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| | ImplicitRungeKutta ()=default |
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| | ImplicitRungeKutta (const runge_kutta_method method, const unsigned int max_it=100, const double tolerance=1e-6) |
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| void | initialize (const runge_kutta_method method) override |
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| double | evolve_one_time_step (const std::function< VectorType(const double, const VectorType &)> &f, const std::function< VectorType(const double, const double, const VectorType &)> &id_minus_tau_J_inverse, double t, double delta_t, VectorType &y) override |
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| void | set_newton_solver_parameters (const unsigned int max_it, const double tolerance) |
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| const Status & | get_status () const override |
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| double | evolve_one_time_step (std::vector< std::function< VectorType(const double, const VectorType &)> > &F, std::vector< std::function< VectorType(const double, const double, const VectorType &)> > &J_inverse, double t, double delta_t, VectorType &y) override |
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| void | compute_stages (const std::function< VectorType(const double, const VectorType &)> &f, const std::function< VectorType(const double, const double, const VectorType &)> &id_minus_tau_J_inverse, double t, double delta_t, VectorType &y, std::vector< VectorType > &f_stages) |
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| void | newton_solve (const std::function< void(const VectorType &, VectorType &)> &get_residual, const std::function< VectorType(const VectorType &)> &id_minus_tau_J_inverse, VectorType &y) |
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| void | compute_residual (const std::function< VectorType(const double, const VectorType &)> &f, double t, double delta_t, const VectorType &new_y, const VectorType &y, VectorType &tendency, VectorType &residual) const |
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template<typename VectorType>
class TimeStepping::ImplicitRungeKutta< VectorType >
This class is derived from RungeKutta and implement the implicit methods. This class works only for Diagonal Implicit Runge-Kutta (DIRK) methods.
Definition at line 528 of file time_stepping.h.
template<typename VectorType >
| double TimeStepping::ImplicitRungeKutta< VectorType >::evolve_one_time_step |
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const std::function< VectorType(const double, const VectorType &)> & |
f, |
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const std::function< VectorType(const double, const double, const VectorType &)> & |
id_minus_tau_J_inverse, |
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double |
t, |
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double |
delta_t, |
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VectorType & |
y |
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overridevirtual |
This function is used to advance from time t to t+ delta_t. f is the function \( f(t,y) \) that should be integrated, the input parameters are the time t and the vector y and the output is value of f at this point. id_minus_tau_J_inverse is a function that computes \(
(I-\tau J)^{-1}\) where \( I \) is the identity matrix, \( \tau \) is given, and \( J \) is the Jacobian \( \frac{\partial J}{\partial y} \). The input parameters this function receives are the time, \( \tau \), and a vector. The output is the value of function at this point. evolve_one_time_step returns the time at the end of the time step.
Implements TimeStepping::RungeKutta< VectorType >.
template<typename VectorType >
| double TimeStepping::RungeKutta< VectorType >::evolve_one_time_step |
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std::vector< std::function< VectorType(const double, const VectorType &)> > & |
F, |
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std::vector< std::function< VectorType(const double, const double, const VectorType &)> > & |
J_inverse, |
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double |
t, |
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double |
delta_t, |
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VectorType & |
y |
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overridevirtualinherited |
This function is used to advance from time t to t+ delta_t. F is a vector of functions \( f(t,y) \) that should be integrated, the input parameters are the time t and the vector y and the output is value of f at this point. J_inverse is a vector functions that compute the inverse of the Jacobians associated to the implicit problems. The input parameters are the time, \( \tau \), and a vector. The output is the value of function at this point. This function returns the time at the end of the time step. When using Runge-Kutta methods, F and @ J_inverse can only contain one element.
Implements TimeStepping::TimeStepping< VectorType >.
1.9.4