mfem::WhiteGaussianNoiseDomainLFIntegrator Class Reference

#include <lininteg.hpp>

Inheritance diagram for mfem::WhiteGaussianNoiseDomainLFIntegrator:

Collaboration diagram for mfem::WhiteGaussianNoiseDomainLFIntegrator:

Public Member Functions
	WhiteGaussianNoiseDomainLFIntegrator (int seed_=0)
	Sets the seed_ of the random number generator. A fixed seed allows for a reproducible sequence of white noise vectors.
	WhiteGaussianNoiseDomainLFIntegrator (MPI_Comm comm_, int seed_)
	Sets the MPI communicator comm_ and the seed_ of the random number generator. A fixed seed allows for a reproducible sequence of white noise vectors.
	WhiteGaussianNoiseDomainLFIntegrator (int seed_=0)
	Sets the seed_ of the random number generator. A fixed seed allows for a reproducible sequence of white noise vectors.
void	SetSeed (int seed)
	Sets/resets the seed of the random number generator.
void	AssembleRHSElementVect (const FiniteElement &el, ElementTransformation &Tr, Vector &elvect) override
void	SaveFactors (int NE)
	Saves the lower triangular matrices in the element-wise Cholesky decomposition. The parameter NE should be the number of elements in the mesh.
void	ResetFactors (int NE)
	Resets the array of saved lower triangular Cholesky decomposition matrices. The parameter NE should be the number of elements in the mesh.
	~WhiteGaussianNoiseDomainLFIntegrator ()
virtual void	AssembleRHSElementVect (const FiniteElement &el, FaceElementTransformations &Tr, Vector &elvect)
virtual void	AssembleRHSElementVect (const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Tr, Vector &elvect)
Public Member Functions inherited from mfem::LinearFormIntegrator
virtual bool	SupportsDevice () const
	Method probing for assembly on device.
virtual void	AssembleDevice (const FiniteElementSpace &fes, const Array< int > &markers, Vector &b)
	Method defining assembly on device.
virtual	~LinearFormIntegrator ()
Public Member Functions inherited from mfem::Integrator
	Integrator (const IntegrationRule *ir=NULL)
	Create a new Integrator, optionally providing a prescribed quadrature rule to use in assembly.
virtual void	SetIntRule (const IntegrationRule *ir)
	Prescribe a fixed IntegrationRule to use, or set to null to let the integrator choose an appropriate rule.
void	SetIntegrationRule (const IntegrationRule &ir)
	Prescribe a fixed IntegrationRule to use. Sets the NURBS patch integration rule to null.
void	SetNURBSPatchIntRule (NURBSMeshRules *pr)
	Sets an integration rule for use on NURBS patches.
bool	HasNURBSPatchIntRule () const
	Check if a NURBS patch integration rule has been set.
const IntegrationRule *	GetIntRule () const
	Directly return the IntRule pointer (possibly null) without checking for NURBS patch rules or falling back on a default.
const IntegrationRule *	GetIntegrationRule () const
	Equivalent to GetIntRule, but retained for backward compatibility with applications.

Additional Inherited Members
Protected Member Functions inherited from mfem::LinearFormIntegrator
	LinearFormIntegrator (const IntegrationRule *ir=NULL)
Protected Member Functions inherited from mfem::Integrator
const IntegrationRule *	GetIntegrationRule (const FiniteElement &trial_fe, const FiniteElement &test_fe, const ElementTransformation &trans) const
	Returns an integration rule based on the arguments and internal state of the Integrator object.
const IntegrationRule *	GetIntegrationRule (const FiniteElement &el, const ElementTransformation &trans) const
	Returns an integration rule based on the arguments and internal state. (Version for identical trial_fe and test_fe)
virtual const IntegrationRule *	GetDefaultIntegrationRule (const FiniteElement &trial_fe, const FiniteElement &test_fe, const ElementTransformation &trans) const
	Subclasses should override to choose a default integration rule.
Protected Attributes inherited from mfem::Integrator
const IntegrationRule *	IntRule
NURBSMeshRules *	patchRules = nullptr

Detailed Description

Class for spatial white Gaussian noise integration.

The target problem is the linear SPDE \( a(u,v) = F(v)\) with \(F(v) := <\dot{W},v> \), where \(\dot{W}\) is spatial white Gaussian noise. When the Galerkin method is used to discretize this problem into a linear system of equations \(Ax = b\), the RHS is a Gaussian random vector \(b \sim N(0,M)\) whose covariance matrix is the same as the mass matrix \(M_{ij} = (v_i,v_j)\). This property can be ensured if \(b = H w\), where \(HH^{\mathrm{T}} = M\) and each component \(w_i\sim N(0,1)\).

There is much flexibility in how we may wish to define \(H\). In this PR, we define \(H = P^{\mathrm{T}} diag(L_e)\), where \(P\) is the local-to-global dof assembly matrix and \(\mathrm{diag}(L_e)\) is a block-diagonal matrix with \(L_e L_e^{\mathrm{T}} = M_e\), where \(M_e\) is the element mass matrix for element \(e\). A straightforward computation shows that \(HH^{\mathrm{T}} = P^{\mathrm{T}} diag(M_e) P = M\), as necessary.

Definition at line 643 of file lininteg.hpp.

Constructor & Destructor Documentation

WhiteGaussianNoiseDomainLFIntegrator() [1/3]

mfem::WhiteGaussianNoiseDomainLFIntegrator::WhiteGaussianNoiseDomainLFIntegrator ( int seed_ = 0 )

inline

Sets the seed_ of the random number generator. A fixed seed allows for a reproducible sequence of white noise vectors.

Definition at line 661 of file lininteg.hpp.

WhiteGaussianNoiseDomainLFIntegrator() [2/3]

mfem::WhiteGaussianNoiseDomainLFIntegrator::WhiteGaussianNoiseDomainLFIntegrator ( MPI_Comm comm_, int seed_ )

inline

Sets the MPI communicator comm_ and the seed_ of the random number generator. A fixed seed allows for a reproducible sequence of white noise vectors.

Definition at line 670 of file lininteg.hpp.

WhiteGaussianNoiseDomainLFIntegrator() [3/3]

mfem::WhiteGaussianNoiseDomainLFIntegrator::WhiteGaussianNoiseDomainLFIntegrator ( int seed_ = 0 )

inline

Sets the seed_ of the random number generator. A fixed seed allows for a reproducible sequence of white noise vectors.

Definition at line 682 of file lininteg.hpp.

~WhiteGaussianNoiseDomainLFIntegrator()

mfem::WhiteGaussianNoiseDomainLFIntegrator::~WhiteGaussianNoiseDomainLFIntegrator ( )

inline

Definition at line 726 of file lininteg.hpp.

Member Function Documentation

AssembleRHSElementVect() [1/3]

void mfem::WhiteGaussianNoiseDomainLFIntegrator::AssembleRHSElementVect ( const FiniteElement & el, ElementTransformation & Tr, Vector & elvect )

overridevirtual

Given a particular Finite Element and a transformation (Tr) computes the element vector, elvect.

Implements mfem::LinearFormIntegrator.

Definition at line 1039 of file lininteg.cpp.

AssembleRHSElementVect() [2/3]

void mfem::LinearFormIntegrator::AssembleRHSElementVect ( const FiniteElement & el, FaceElementTransformations & Tr, Vector & elvect )

virtual

Reimplemented from mfem::LinearFormIntegrator.

Definition at line 46 of file lininteg.cpp.

AssembleRHSElementVect() [3/3]

void mfem::LinearFormIntegrator::AssembleRHSElementVect ( const FiniteElement & el1, const FiniteElement & el2, FaceElementTransformations & Tr, Vector & elvect )

virtual

Reimplemented from mfem::LinearFormIntegrator.

Definition at line 49 of file lininteg.cpp.

ResetFactors()

void mfem::WhiteGaussianNoiseDomainLFIntegrator::ResetFactors ( int NE )

inline

Resets the array of saved lower triangular Cholesky decomposition matrices. The parameter NE should be the number of elements in the mesh.

Definition at line 711 of file lininteg.hpp.

SaveFactors()

void mfem::WhiteGaussianNoiseDomainLFIntegrator::SaveFactors ( int NE )

inline

Saves the lower triangular matrices in the element-wise Cholesky decomposition. The parameter NE should be the number of elements in the mesh.

Definition at line 702 of file lininteg.hpp.

SetSeed()

void mfem::WhiteGaussianNoiseDomainLFIntegrator::SetSeed ( int seed )

inline

Sets/resets the seed of the random number generator.

Definition at line 689 of file lininteg.hpp.

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The documentation for this class was generated from the following files:

• fem/lininteg.hpp
• fem/lininteg.cpp