template<class LinearSystem>
Rodin::Variational::ProblemBase class

Base class for variational problem objects.

Template parameters
LinearSystem	Type of linear system (e.g., sparse or dense)

Abstract base class for variational problems.

This class provides the foundation for defining and solving variational problems in finite element analysis. It encapsulates the discrete linear system arising from the weak formulation of PDEs and provides a unified interface for assembly and solution operations.

Usage Example

// Define a problem and solve
auto problem = Problem(trialSpace, testSpace);
problem = bilinearForm == linearForm;
problem.assemble();
problem.solve(solver);

Base classes

class Base: Base class for all objects in Rodin's FormLanguage system.

Derived classes

template<class LinearSystem, class U, class V> class ProblemUVBase: General class to assemble linear systems with Operator and Vector generic types in a sequential context.
template<class LinearSystem, class U, class V> class ProblemUVBase: General class to assemble linear systems with Operator and Vector generic types in a sequential context.
template<class LinearSystem, class U, class V> class ProblemUVBase: General class to assemble linear systems with Operator and Vector generic types in a sequential context.

Public types

using OperatorType = typename FormLanguage::Traits<LinearSystem>::OperatorType: Matrix operator type from linear system traits.
using VectorType = typename FormLanguage::Traits<LinearSystem>::VectorType: Vector type from linear system traits.
using ScalarType = typename FormLanguage::Traits<LinearSystem>::ScalarType: Scalar type from linear system traits
using ProblemBodyType = ProblemBody<OperatorType, VectorType, ScalarType>: Problem body type containing bilinear and linear forms.

Constructors, destructors, conversion operators

ProblemBase() defaulted: Default constructor.
ProblemBase(ProblemBase&& other) defaulted: Move constructor.
ProblemBase(const ProblemBase& other) defaulted: Copy constructor.

Public functions

auto operator=(const ProblemBodyType& rhs) -> ProblemBase& pure virtual: Assigns a problem body to this problem.
void solve(Solver::SolverBase<LinearSystem>& solver) pure virtual: Solves the assembled linear system.
auto assemble() -> ProblemBase& pure virtual: Assembles the underlying linear system to solve.
auto getLinearSystem() -> LinearSystem& pure virtual: Gets the assembled linear system.
auto getLinearSystem() const -> const LinearSystem& pure virtual: Gets the assembled linear system (const version).
auto copy() const -> ProblemBase* override noexcept: Creates a polymorphic copy of this problem.

Function documentation

template<class LinearSystem>
ProblemBase& Rodin::Variational::ProblemBase<LinearSystem>::operator=(const ProblemBodyType& rhs) pure virtual

Assigns a problem body to this problem.

Parameters
rhs	Problem body containing bilinear and linear forms
Returns	Reference to this problem instance

This operator allows setting up the variational problem by assigning a problem body that contains the bilinear form and linear form defining the weak formulation.

template<class LinearSystem>
void Rodin::Variational::ProblemBase<LinearSystem>::solve(Solver::SolverBase<LinearSystem>& solver) pure virtual

Solves the assembled linear system.

Parameters
solver	Solver instance to use for solving the linear system

Solves the discrete system using the provided solver. The problem must be assembled before calling this method.

template<class LinearSystem>
ProblemBase& Rodin::Variational::ProblemBase<LinearSystem>::assemble() pure virtual

Assembles the underlying linear system to solve.

Returns	Reference to this problem instance for method chaining

Assembles the bilinear form into the system matrix and the linear form into the right-hand side vector , creating the discrete linear system .

template<class LinearSystem>
LinearSystem& Rodin::Variational::ProblemBase<LinearSystem>::getLinearSystem() pure virtual

Gets the assembled linear system.

Returns	Reference to the linear system

template<class LinearSystem>
const LinearSystem& Rodin::Variational::ProblemBase<LinearSystem>::getLinearSystem() const pure virtual

Gets the assembled linear system (const version).

Returns	Const reference to the linear system

template<class LinearSystem>
ProblemBase* Rodin::Variational::ProblemBase<LinearSystem>::copy() const override noexcept

Creates a polymorphic copy of this problem.

Returns	Pointer to a new copy of this problem

template<class LinearSystem> Rodin::Variational::ProblemBase class