Variational Module module

Variational formulations and finite element problem definitions.

The Variational module provides the infrastructure for defining and solving variational problems in finite element analysis. It supports the formulation of linear and nonlinear problems, boundary conditions, and various finite element spaces.

Mathematical Foundation

The module implements the standard finite element methodology:

  • Bilinear Forms: $ a(u,v) : V \times V \to \mathbb{R} $
  • Linear Forms: $ l(v) : V \to \mathbb{R} $
  • Weak Formulation: Find $ u \in V $ such that $ a(u,v) = l(v) $ for all $ v \in V $
  • Discrete System: $ Au = b $ where $ A_{ij} = a(\phi_j, \psi_i) $ and $ b_i = l(\psi_i) $

Classes

template<class Operator>
class Rodin::Variational::BilinearFormBase
Base class for bilinear form representations.
class Rodin::Variational::FiniteElementSpaceBase
Base class for finite element spaces.
template<class Derived>
class Rodin::Variational::FunctionBase
Base class for function objects which can be evaluated over a mesh.
template<class StrictType>
class Rodin::Variational::GridFunctionBaseReference
Base class for discrete finite element functions.
template<class Vector>
class Rodin::Variational::LinearFormBase
Base class for linear form objects.
template<class LinearSystem>
class Rodin::Variational::ProblemBase
Base class for variational problem objects.