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.
virtual void	AssembleRHSElementVect (const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
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 void	SetIntRule (const IntegrationRule *ir)
const IntegrationRule *	GetIntRule ()
virtual	~LinearFormIntegrator ()

Additional Inherited Members
Protected Member Functions inherited from mfem::LinearFormIntegrator
	LinearFormIntegrator (const IntegrationRule *ir=NULL)
Protected Attributes inherited from mfem::LinearFormIntegrator
const IntegrationRule *	IntRule

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 $b=Hw$, where $H{H}^{\mathrm{T}}=M$ 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 $H{H}^{\mathrm{T}}=P^{\mathrm{T}}diag(M_e)P=M$, as necessary.

Definition at line 627 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 645 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 654 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 666 of file lininteg.hpp.

~WhiteGaussianNoiseDomainLFIntegrator()

mfem::WhiteGaussianNoiseDomainLFIntegrator::~WhiteGaussianNoiseDomainLFIntegrator ( )

inline

Definition at line 710 of file lininteg.hpp.

Member Function Documentation

AssembleRHSElementVect() [1/3]

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

virtual

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

Implements mfem::LinearFormIntegrator.

Definition at line 1005 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 695 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 686 of file lininteg.hpp.

SetSeed()

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

inline

Sets/resets the seed of the random number generator.

Definition at line 673 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