TrialFunction

Represents a function which belongs to a trial space.

Defined in Rodin/Variational/TrialFunction.h

template <
  class Solution,
  class FES>
class TrialFunction;

Template parameters
FES	Type of finite element space

Trial function (unknown solution) in a finite element space.

In the weak formulation of a partial differential equation, the trial function represents the unknown solution being sought. Given a finite element space , the trial function is the function to be determined by solving the variational problem.

Mathematical Foundation

The weak formulation seeks such that:

where:

is the trial function (unknown)
is a test function
is a bilinear form
is a linear functional
is the trial space

The TrialFunction internally manages a GridFunction that stores the degrees of freedom of the solution after the problem is solved.

Usage Example

P1 Uh(mesh);                    // Define finite element space
TrialFunction u(Uh);             // Define trial function
TestFunction v(Uh);              // Define test function

// Define problem
Problem problem(u, v);
problem = Integral(Grad(u), Grad(v)) - Integral(f, v);

// Solve
problem.solve(solver);

// Access solution
auto& solution = u.getSolution();

Direct inheritance by class family

TrialFunctionReference

↓

TrialFunction

↓

PETSc::Variational::TrialFunction

Inherits from

Base class	Responsibility
`TrialFunctionReference<Solution, FES>`public Full type TrialFunctionReference< Solution, FES >	Reference wrapper for trial functions.

Derived classes

Derived class	Description
`PETSc::Variational::TrialFunction<Solution, …>`public Full type PETSc::Variational::TrialFunction< Solution, FES >	PETSc-aware trial function wrapper.

Inherited interface

Declared in	Members
`TrialFunctionReference`	6 members `copy()` `getBasis()` `getIntegrationPoint()` `setIntegrationPoint()` `setPolytope()` `SpaceType`

Public types

using FESType = FES: Finite element space type.
using SolutionType = Solution: Solution grid function type.
using Parent = TrialFunctionReference<SolutionType, FESType>: Parent class type.

Public static variables

static ShapeFunctionSpaceType Space constexpr: Space type (trial space).

Constructors, destructors, conversion operators

TrialFunction(const FES& fes) constexpr: Constructs a trial function in the given finite element space.
TrialFunction(const TrialFunction& other) constexpr: Copy constructor.
TrialFunction(TrialFunction&& other) constexpr: Move constructor.

Public functions

void operator=(const TrialFunction& other) deleted: Copy assignment is deleted.
void operator=(TrialFunction&& other) deleted: Move assignment is deleted.
auto x() const -> auto constexpr: Gets the x-component of a vector-valued trial function.
auto y() const -> auto constexpr: Gets the y-component of a vector-valued trial function.
auto z() const -> auto constexpr: Gets the z-component of a vector-valued trial function.
auto getLeaf() const -> const TrialFunction& constexpr: Gets the leaf (innermost) expression in the shape function tree.
auto getSolution() -> SolutionType& constexpr: Gets the solution grid function (mutable).
auto getSolution() const -> const SolutionType& constexpr: Gets the solution grid function (const).
auto setName(const std::string& name) -> TrialFunction&: Sets the name of the field.
auto getName() const -> Optional<StringView> override: Gets the name of the field.

Function documentation

TrialFunction(const FES& fes) constexpr

Constructs a trial function in the given finite element space.

Parameters
fes in	Finite element space

Creates a trial function with an associated solution grid function initialized to zero.

TrialFunction(const TrialFunction& other) constexpr

Copy constructor.

Parameters
other in	Trial function to copy

TrialFunction(TrialFunction&& other) constexpr

Move constructor.

Parameters
other in	Trial function to move

void operator=(const TrialFunction& other) deleted

Copy assignment is deleted.

Parameters
other	Object to copy from.

void operator=(TrialFunction&& other) deleted

Move assignment is deleted.

Parameters
other	Object to move from.

auto x() const constexpr

Gets the x-component of a vector-valued trial function.

Returns	Component expression representing

auto y() const constexpr

Gets the y-component of a vector-valued trial function.

Returns	Component expression representing

auto z() const constexpr

Gets the z-component of a vector-valued trial function.

Returns	Component expression representing

const TrialFunction& getLeaf() const constexpr

Gets the leaf (innermost) expression in the shape function tree.

Returns	Reference to this trial function

SolutionType& getSolution() constexpr

Gets the solution grid function (mutable).

Returns	Reference to the solution

The solution grid function stores the degrees of freedom of the computed solution after solving the variational problem.

const SolutionType& getSolution() const constexpr

Gets the solution grid function (const).

Returns	Const reference to the solution

TrialFunction& setName(const std::string& name)

Sets the name of the field.

Parameters
name	Name of the object.
Returns	Reference to this object after the operation.

Optional<StringView> getName() const override

Gets the name of the field.

Returns	The name of the field.