BiLinearFormsIntegrators.hpp File Reference

Bilinear forms integrators for finite element assembly. More...

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Classes
struct	MoFEM::FormsIntegrators< EleOp >::Assembly< A >
	Bilinear integrator form. More...

Namespaces
namespace	MoFEM
	implementation of Data Operators for Forces and Sources

Detailed Description

Bilinear forms integrators for finite element assembly.

This file provides template aliases for bilinear form integrators used in finite element assembly. Bilinear forms represent the system matrices (left-hand side) in finite element formulations through the mathematical expression \((u, v)_\Omega\), where \(u\) and \(v\) are trial and test functions respectively.

The integrators encompass fundamental finite element operations:

• Gradient operators: \((v_{,i}, u_{,j})_\Omega\) for diffusion and elasticity
• Mass matrices: \((v, u)_\Omega\) for dynamic and parabolic problems
• Mixed formulations: Coupling different field types for constrained problems
• Tensor operations: Anisotropic material behavior with full tensor coupling
• Hybridization: Interface constraints for discontinuous Galerkin methods

All template aliases reference concrete implementations in BiLinearFormsIntegratorsImpl.hpp, providing a clean interface while maintaining computational efficiency. The operators support various coordinate systems, field dimensions, and specializations for different problem types in computational mechanics and multi-physics simulations.

Todo:

Some operators could be optimized. To do that, we need to write tests and use Valgrind to profile code, checking cache misses. For example, some operators should have iteration first over columns, then rows for optimal memory access patterns. Since these operators are used in many problems, implementation efficiency is critical for overall performance.

Definition in file BiLinearFormsIntegrators.hpp.