MFEM  v4.2.0
Finite element discretization library
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Pages
Public Member Functions | Static Protected Member Functions | Protected Attributes | List of all members
mfem::DGElasticityIntegrator Class Reference

#include <bilininteg.hpp>

Inheritance diagram for mfem::DGElasticityIntegrator:
[legend]
Collaboration diagram for mfem::DGElasticityIntegrator:
[legend]

Public Member Functions

 DGElasticityIntegrator (double alpha_, double kappa_)
 
 DGElasticityIntegrator (Coefficient &lambda_, Coefficient &mu_, double alpha_, double kappa_)
 
virtual void AssembleFaceMatrix (const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Trans, DenseMatrix &elmat)
 
- Public Member Functions inherited from mfem::BilinearFormIntegrator
virtual void AssemblePA (const FiniteElementSpace &fes)
 Method defining partial assembly. More...
 
virtual void AssemblePA (const FiniteElementSpace &trial_fes, const FiniteElementSpace &test_fes)
 
virtual void AssemblePAInteriorFaces (const FiniteElementSpace &fes)
 
virtual void AssemblePABoundaryFaces (const FiniteElementSpace &fes)
 
virtual void AssembleDiagonalPA (Vector &diag)
 Assemble diagonal and add it to Vector diag. More...
 
virtual void AssembleDiagonalPA_ADAt (const Vector &D, Vector &diag)
 Assemble diagonal of ADA^T (A is this integrator) and add it to diag. More...
 
virtual void AddMultPA (const Vector &x, Vector &y) const
 Method for partially assembled action. More...
 
virtual void AddMultTransposePA (const Vector &x, Vector &y) const
 Method for partially assembled transposed action. More...
 
virtual void AssembleEA (const FiniteElementSpace &fes, Vector &emat, const bool add=true)
 Method defining element assembly. More...
 
virtual void AssembleMF (const FiniteElementSpace &fes)
 Method defining matrix-free assembly. More...
 
virtual void AddMultMF (const Vector &x, Vector &y) const
 
virtual void AddMultTransposeMF (const Vector &x, Vector &y) const
 
virtual void AssembleDiagonalMF (Vector &diag)
 Assemble diagonal and add it to Vector diag. More...
 
virtual void AssembleEAInteriorFaces (const FiniteElementSpace &fes, Vector &ea_data_int, Vector &ea_data_ext, const bool add=true)
 
virtual void AssembleEABoundaryFaces (const FiniteElementSpace &fes, Vector &ea_data_bdr, const bool add=true)
 
virtual void AssembleElementMatrix (const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
 Given a particular Finite Element computes the element matrix elmat. More...
 
virtual void AssembleElementMatrix2 (const FiniteElement &trial_fe, const FiniteElement &test_fe, ElementTransformation &Trans, DenseMatrix &elmat)
 
virtual void AssembleFaceMatrix (const FiniteElement &trial_face_fe, const FiniteElement &test_fe1, const FiniteElement &test_fe2, FaceElementTransformations &Trans, DenseMatrix &elmat)
 
virtual void AssembleElementVector (const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun, Vector &elvect)
 Perform the local action of the BilinearFormIntegrator. Note that the default implementation in the base class is general but not efficient. More...
 
virtual void AssembleFaceVector (const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Tr, const Vector &elfun, Vector &elvect)
 Perform the local action of the BilinearFormIntegrator resulting from a face integral term. Note that the default implementation in the base class is general but not efficient. More...
 
virtual void AssembleElementGrad (const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun, DenseMatrix &elmat)
 Assemble the local gradient matrix. More...
 
virtual void AssembleFaceGrad (const FiniteElement &el1, const FiniteElement &el2, FaceElementTransformations &Tr, const Vector &elfun, DenseMatrix &elmat)
 Assemble the local action of the gradient of the NonlinearFormIntegrator resulting from a face integral term. More...
 
virtual void ComputeElementFlux (const FiniteElement &el, ElementTransformation &Trans, Vector &u, const FiniteElement &fluxelem, Vector &flux, bool with_coef=true)
 Virtual method required for Zienkiewicz-Zhu type error estimators. More...
 
virtual double ComputeFluxEnergy (const FiniteElement &fluxelem, ElementTransformation &Trans, Vector &flux, Vector *d_energy=NULL)
 Virtual method required for Zienkiewicz-Zhu type error estimators. More...
 
virtual ~BilinearFormIntegrator ()
 
- Public Member Functions inherited from mfem::NonlinearFormIntegrator
void SetIntRule (const IntegrationRule *ir)
 Prescribe a fixed IntegrationRule to use (when ir != NULL) or let the integrator choose (when ir == NULL). More...
 
void SetIntegrationRule (const IntegrationRule &irule)
 Prescribe a fixed IntegrationRule to use. More...
 
virtual double GetElementEnergy (const FiniteElement &el, ElementTransformation &Tr, const Vector &elfun)
 Compute the local energy. More...
 
virtual ~NonlinearFormIntegrator ()
 

Static Protected Member Functions

static void AssembleBlock (const int dim, const int row_ndofs, const int col_ndofs, const int row_offset, const int col_offset, const double jmatcoef, const Vector &col_nL, const Vector &col_nM, const Vector &row_shape, const Vector &col_shape, const Vector &col_dshape_dnM, const DenseMatrix &col_dshape, DenseMatrix &elmat, DenseMatrix &jmat)
 

Protected Attributes

Coefficientlambda
 
Coefficientmu
 
double alpha
 
double kappa
 
Vector shape1
 
Vector shape2
 
DenseMatrix dshape1
 
DenseMatrix dshape2
 
DenseMatrix adjJ
 
DenseMatrix dshape1_ps
 
DenseMatrix dshape2_ps
 
Vector nor
 
Vector nL1
 
Vector nL2
 
Vector nM1
 
Vector nM2
 
Vector dshape1_dnM
 
Vector dshape2_dnM
 
DenseMatrix jmat
 
- Protected Attributes inherited from mfem::NonlinearFormIntegrator
const IntegrationRuleIntRule
 

Additional Inherited Members

- Protected Member Functions inherited from mfem::BilinearFormIntegrator
 BilinearFormIntegrator (const IntegrationRule *ir=NULL)
 
- Protected Member Functions inherited from mfem::NonlinearFormIntegrator
 NonlinearFormIntegrator (const IntegrationRule *ir=NULL)
 

Detailed Description

Integrator for the DG elasticity form, for the formulations see:

where \( \left<u, v\right> = \int_{F} u \cdot v \), and \( F \) is a face which is either a boundary face \( F_b \) of an element \( K \) or an interior face \( F_i \) separating elements \( K_1 \) and \( K_2 \).

In the bilinear form above \( \tau(u) \) is traction, and it's also \( \tau(u) = \sigma(u) \cdot \vec{n} \), where \( \sigma(u) \) is stress, and \( \vec{n} \) is the unit normal vector w.r.t. to \( F \).

In other words, we have

\[ - \left< \{ \sigma(u) \cdot \vec{n} \}, [v] \right> + \alpha \left< \{ \sigma(v) \cdot \vec{n} \}, [u] \right> + \kappa \left< h^{-1} \{ \lambda + 2 \mu \} [u], [v] \right> \]

For isotropic media

\[ \begin{split} \sigma(u) &= \lambda \nabla \cdot u I + 2 \mu \varepsilon(u) \\ &= \lambda \nabla \cdot u I + 2 \mu \frac{1}{2} (\nabla u + \nabla u^T) \\ &= \lambda \nabla \cdot u I + \mu (\nabla u + \nabla u^T) \end{split} \]

where \( I \) is identity matrix, \( \lambda \) and \( \mu \) are Lame coefficients (see ElasticityIntegrator), \( u, v \) are the trial and test functions, respectively.

The parameters \( \alpha \) and \( \kappa \) determine the DG method to use (when this integrator is added to the "broken" ElasticityIntegrator):

This is a 'Vector' integrator, i.e. defined for FE spaces using multiple copies of a scalar FE space.

Definition at line 2815 of file bilininteg.hpp.

Constructor & Destructor Documentation

mfem::DGElasticityIntegrator::DGElasticityIntegrator ( double  alpha_,
double  kappa_ 
)
inline

Definition at line 2818 of file bilininteg.hpp.

mfem::DGElasticityIntegrator::DGElasticityIntegrator ( Coefficient lambda_,
Coefficient mu_,
double  alpha_,
double  kappa_ 
)
inline

Definition at line 2821 of file bilininteg.hpp.

Member Function Documentation

void mfem::DGElasticityIntegrator::AssembleBlock ( const int  dim,
const int  row_ndofs,
const int  col_ndofs,
const int  row_offset,
const int  col_offset,
const double  jmatcoef,
const Vector col_nL,
const Vector col_nM,
const Vector row_shape,
const Vector col_shape,
const Vector col_dshape_dnM,
const DenseMatrix col_dshape,
DenseMatrix elmat,
DenseMatrix jmat 
)
staticprotected

Definition at line 2975 of file bilininteg.cpp.

void mfem::DGElasticityIntegrator::AssembleFaceMatrix ( const FiniteElement el1,
const FiniteElement el2,
FaceElementTransformations Trans,
DenseMatrix elmat 
)
virtual

Reimplemented from mfem::BilinearFormIntegrator.

Definition at line 3018 of file bilininteg.cpp.

Member Data Documentation

DenseMatrix mfem::DGElasticityIntegrator::adjJ
protected

Definition at line 2843 of file bilininteg.hpp.

double mfem::DGElasticityIntegrator::alpha
protected

Definition at line 2833 of file bilininteg.hpp.

DenseMatrix mfem::DGElasticityIntegrator::dshape1
protected

Definition at line 2841 of file bilininteg.hpp.

Vector mfem::DGElasticityIntegrator::dshape1_dnM
protected

Definition at line 2851 of file bilininteg.hpp.

DenseMatrix mfem::DGElasticityIntegrator::dshape1_ps
protected

Definition at line 2847 of file bilininteg.hpp.

DenseMatrix mfem::DGElasticityIntegrator::dshape2
protected

Definition at line 2841 of file bilininteg.hpp.

Vector mfem::DGElasticityIntegrator::dshape2_dnM
protected

Definition at line 2851 of file bilininteg.hpp.

DenseMatrix mfem::DGElasticityIntegrator::dshape2_ps
protected

Definition at line 2847 of file bilininteg.hpp.

DenseMatrix mfem::DGElasticityIntegrator::jmat
protected

Definition at line 2853 of file bilininteg.hpp.

double mfem::DGElasticityIntegrator::kappa
protected

Definition at line 2833 of file bilininteg.hpp.

Coefficient* mfem::DGElasticityIntegrator::lambda
protected

Definition at line 2832 of file bilininteg.hpp.

Coefficient * mfem::DGElasticityIntegrator::mu
protected

Definition at line 2832 of file bilininteg.hpp.

Vector mfem::DGElasticityIntegrator::nL1
protected

Definition at line 2849 of file bilininteg.hpp.

Vector mfem::DGElasticityIntegrator::nL2
protected

Definition at line 2849 of file bilininteg.hpp.

Vector mfem::DGElasticityIntegrator::nM1
protected

Definition at line 2850 of file bilininteg.hpp.

Vector mfem::DGElasticityIntegrator::nM2
protected

Definition at line 2850 of file bilininteg.hpp.

Vector mfem::DGElasticityIntegrator::nor
protected

Definition at line 2848 of file bilininteg.hpp.

Vector mfem::DGElasticityIntegrator::shape1
protected

Definition at line 2838 of file bilininteg.hpp.

Vector mfem::DGElasticityIntegrator::shape2
protected

Definition at line 2838 of file bilininteg.hpp.


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