Reference documentation for deal.II version GIT relicensing31gf283a0fc39 20240229 06:50:02+00:00

Modules  
The MeshWorker interface  
Namespaces  
namespace  LocalIntegrators 
Library of integrals over cells and faces.  
namespace  LocalIntegrators::Maxwell 
Local integrators related to curl operators and their traces.  
namespace  LocalIntegrators::Advection 
Local integrators related to advection along a vector field and its DG formulations.  
namespace  LocalIntegrators::Elasticity 
Local integrators related to elasticity problems.  
namespace  LocalIntegrators::L2 
Local integrators related to L^{2}inner products.  
namespace  LocalIntegrators::Divergence 
Local integrators related to the divergence operator and its trace.  
namespace  LocalIntegrators::Laplace 
Local integrators related to the Laplacian and its DG formulations.  
namespace  LocalIntegrators::GradDiv 
namespace  MeshWorker 
A collection of namespaces and functions which simplify the coding of forms and bilinear forms on finite element spaces. Functions for two different purposes are gathered here: the abstract integration on finite element meshes in MeshWorker and actual implementations of the integration of cell and face terms for concrete problems in LocalIntegrators.
When we integrate a function or a functional on a finite element space, the structure of the integration loop is always the same. We have between 3 and 5 nested loops, from outside to inside:
These loops naturally fall into two classes, namely the computation of cell and face contributions (loops 3 to 5), and the outer loops over the mesh objects, often referred to as assembling.
Support for the outer loop in deal.II can be found in the namespace MeshWorker (see the documentation there). In order to support the cell and face contributions (referred to as local contributions from now on), deal.II offers FEValuesBase and its derived classes. While the outer loop is generic (with exception of the data types), the computation of local contributions is problem dependent. Therefore, no generic algorithm is possible here. Nevertheless, we can define a generic interface for functions for this purpose and provide a library of local integrators for use in applications. These are collected in the namespace LocalIntegrators