cells.size(); ++i)
{
for (unsigned int f = 0; f < GeometryInfo<dim>::faces_per_cell; ++f)
{
if (!neighbor_cells[i]->face(f)->at_boundary())
{
int test_cell_no = neighbor_cells[i]->neighbor_index(f);
if (!cell_touched[test_cell_no])
if (cell->center().distance(neighbor_cells[i]->neighbor(f)->center()) < 2 * system_parameters::smoothing_radius)
{
What to do if another nearby cell is found that hasn't been found before
neighbor_cells.push_back(neighbor_cells[i]->neighbor(f));
neighbor_indices.push_back(test_cell_no);
cell_touched[test_cell_no] = true;
start_cell++;
new_cells_found++;
}
}
}
}
if (new_cells_found == 0)
{
find_more_cells = false;
}
else
start_cell = neighbor_cells.size() - new_cells_found;
}
fe_values.reinit(cell);
Collect the viscosities at nearby quadrature points
for (unsigned int q = 0; q < quadrature_formula.size(); ++q)
{
std::vector<double> nearby_etas_q;
for (unsigned int i = 0; i<neighbor_indices.size(); ++i)
for (unsigned int j=0; j<quadrature_formula.size(); ++j)
{
for (unsigned int d=0; d<dim; ++d)
test_q(d) = quad_viscosities[neighbor_indices[i]][j][d];
double qq_distance = fe_values.quadrature_point(q).
distance(test_q);
if (qq_distance < system_parameters::smoothing_radius)
nearby_etas_q.push_back(quad_viscosities[neighbor_indices[i]][j][dim]);
}
numbers::NumberTraits< Number >::real_type distance(const Point< dim, Number > &p) const
Write smoothed viscosities to quadrature_points_history; simple boxcar function is the smoothing kernel
double mean_eta = 0;
for (unsigned int l = 0; l<nearby_etas_q.size(); ++l)
{
mean_eta += nearby_etas_q[l];
}
mean_eta /= nearby_etas_q.size();
local_quadrature_points_history[q].new_eta = mean_eta;
std::cout << local_quadrature_points_history[q].new_eta << " ";
====================== SAVE STRESS TENSOR AT QUADRATURE POINTS ======================
template<int dim>
void StokesProblem<dim>::update_quadrature_point_history()
{
std::cout << " Updating stress field...";
Make the object that will hold the velocity gradients
std::vector < std::vector<Tensor<1, dim> >> velocity_grads(quadrature_formula.size(),
std::vector<Vector<double> > velocities(quadrature_formula.size(),
dof_handler.begin_active(); cell != dof_handler.end(); ++cell)
{
PointHistory<dim> *local_quadrature_points_history =
reinterpret_cast<PointHistory<dim> *>(cell->user_pointer());
local_quadrature_points_history >= &quadrature_point_history.front(),
ExcInternalError());
local_quadrature_points_history < &quadrature_point_history.back(),
ExcInternalError());
fe_values.reinit(cell);
fe_values.get_function_gradients(solution, velocity_grads);
fe_values.get_function_values(solution, velocities);
for (unsigned int q = 0; q < quadrature_formula.size(); ++q)
{
Define the local viscoelastic constants
double local_eta_ve = 2
/ ((1 / local_quadrature_points_history[q].new_eta)
+ (1 / local_quadrature_points_history[q].G
/ system_parameters::current_time_interval));
double local_chi_ve =
1
/ (1
+ (local_quadrature_points_history[q].G
* system_parameters::current_time_interval
/ local_quadrature_points_history[q].new_eta));
Compute new stress at each quadrature point
for (unsigned int i = 0; i < dim; ++i)
new_stress[i][i] =
local_eta_ve * velocity_grads[q][i][i]
+ local_chi_ve
* local_quadrature_points_history[q].old_stress[i][i];
for (unsigned int i = 0; i < dim; ++i)
for (unsigned int j = i + 1; j < dim; ++j)
new_stress[i][j] =
local_eta_ve
* (velocity_grads[q][i][j]
+ velocity_grads[q][j][i]) / 2
+ local_chi_ve
* local_quadrature_points_history[q].old_stress[i][j];
Rotate new stress
AuxFunctions<dim> rotation_object;
velocity_grads[q]);
* rotation);
local_quadrature_points_history[q].old_stress = rotated_new_stress;
DEAL_II_HOST constexpr SymmetricTensor< 2, dim, Number > symmetrize(const Tensor< 2, dim, Number > &t)
For axisymmetric case, make the phi-phi element of stress tensor
local_quadrature_points_history[q].old_phiphi_stress =
(2 * local_eta_ve * velocities[q](0)
/ fe_values.quadrature_point(q)[0]
+ local_chi_ve
* local_quadrature_points_history[q].old_phiphi_stress);
}
}
}
====================== REDEFINE THE TIME INTERVAL FOR THE VISCOUS STEPS ======================
template<int dim>
void StokesProblem<dim>::update_time_interval()
{
double move_goal_per_step = system_parameters::initial_disp_target;
if (system_parameters::present_timestep > system_parameters::initial_elastic_iterations)
{
move_goal_per_step = system_parameters::initial_disp_target -
((system_parameters::initial_disp_target - system_parameters::final_disp_target) /
system_parameters::total_viscous_steps *
(system_parameters::present_timestep - system_parameters::initial_elastic_iterations));
}
double zero_tolerance = 1e-3;
double max_velocity = 0;
dof_handler.begin_active(); cell != dof_handler.end(); ++cell)
{
if (cell->at_boundary())
{
int zero_faces = 0;
for (unsigned int f=0; f<GeometryInfo<dim>::faces_per_cell; ++f)
for (unsigned int i=0; i<dim; ++i)
if (fabs(cell->face(f)->center()[i]) < zero_tolerance)
zero_faces++;
if (zero_faces==0)
{
for (unsigned int v = 0; v < GeometryInfo<dim>::vertices_per_cell; ++v)
{
for (unsigned int d = 0; d < dim; ++d)
{
vertex_velocity[d] = solution(cell->vertex_dof_index(v, d));
vertex_position[d] = cell->vertex(v)[d];
}
velocity to be evaluated is the radial component of a surface vertex
double local_velocity = 0;
for (unsigned int d = 0; d < dim; ++d)
{
local_velocity += vertex_velocity[d] * vertex_position [d];
}
local_velocity /=
std::sqrt( vertex_position.square() );
if (local_velocity < 0)
local_velocity *= -1;
if (local_velocity > max_velocity)
{
max_velocity = local_velocity;
}
}
}
}
}
NOTE: It is possible for this time interval to be very different from that used in the viscoelasticity calculation.
system_parameters::current_time_interval = move_goal_per_step / max_velocity;
double step_time_yr = system_parameters::current_time_interval / SECSINYEAR;
std::cout << "Timestep interval changed to: "
<< step_time_yr
<< " years\n";
}
====================== MOVE MESH ======================
template<int dim>
void StokesProblem<dim>::move_mesh()
{
std::cout << "\n" << " Moving mesh...\n";
dof_handler.begin_active(); cell != dof_handler.end(); ++cell)
for (unsigned int v = 0; v < GeometryInfo<dim>::vertices_per_cell; ++v)
if (vertex_touched[cell->vertex_index(v)] == false)
{
vertex_touched[cell->vertex_index(v)] = true;
for (unsigned int d = 0; d < dim; ++d)
vertex_displacement[d] = solution(
cell->vertex_dof_index(v, d));
cell->vertex(v) += vertex_displacement
* system_parameters::current_time_interval;
}
}
unsigned int n_vertices() const
====================== WRITE MESH TO FILE ======================
template<int dim>
void StokesProblem<dim>::write_mesh()
{
output mesh in ucd
std::ostringstream initial_mesh_file;
initial_mesh_file << system_parameters::output_folder << "/time" <<
"_mesh.inp";
std::ofstream out_ucd (initial_mesh_file.str().c_str());
}
void write_ucd(const Triangulation< dim, spacedim > &tria, std::ostream &out) const
====================== FIT ELLIPSE TO SURFACE AND WRITE RADII TO FILE ======================
template<int dim>
void StokesProblem<dim>::do_ellipse_fits()
{
std::ostringstream ellipses_filename;
ellipses_filename << system_parameters::output_folder << "/ellipse_fits.txt";
Find ellipsoidal axes for all layers
std::vector<double> ellipse_axes(0);
compute fit to boundary 0, 1, 2 ...
std::cout << endl;
for (unsigned int i = 0; i<system_parameters::sizeof_material_id; ++i)
{
ellipsoid.compute_fit(ellipse_axes, system_parameters::material_id[i]);
system_parameters::q_axes.push_back(ellipse_axes[0]);
system_parameters::p_axes.push_back(ellipse_axes[1]);
std::cout << "a_"<< system_parameters::material_id[i] <<" = " << ellipse_axes[0]
<< " " << " c_"<< system_parameters::material_id[i] <<" = " << ellipse_axes[1] << std::endl;
ellipse_axes.clear();
std::ofstream fout_ellipses(ellipses_filename.str().c_str(), std::ios::app);
fout_ellipses << system_parameters::present_timestep << " a_"<< system_parameters::material_id[i] <<" = " << ellipse_axes[0]
<< " " << " c_"<< system_parameters::material_id[i] <<" = " << ellipse_axes[1] << endl;
fout_ellipses.close();
}
}
====================== APPEND LINE TO PHYSICAL_TIMES.TXT FILE WITH STEP NUMBER, PHYSICAL TIME, AND # PLASTIC ITERATIONS ======================
template<int dim>
void StokesProblem<dim>::append_physical_times(int max_plastic)
{
std::ostringstream times_filename;
times_filename << system_parameters::output_folder << "/physical_times.txt";
std::ofstream fout_times(times_filename.str().c_str(), std::ios::app);
fout_times << system_parameters::present_timestep << " "
<< system_parameters::present_time/SECSINYEAR << " "
<< max_plastic << "\n";
<< system_parameters::q_axes[0] << " " << system_parameters::p_axes[0] << " " << system_parameters::q_axes[1] << " " << system_parameters::p_axes[1] << "\n";
====================== WRITE VERTICES TO FILE ======================
template<int dim>
void StokesProblem<dim>::write_vertices(unsigned char boundary_that_we_need)
{
std::ostringstream vertices_output;
vertices_output << system_parameters::output_folder << "/time" <<
"_surface.txt";
std::ofstream fout_final_vertices(vertices_output.str().c_str());
fout_final_vertices.close();
if (boundary_that_we_need == 0)
{
Figure out if the vertex is on the boundary of the domain
for (unsigned int f = 0; f < GeometryInfo<dim>::faces_per_cell; ++f)
{
unsigned char boundary_ids = cell->face(f)->boundary_id();
if (boundary_ids == boundary_that_we_need)
{
for (unsigned int v=0; v<GeometryInfo<dim>::vertices_per_face; ++v)
if (vertex_touched[cell->face(f)->vertex_index(v)] == false)
{
vertex_touched[cell->face(f)->vertex_index(v)] = true;
std::ofstream fout_final_vertices(vertices_output.str().c_str(), std::ios::app);
fout_final_vertices << cell->face(f)->vertex(v) << "\n";
fout_final_vertices.close();
}
}
}
}
else
{
cell_iterator end() const
active_cell_iterator begin_active(const unsigned int level=0) const
Figure out if the vertex is on an internal boundary
for (unsigned int f = 0; f < GeometryInfo<dim>::faces_per_cell; ++f)
{
{
if (cell->material_id() != cell->neighbor(f)->material_id())
{
int high_mat_id =
std::max(cell->material_id(),
cell->neighbor(f)->material_id());
if (high_mat_id == boundary_that_we_need)
{
for (unsigned int v = 0;
v < GeometryInfo<dim>::vertices_per_face;
++v)
if (vertex_touched[cell->face(f)->vertex_index(
v)] == false)
{
vertex_touched[cell->face(f)->vertex_index(
v)] = true;
std::ofstream fout_final_vertices(vertices_output.str().c_str(), std::ios::app);
fout_final_vertices << cell->face(f)->vertex(v) << "\n";
fout_final_vertices.close();
}
}
}
}
}
}
}
::VectorizedArray< Number, width > max(const ::VectorizedArray< Number, width > &, const ::VectorizedArray< Number, width > &)
====================== SETUP INITIAL MESH ======================
template<int dim>
void StokesProblem<dim>::setup_initial_mesh()
{
std::ifstream mesh_stream(system_parameters::mesh_filename,
std::ifstream::in);
grid_in.read_ucd(mesh_stream);
void attach_triangulation(Triangulation< dim, spacedim > &tria)
output initial mesh in eps
std::ostringstream initial_mesh_file;
initial_mesh_file << system_parameters::output_folder << "/initial_mesh.eps";
std::ofstream out_eps (initial_mesh_file.str().c_str());
out_eps.close();
void write_eps(const Triangulation< dim, spacedim > &tria, std::ostream &out, const Mapping< dim, spacedim > *mapping=nullptr) const
set boundary ids boundary indicator 0 is outer free surface; 1, 2, 3 ... is boundary between layers, 99 is flat boundaries
unsigned int how_many;
std::ostringstream boundaries_file;
boundaries_file << system_parameters::output_folder << "/boundaries.txt";
std::ofstream fout_boundaries(boundaries_file.str().c_str());
fout_boundaries.close();
double zero_tolerance = 1e-3;
for (; cell != endc; ++cell)
{
for (unsigned int f = 0; f < GeometryInfo<dim>::faces_per_cell; ++f)
{
if (cell->face(f)->at_boundary())
{
print boundary
std::ofstream fout_boundaries(boundaries_file.str().c_str(), std::ios::app);
fout_boundaries << cell->face(f)->center()[0] << " " << cell->face(f)->center()[1]<< "\n";
fout_boundaries.close();
how_many = 0;
for (unsigned int i=0; i<dim; ++i)
if (fabs(cell->face(f)->center()[i]) > zero_tolerance)
how_many++;
if (how_many==dim)
cell->face(f)->set_all_boundary_ids(0);
else
cell->face(f)->set_all_boundary_ids(99);
}
}
}
std::ostringstream ellipses_filename;
ellipses_filename << system_parameters::output_folder << "/ellipse_fits.txt";
std::ofstream fout_ellipses(ellipses_filename.str().c_str());
fout_ellipses.close();
Find ellipsoidal axes for all layers
std::vector<double> ellipse_axes(0);
compute fit to boundary 0, 1, 2 ...
std::cout << endl;
for (unsigned int i = 0; i<system_parameters::sizeof_material_id; ++i)
{
ellipsoid.compute_fit(ellipse_axes, system_parameters::material_id[i]);
system_parameters::q_axes.push_back(ellipse_axes[0]);
system_parameters::p_axes.push_back(ellipse_axes[1]);
std::cout << "a_"<< system_parameters::material_id[i] <<" = " << ellipse_axes[0]
<< " " << " c_"<< system_parameters::material_id[i] <<" = " << ellipse_axes[1] << std::endl;
ellipse_axes.clear();
std::ofstream fout_ellipses(ellipses_filename.str().c_str(), std::ios::app);
fout_ellipses << system_parameters::present_timestep << " a_"<< system_parameters::material_id[i] <<" = " << ellipse_axes[0]
<< " " << " c_"<< system_parameters::material_id[i] <<" = " << ellipse_axes[1] << endl;
fout_ellipses.close();
}
void refine_global(const unsigned int times=1)
refines crustal region
if (system_parameters::crustal_refinement != 0)
{
double a = system_parameters::q_axes[0] - system_parameters::crust_refine_region;
double b = system_parameters::p_axes[0] - system_parameters::crust_refine_region;
for (unsigned int step = 0;
step < system_parameters::crustal_refinement; ++step)
{
typename ::Triangulation<dim>::active_cell_iterator cell =
for (; cell != endc; ++cell)
for (unsigned int v = 0;
v < GeometryInfo<dim>::vertices_per_cell; ++v)
{
const double x_coord = current_vertex.operator()(0);
const double y_coord = current_vertex.operator()(1);
double expected_z = -1;
if ((x_coord - a) < -1e-10)
expected_z = b
*
std::sqrt(1 - (x_coord * x_coord / a / a));
if (y_coord >= expected_z)
{
cell->set_refine_flag();
break;
}
}
}
}
virtual void execute_coarsening_and_refinement() override
output initial mesh in eps
std::ostringstream refined_mesh_file;
refined_mesh_file << system_parameters::output_folder << "/refined_mesh.eps";
std::ofstream out_eps_refined (refined_mesh_file.str().c_str());
out_eps_refined.close();
write_vertices(0);
write_vertices(1);
write_mesh();
}
====================== REFINE MESH ======================
template<int dim>
void StokesProblem<dim>::refine_mesh()
{
using FunctionMap = std::map<types::boundary_id, const Function<dim> *>;
std::vector<bool> component_mask(dim + 1, false);
component_mask[dim] = true;
FunctionMap(), solution,
estimated_error_per_cell, component_mask);
estimated_error_per_cell, 0.3, 0.0);
}
static void estimate(const Mapping< dim, spacedim > &mapping, const DoFHandler< dim, spacedim > &dof, const Quadrature< dim - 1 > &quadrature, const std::map< types::boundary_id, const Function< spacedim, Number > * > &neumann_bc, const ReadVector< Number > &solution, Vector< float > &error, const ComponentMask &component_mask={}, const Function< spacedim > *coefficients=nullptr, const unsigned int n_threads=numbers::invalid_unsigned_int, const types::subdomain_id subdomain_id=numbers::invalid_subdomain_id, const types::material_id material_id=numbers::invalid_material_id, const Strategy strategy=cell_diameter_over_24)
void refine_and_coarsen_fixed_number(Triangulation< dim, spacedim > &triangulation, const Vector< Number > &criteria, const double top_fraction_of_cells, const double bottom_fraction_of_cells, const unsigned int max_n_cells=std::numeric_limits< unsigned int >::max())
====================== SET UP THE DATA STRUCTURES TO REMEMBER STRESS FIELD ======================
template<int dim>
void StokesProblem<dim>::setup_quadrature_point_history()
{
unsigned int our_cells = 0;
++our_cells;
quadrature_point_history.resize(our_cells * quadrature_formula.size());
unsigned int history_index = 0;
{
cell->set_user_pointer(&quadrature_point_history[history_index]);
history_index += quadrature_formula.size();
}
Assert(history_index == quadrature_point_history.size(), ExcInternalError());
}
====================== DOES ELASTIC STEPS ======================
template<int dim>
void StokesProblem<dim>::do_elastic_steps()
{
unsigned int elastic_iteration = 0;
while (elastic_iteration < system_parameters::initial_elastic_iterations)
{
std::cout << "\n\nElastic iteration " << elastic_iteration
<< "\n";
setup_dofs();
if (system_parameters::present_timestep == 0)
initialize_eta_and_G();
if (elastic_iteration == 0)
system_parameters::current_time_interval =
system_parameters::viscous_time;
std::cout << " Assembling..." << std::endl << std::flush;
assemble_system();
std::cout << " Solving..." << std::flush;
solve();
output_results();
update_quadrature_point_history();
append_physical_times(0);
elastic_iteration++;
system_parameters::present_timestep++;
do_ellipse_fits();
write_vertices(0);
write_vertices(1);
write_mesh();
update_time_interval();
}
}
====================== DO A SINGLE VISCOELASTOPLASTIC TIMESTEP ======================
template<int dim>
void StokesProblem<dim>::do_flow_step()
{
plastic_iteration = 0;
while (plastic_iteration < system_parameters::max_plastic_iterations)
{
if (system_parameters::continue_plastic_iterations == true)
{
std::cout << "Plasticity iteration " << plastic_iteration << "\n";
setup_dofs();
std::cout << " Assembling..." << std::endl << std::flush;
assemble_system();
std::cout << " Solving..." << std::flush;
solve();
output_results();
solution_stesses();
if (system_parameters::continue_plastic_iterations == false)
break;
plastic_iteration++;
}
}
}
====================== RUN ======================
template<int dim>
void StokesProblem<dim>::run()
{
Sets up mesh and data structure for viscosity and stress at quadrature points
setup_initial_mesh();
setup_quadrature_point_history();
Makes the physical_times.txt file
std::ostringstream times_filename;
times_filename << system_parameters::output_folder << "/physical_times.txt";
std::ofstream fout_times(times_filename.str().c_str());
fout_times.close();
Computes elastic timesteps
Computes viscous timesteps
unsigned int VEPstep = 0;
while (system_parameters::present_timestep
< (system_parameters::initial_elastic_iterations
+ system_parameters::total_viscous_steps))
{
if (system_parameters::continue_plastic_iterations == false)
system_parameters::continue_plastic_iterations = true;
std::cout << "\n\nViscoelastoplastic iteration " << VEPstep << "\n\n";
Computes plasticity
do_flow_step();
update_quadrature_point_history();
move_mesh();
append_physical_times(plastic_iteration);
system_parameters::present_timestep++;
system_parameters::present_time = system_parameters::present_time + system_parameters::current_time_interval;
do_ellipse_fits();
write_vertices(0);
write_vertices(1);
write_mesh();
VEPstep++;
}
append_physical_times(-1);
}
}
====================== MAIN ======================
int main(int argc, char *argv[])
{
output program name
std::cout << "Running: " << argv[0] << std::endl;
char *cfg_filename = new char[120];
if (argc == 1)
{
std::strcpy(cfg_filename,"config/sample_CeresFE_config.cfg");
}
else
std::strcpy(cfg_filename,argv[1]);
try
{
using namespace Step22;
config_in cfg(cfg_filename);
std::clock_t t1;
std::clock_t t2;
t1 = std::clock();
StokesProblem<2> flow_problem(1);
flow_problem.run();
std::cout << std::endl << "\a";
t2 = std::clock();
float diff (((float)t2 - (float)t1) / (float)CLOCKS_PER_SEC);
std::cout << "\n Program run in: " << diff << " seconds" << endl;
}
catch (std::exception &exc)
{
std::cerr << std::endl << std::endl
<< "----------------------------------------------------"
<< std::endl;
std::cerr << "Exception on processing: " << std::endl << exc.what()
<< std::endl << "Aborting!" << std::endl
<< "----------------------------------------------------"
<< std::endl;
return 1;
}
catch (...)
{
std::cerr << std::endl << std::endl
<< "----------------------------------------------------"
<< std::endl;
std::cerr << "Unknown exception!" << std::endl << "Aborting!"
<< std::endl
<< "----------------------------------------------------"
<< std::endl;
return 1;
}
return 0;
}
unsigned int depth_console(const unsigned int n)
Annotated version of support_code/config_in.h
#include <iostream>
#include <iomanip>
#include <cstdlib>
#include <string>
#include <libconfig.h++>
#include "local_math.h"
using namespace libconfig;
namespace Step22
{
namespace system_parameters
{
Mesh file name
string mesh_filename;
string output_folder;
Body parameters
double r_mean;
double period;
double omegasquared;
double beta;
double intercept;
Rheology parameters
vector<double> depths_eta;
vector<double> eta_kinks;
vector<double> depths_rho;
vector<double> rho;
vector<int> material_id;
vector<double> G;
double eta_ceiling;
double eta_floor;
double eta_Ea;
bool lat_dependence;
unsigned int sizeof_depths_eta;
unsigned int sizeof_depths_rho;
unsigned int sizeof_rho;
unsigned int sizeof_eta_kinks;
unsigned int sizeof_material_id;
unsigned int sizeof_G;
double pressure_scale;
double q;
bool cylindrical;
bool continue_plastic_iterations;
plasticity variables
bool plasticity_on;
unsigned int failure_criterion;
unsigned int max_plastic_iterations;
double smoothing_radius;
viscoelasticity variables
unsigned int initial_elastic_iterations;
double elastic_time;
double viscous_time;
double initial_disp_target;
double final_disp_target;
double current_time_interval;
mesh refinement variables
unsigned int global_refinement;
unsigned int small_r_refinement;
unsigned int crustal_refinement;
double crust_refine_region;
unsigned int surface_refinement;
solver variables
int iteration_coefficient;
double tolerance_coefficient;
time step variables
double present_time;
unsigned int present_timestep;
unsigned int total_viscous_steps;
ellipse axes
vector<double> q_axes;
vector<double> p_axes;
}
class config_in
{
public:
config_in(char *);
private:
void write_config();
};
void config_in::write_config()
{
std::ostringstream config_parameters;
config_parameters << system_parameters::output_folder << "/run_parameters.txt";
std::ofstream fout_config(config_parameters.str().c_str());
mesh filename
fout_config << "mesh filename: " << system_parameters::mesh_filename << endl << endl;
body parameters
fout_config << "r_mean = " << system_parameters::r_mean << endl;
fout_config << "period = " << system_parameters::period << endl;
fout_config << "omegasquared = " << system_parameters::omegasquared << endl;
fout_config << "beta = " << system_parameters::beta << endl;
fout_config << "intercept = " << system_parameters::intercept << endl;
rheology parameters
for (unsigned int i=0; i<system_parameters::sizeof_depths_eta; ++i)
fout_config << "depths_eta[" << i << "] = " << system_parameters::depths_eta[i] << endl;
for (unsigned int i=0; i<system_parameters::sizeof_eta_kinks; ++i)
fout_config << "eta_kinks[" << i << "] = " << system_parameters::eta_kinks[i] << endl;
for (unsigned int i=0; i<system_parameters::sizeof_depths_rho; ++i)
fout_config << "depths_rho[" << i << "] = " << system_parameters::depths_rho[i] << endl;
for (unsigned int i=0; i<system_parameters::sizeof_rho; ++i)
fout_config << "rho[" << i << "] = " << system_parameters::rho[i] << endl;
for (unsigned int i=0; i<system_parameters::sizeof_material_id; ++i)
fout_config << "material_id[" << i << "] = " << system_parameters::material_id[i] << endl;
for (unsigned int i=0; i<system_parameters::sizeof_G; ++i)
fout_config << "G[" << i << "] = " << system_parameters::G[i] << endl;
fout_config << "eta_ceiling = " << system_parameters::eta_ceiling << endl;
fout_config << "eta_floor = " << system_parameters::eta_floor << endl;
fout_config << "eta_Ea = " << system_parameters::eta_Ea << endl;
fout_config << "lat_dependence = " << system_parameters::lat_dependence << endl;
fout_config << "pressure_scale = " << system_parameters::pressure_scale << endl;
fout_config << "q = " << system_parameters::q << endl;
fout_config << "cylindrical = " << system_parameters::cylindrical << endl;
fout_config << "continue_plastic_iterations = " << system_parameters::continue_plastic_iterations << endl;
Plasticity parameters
fout_config << "plasticity_on = " << system_parameters::plasticity_on << endl;
fout_config << "failure_criterion = " << system_parameters::failure_criterion << endl;
fout_config << "max_plastic_iterations = " << system_parameters::max_plastic_iterations << endl;
fout_config << "smoothing_radius = " << system_parameters::smoothing_radius << endl;
Viscoelasticity parameters
fout_config << "initial_elastic_iterations = " << system_parameters::initial_elastic_iterations << endl;
fout_config << "elastic_time = " << system_parameters::elastic_time << endl;
fout_config << "viscous_time = " << system_parameters::viscous_time << endl;
fout_config << "initial_disp_target = " << system_parameters::initial_disp_target << endl;
fout_config << "final_disp_target = " << system_parameters::final_disp_target << endl;
fout_config << "current_time_interval = " << system_parameters::current_time_interval << endl;
Mesh refinement parameters
fout_config << "global_refinement = " << system_parameters::global_refinement << endl;
fout_config << "small_r_refinement = " << system_parameters::small_r_refinement << endl;
fout_config << "crustal_refinement = " << system_parameters::crustal_refinement << endl;
fout_config << "crust_refine_region = " << system_parameters::crust_refine_region << endl;
fout_config << "surface_refinement = " << system_parameters::surface_refinement << endl;
Solver parameters
fout_config << "iteration_coefficient = " << system_parameters::iteration_coefficient << endl;
fout_config << "tolerance_coefficient = " << system_parameters::tolerance_coefficient << endl;
Time step parameters
fout_config << "present_time = " << system_parameters::present_time << endl;
fout_config << "present_timestep = " << system_parameters::present_timestep << endl;
fout_config << "total_viscous_steps = " << system_parameters::total_viscous_steps << endl;
fout_config.close();
}
config_in::config_in(char *filename)
{
This example reads the configuration file 'example.cfg' and displays some of its contents.
Read the file. If there is an error, report it and exit.
try
{
cfg.readFile(filename);
}
catch (const FileIOException &fioex)
{
std::cerr << "I/O error while reading file:" << filename << std::endl;
}
catch (const ParseException &pex)
{
std::cerr <<
"Parse error at " <<
pex.getFile() <<
":" <<
pex.getLine()
<<
" - " <<
pex.getError() << std::endl;
}
std::vector< unsigned int > pex(const std::vector< unsigned int > &targets, const std::function< RequestType(const unsigned int)> &create_request, const std::function< AnswerType(const unsigned int, const RequestType &)> &answer_request, const std::function< void(const unsigned int, const AnswerType &)> &process_answer, const MPI_Comm comm)
Get mesh name.
try
{
string msh = cfg.lookup("mesh_filename");
system_parameters::mesh_filename = msh;
}
catch (const SettingNotFoundException &nfex)
{
cerr << "No 'mesh_filename' setting in configuration file." << endl;
}
get output folder
try
{
string output = cfg.lookup("output_folder");
system_parameters::output_folder = output;
std::cout << "Writing to folder: " << output << endl;
}
catch (const SettingNotFoundException &nfex)
{
cerr << "No 'output_folder' setting in configuration file." << endl;
}
get radii
const Setting &root = cfg.getRoot();
get body parameters
try
{
const Setting &body_parameters = root["body_parameters"];
body_parameters.lookupValue("period", system_parameters::period);
system_parameters::omegasquared = pow(TWOPI / 3600.0 / system_parameters::period, 2.0);
body_parameters.lookupValue("r_mean", system_parameters::r_mean);
body_parameters.lookupValue("beta", system_parameters::beta);
body_parameters.lookupValue("intercept", system_parameters::intercept);
}
catch (const SettingNotFoundException &nfex)
{
cerr << "We've got a problem in the body parameters block" << endl;
}
Rheology parameters
get depths_eta ------------------—
const Setting &set_depths_eta = cfg.lookup("rheology_parameters.depths_eta");
unsigned int ndepths_eta = set_depths_eta.getLength();
system_parameters::sizeof_depths_eta = ndepths_eta;
for (unsigned int i=0; i<ndepths_eta; ++i)
{
system_parameters::depths_eta.push_back(set_depths_eta[i]);
cout << "depth_eta[" << i << "] = " << system_parameters::depths_eta[i] << endl;
}
get eta_kinks ----------------------—
const Setting &set_eta_kinks = cfg.lookup("rheology_parameters.eta_kinks");
unsigned int neta_kinks = set_eta_kinks.getLength();
system_parameters::sizeof_eta_kinks = neta_kinks;
cout << "Number of depth = " << ndepths << endl;
for (unsigned int i=0; i<neta_kinks; ++i)
{
system_parameters::eta_kinks.push_back(set_eta_kinks[i]);
cout << "eta_kinks[" << i << "] = " << system_parameters::eta_kinks[i] << endl;
}
get depths_rho ----------------------—
const Setting &set_depths_rho = cfg.lookup("rheology_parameters.depths_rho");
unsigned int ndepths_rho = set_depths_rho.getLength();
system_parameters::sizeof_depths_rho = ndepths_rho;
cout << "Number of depth = " << ndepths << endl;
for (unsigned int i=0; i<ndepths_rho; ++i)
{
system_parameters::depths_rho.push_back(set_depths_rho[i]);
cout << "depths_rho[" << i << "] = " << system_parameters::depths_rho[i] << endl;
}
get rho ----------------------—
const Setting &set_rho = cfg.lookup("rheology_parameters.rho");
unsigned int nrho = set_rho.getLength();
system_parameters::sizeof_rho = nrho;
cout << "Number of depth = " << ndepths << endl;
for (unsigned int i=0; i<nrho; ++i)
{
system_parameters::rho.push_back(set_rho[i]);
cout << "rho[" << i << "] = " << system_parameters::rho[i] << endl;
}
get material_id ----------------------—
const Setting &set_material_id = cfg.lookup("rheology_parameters.material_id");
unsigned int nmaterial_id = set_material_id.getLength();
system_parameters::sizeof_material_id = nmaterial_id;
cout << "Number of depth = " << ndepths << endl;
for (unsigned int i=0; i<nmaterial_id; ++i)
{
system_parameters::material_id.push_back(set_material_id[i]);
cout << "material_id[" << i << "] = " << system_parameters::material_id[i] << endl;
}
get G ----------------------—
const Setting &set_G = cfg.lookup("rheology_parameters.G");
unsigned int nG = set_G.getLength();
system_parameters::sizeof_G = nG;
cout << "Number of depth = " << ndepths << endl;
for (unsigned int i=0; i<nG; ++i)
{
system_parameters::G.push_back(set_G[i]);
cout << "G[" << i << "] = " << system_parameters::G[i] << endl;
}
const Setting &rheology_parameters = root["rheology_parameters"];
rheology_parameters.lookupValue("eta_ceiling", system_parameters::eta_ceiling);
rheology_parameters.lookupValue("eta_floor", system_parameters::eta_floor);
rheology_parameters.lookupValue("eta_Ea", system_parameters::eta_Ea);
rheology_parameters.lookupValue("lat_dependence", system_parameters::lat_dependence);
rheology_parameters.lookupValue("pressure_scale", system_parameters::pressure_scale);
rheology_parameters.lookupValue("q", system_parameters::q);
rheology_parameters.lookupValue("cylindrical", system_parameters::cylindrical);
rheology_parameters.lookupValue("continue_plastic_iterations", system_parameters::continue_plastic_iterations);
}
catch (const SettingNotFoundException &nfex)
{
cerr << "We've got a problem in the rheology parameters block" << endl;
}
Plasticity parameters
try
{
const Setting &plasticity_parameters = root["plasticity_parameters"];
plasticity_parameters.lookupValue("plasticity_on", system_parameters::plasticity_on);
plasticity_parameters.lookupValue("failure_criterion", system_parameters::failure_criterion);
plasticity_parameters.lookupValue("max_plastic_iterations", system_parameters::max_plastic_iterations);
plasticity_parameters.lookupValue("smoothing_radius", system_parameters::smoothing_radius);
}
catch (const SettingNotFoundException &nfex)
{
cerr << "We've got a problem in the plasticity parameters block" << endl;
}
Viscoelasticity parameters
try
{
const Setting &viscoelasticity_parameters = root["viscoelasticity_parameters"];
viscoelasticity_parameters.lookupValue("initial_elastic_iterations", system_parameters::initial_elastic_iterations);
viscoelasticity_parameters.lookupValue("elastic_time", system_parameters::elastic_time);
viscoelasticity_parameters.lookupValue("viscous_time", system_parameters::viscous_time);
viscoelasticity_parameters.lookupValue("initial_disp_target", system_parameters::initial_disp_target);
viscoelasticity_parameters.lookupValue("final_disp_target", system_parameters::final_disp_target);
viscoelasticity_parameters.lookupValue("current_time_interval", system_parameters::current_time_interval);
system_parameters::viscous_time *= SECSINYEAR;
}
catch (const SettingNotFoundException &nfex)
{
cerr << "We've got a problem in the viscoelasticity parameters block" << endl;
}
Mesh refinement parameters
try
{
const Setting &mesh_refinement_parameters = root["mesh_refinement_parameters"];
mesh_refinement_parameters.lookupValue("global_refinement", system_parameters::global_refinement);
mesh_refinement_parameters.lookupValue("small_r_refinement", system_parameters::small_r_refinement);
mesh_refinement_parameters.lookupValue("crustal_refinement", system_parameters::crustal_refinement);
mesh_refinement_parameters.lookupValue("crust_refine_region", system_parameters::crust_refine_region);
mesh_refinement_parameters.lookupValue("surface_refinement", system_parameters::surface_refinement);
}
catch (const SettingNotFoundException &nfex)
{
cerr << "We've got a problem in the mesh refinement parameters block" << endl;
}
Solver parameters
try
{
const Setting &solve_parameters = root["solve_parameters"];
solve_parameters.lookupValue("iteration_coefficient", system_parameters::iteration_coefficient);
solve_parameters.lookupValue("tolerance_coefficient", system_parameters::tolerance_coefficient);
}
catch (const SettingNotFoundException &nfex)
{
cerr << "We've got a problem in the solver parameters block" << endl;
}
Time step parameters
try
{
const Setting &time_step_parameters = root["time_step_parameters"];
time_step_parameters.lookupValue("present_time", system_parameters::present_time);
time_step_parameters.lookupValue("present_timestep", system_parameters::present_timestep);
time_step_parameters.lookupValue("total_viscous_steps", system_parameters::total_viscous_steps);
}
catch (const SettingNotFoundException &nfex)
{
cerr << "We've got a problem in the time step parameters block" << endl;
}
write_config();
}
}
Annotated version of support_code/ellipsoid_fit.h
#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/function.h>
#include <deal.II/base/logstream.h>
#include <deal.II/lac/vector.h>
#include <deal.II/lac/full_matrix.h>
#include <deal.II/lac/sparse_matrix.h>
#include <deal.II/lac/solver_cg.h>
#include <deal.II/lac/precondition.h>
#include <deal.II/grid/tria.h>
#include <deal.II/dofs/dof_handler.h>
#include <deal.II/grid/tria_accessor.h>
#include <deal.II/grid/tria_iterator.h>
#include <deal.II/dofs/dof_accessor.h>
#include <deal.II/dofs/dof_tools.h>
#include <deal.II/fe/fe_q.h>
#include <deal.II/fe/fe_values.h>
#include <deal.II/numerics/vector_tools.h>
#include <deal.II/numerics/matrix_tools.h>
#include <deal.II/numerics/data_out.h>
#include <deal.II/grid/grid_in.h>
#include <deal.II/grid/grid_out.h>
#include <deal.II/base/point.h>
#include <deal.II/grid/grid_generator.h>
#include <fstream>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdlib>
#include "local_math.h"
template <int dim>
class ellipsoid_fit
{
public:
{
p_triangulation = pi;
};
void compute_fit(std::vector<double> &ell, unsigned char bndry);
private:
};
This function computes ellipsoid fit to a set of vertices that lie on the boundary_that_we_need
template <int dim>
void ellipsoid_fit<dim>::compute_fit(std::vector<double> &ell, unsigned char boundary_that_we_need)
{
std::vector<bool> vertex_touched (p_triangulation->n_vertices(),
false);
unsigned int j = 0;
unsigned char boundary_ids;
std::vector<unsigned int> ind_bnry_row;
std::vector<unsigned int> ind_bnry_col;
assemble the sensitivity matrix and r.h.s.
for (; cell != endc; ++cell)
{
if (boundary_that_we_need != 0)
cell->set_manifold_id(cell->material_id());
for (unsigned int f = 0; f < GeometryInfo<dim>::faces_per_cell; ++f)
{
if (boundary_that_we_need == 0)
{
boundary_ids = cell->face(f)->boundary_id();
if (boundary_ids == boundary_that_we_need)
{
for (unsigned int v = 0;
v < GeometryInfo<dim>::vertices_per_face; ++v)
if (vertex_touched[cell->face(f)->vertex_index(v)]
== false)
{
vertex_touched[cell->face(f)->vertex_index(v)] =
true;
for (unsigned int i = 0; i < dim; ++i)
{
stiffness matrix entry
A(j, i) = pow(cell->face(f)->vertex(v)[i], 2);
r.h.s. entry
if mesh if not full: set the indicator
}
ind_bnry_row.push_back(j);
j++;
}
}
}
else
{
if (cell->neighbor(f) != endc)
{
if (cell->material_id() != cell->neighbor(f)->material_id())
{
int high_mat_id =
std::max(cell->material_id(),
cell->neighbor(f)->material_id());
if (high_mat_id == boundary_that_we_need)
{
for (unsigned int v = 0;
v < GeometryInfo<dim>::vertices_per_face;
++v)
if (vertex_touched[cell->face(f)->vertex_index(
v)] == false)
{
vertex_touched[cell->face(f)->vertex_index(
v)] = true;
for (unsigned int i = 0; i < dim; ++i)
{
stiffness matrix entry
A(j, i) = pow(
cell->face(f)->vertex(v)[i], 2);
r.h.s. entry
if mesh if not full: set the indicator
}
ind_bnry_row.push_back(j);
j++;
}
}
}
}
}
}
}
if (ind_bnry_row.size()>0)
{
maxtrix A'*A and vector A'*b; A'*A*x = A'*b – normal system of equations
for (unsigned int i=0; i<dim; ++i)
ind_bnry_col.push_back(i);
for (unsigned int i=0; i<ind_bnry_row.size(); ++i)
b_out(i) = 1;
A_out.extract_submatrix_from(A, ind_bnry_row, ind_bnry_col);
A_out.Tmmult(AtA,A_out,true);
A_out.Tvmult(Atb,b_out,true);
solve normal system of equations
find ellipsoidal axes
for (unsigned int i=0; i<dim; ++i)
ell.push_back(sqrt(1.0/x[i]));
}
else
std::cerr << "fit_ellipsoid: no points to fit" << std::endl;
}
Annotated version of support_code/ellipsoid_grav.h
#include <math.h>
#include <deal.II/base/point.h>
#include <fstream>
#include <iostream>
namespace A_Grav_namespace
{
namespace system_parameters
{
double mantle_rho;
double core_rho;
double excess_rho;
double r_eq;
double r_polar;
double r_core_eq;
double r_core_polar;
}
template <int dim>
class AnalyticGravity
{
public:
void setup_vars (std::vector<double> v);
void get_gravity (const ::Point<dim> &p, std::vector<double> &g);
private:
double ecc;
double eV;
double ke;
double r00;
double r01;
double r11;
double ecc_c;
double eV_c;
double ke_c;
double r00_c;
double r01_c;
double r11_c;
double g_coeff;
double g_coeff_c;
};
template <int dim>
void AnalyticGravity<dim>::get_gravity (const ::Point<dim> &p, std::vector<double> &g)
{
double rsph =
std::sqrt(p[0] * p[0] + p[1] * p[1]);
double thetasph = std::atan2(p[0], p[1]);
double costhetasph =
std::cos(thetasph);
convert to elliptical coordinates for silicates
double stemp =
std::sqrt((rsph * rsph - eV * eV +
std::sqrt((rsph * rsph - eV * eV) * (rsph * rsph - eV * eV)
+ 4 * eV * eV * rsph * rsph * costhetasph *costhetasph)) / 2);
double vout = stemp / system_parameters::r_eq /
std::sqrt(1 - ecc * ecc);
double eout =
std::acos(rsph * costhetasph / stemp);
inline ::VectorizedArray< Number, width > acos(const ::VectorizedArray< Number, width > &x)
convert to elliptical coordinates for core correction
double stemp_c =
std::sqrt((rsph * rsph - eV_c * eV_c +
std::sqrt((rsph * rsph - eV_c * eV_c) * (rsph * rsph - eV_c * eV_c)
+ 4 * eV_c * eV_c * rsph * rsph * costhetasph *costhetasph)) / 2);
double vout_c = stemp_c / system_parameters::r_core_eq /
std::sqrt(1 - ecc_c * ecc_c);
double eout_c =
std::acos(rsph * costhetasph / stemp_c);
shell contribution
g[0] = g_coeff * r11 *
std::sqrt((1 - ecc * ecc) * vout * vout + ecc * ecc) *
std::sin(eout);
core contribution
double expected_y = system_parameters::r_core_polar *
std::sqrt(1 -
(p[0] * p[0] / system_parameters::r_core_eq / system_parameters::r_core_eq));
if (p[1] <= expected_y)
{
g[0] += g_coeff_c * r11_c *
std::sqrt((1 - ecc_c * ecc_c) * vout_c * vout_c + ecc_c * ecc_c) *
std::sin(eout_c);
g[1] += g_coeff_c * r01_c * vout_c *
std::cos(eout_c) /
std::sqrt(1 - ecc_c * ecc_c);
}
else
{
double g_coeff_co = - 2.795007963255562e-10 * system_parameters::excess_rho * system_parameters::r_core_eq
/ vout_c / vout_c;
double r00_co = 0;
double r01_co = 0;
double r11_co = 0;
if (system_parameters::r_core_polar == system_parameters::r_core_eq)
{
r00_co = 1;
r01_co = 1;
r11_co = 1;
}
else
{
r00_co = ke_c * vout_c * std::atan2(1, ke_c * vout_c);
double ke_co2 = ke_c * ke_c * vout_c * vout_c;
r01_co = 3 * ke_co2 * (1 - r00_co);
r11_co = 3 * ((ke_co2 + 1) * r00_co - ke_co2) / 2;
}
g[0] += g_coeff_co * vout_c * r11_co /
std::sqrt((1 - ecc_c* ecc_c) * vout_c * vout_c + ecc_c * ecc_c) *
std::sin(eout_c);
}
}
template <int dim>
void AnalyticGravity<dim>::setup_vars (std::vector<double> v)
{
system_parameters::r_eq = v[0];
system_parameters::r_polar = v[1];
system_parameters::r_core_eq = v[2];
system_parameters::r_core_polar = v[3];
system_parameters::mantle_rho = v[4];
system_parameters::core_rho = v[5];
system_parameters::excess_rho = system_parameters::core_rho - system_parameters::mantle_rho;
Shell
if (system_parameters::r_polar > system_parameters::r_eq)
{
This makes the gravity field nearly that of a sphere in case the body becomes prolate
std::cout << "\nWarning: The model body has become prolate. \n";
ecc = 0.001;
}
else
{
ecc =
std::sqrt(1 - (system_parameters::r_polar * system_parameters::r_polar / system_parameters::r_eq / system_parameters::r_eq));
}
eV = ecc * system_parameters::r_eq;
r00 = ke * std::atan2(1, ke);
double ke2 = ke * ke;
r01 = 3 * ke2 * (1 - r00);
r11 = 3 * ((ke2 + 1) * r00 - ke2) / 2;
g_coeff = - 2.795007963255562e-10 * system_parameters::mantle_rho * system_parameters::r_eq;
Core
if (system_parameters::r_core_polar > system_parameters::r_core_eq)
{
std::cout << "\nWarning: The model core has become prolate. \n";
ecc_c = 0.001;
}
else
{
ecc_c =
std::sqrt(1 - (system_parameters::r_core_polar * system_parameters::r_core_polar / system_parameters::r_core_eq / system_parameters::r_core_eq));
}
eV_c = ecc_c * system_parameters::r_core_eq;
if (system_parameters::r_core_polar == system_parameters::r_core_eq)
{
ke_c = 1;
r00_c = 1;
r01_c = 1;
r11_c = 1;
g_coeff_c = - 2.795007963255562e-10 * system_parameters::excess_rho * system_parameters::r_core_eq;
}
else
{
ke_c =
std::sqrt(1 - (ecc_c * ecc_c)) / ecc_c;
r00_c = ke_c * std::atan2(1, ke_c);
double ke2_c = ke_c * ke_c;
r01_c = 3 * ke2_c * (1 - r00_c);
r11_c = 3 * ((ke2_c + 1) * r00_c - ke2_c) / 2;
g_coeff_c = - 2.795007963255562e-10 * system_parameters::excess_rho * system_parameters::r_core_eq;
}
std::cout << "Loaded variables: ecc = " << ecc_c << " ke = " << ke_c << " r00 = " << r00_c << " r01 = " << r01_c << " r11 = " << r11_c << "\n";
Annotated version of support_code/local_math.h
#ifndef LOCAL_MATH_
#define LOCAL_MATH_
#define PI 3.14159265358979323846
#define TWOPI 6.283185307179586476925287
#define SECSINYEAR 3.155692608e+07
#define ABS(a) ((a) < 0 ? -(a) : (a))
double factorial(int n) { if(n == 0) { return(1.); } else if(n == 1) { return(1.); } else if(n == 2) { return(2.); } else if(n == 3) { return(6.); } else if(n == 4) { return(24.); } else { exit(-1); } }
double fudge(int m) { if(m == 0) { return(1.0); } else { return(2.0); } }
double sign(double x) { if(x > 0) { return(1.0); } else if(x < 0.0) { return(-1.0); } else { return(0.0); } }
double pv0(double x) { double ans;
ans = x - TWOPI*floor(x/TWOPI); if(ans > TWOPI/2.0) { ans = ans - TWOPI; }
return(ans); }
double System::Plm(int m, double x) { if(m == 0) { return(1.5*x*x - 0.5); } else if(m == 1) { return(3.0*x*sqrt(1.0 - x*x)); } else if(m == 2) { return(3.0 - 3.0*x*x); } else { exit(-1); } }
double System::DP(int m, double x) { if(m == 0) { return(3.0*x); } else if(m == 1) { return((3.0 - 6.0*x*x)/sqrt(1.0 - x*x)); } else if(m == 2) { return(- 6.0*x); } else { exit(-1); } }
1.11.0