The Combined Spaces Material Group

Combined Spaces Materials

The TPZMatCombinedSpacesT interface is dedicated for implementing weak formulations using a combination approximation spaces. Any given material using only one approximation space should then inherit from TPZMatBase<TPZMatCombinedSpacesT<TVar>, AnyInterfaces>. As an example of a combined spaces material, check TPZWaveguideModalAnalysis.

class TPZMatCombinedSpaces : public virtual TPZSavable

This class is a fundamental part of the TPZMaterial group.

It contains the type-agnostic interfaces that multiphysics materials should implement.

Subclassed by TPZMatCombinedSpacesT< STATE >, TPZMatCombinedSpacesT< TVar >

Public Functions

TPZMatCombinedSpaces() = default

Default constructor.

virtual int IntegrationRuleOrder(const TPZVec<int> &elPMaxOrder) const = 0

Gets the order of the integration rule necessary to integrate an element with polynomial order p taking the forcing function order into account.

Parameters

elPMaxOrder – [in] maximum element order for each space

Returns

adjusted integration rule order

virtual int ClassId() const override

Unique identifier for each class.

template<class TVar>
class TPZMatCombinedSpacesT : public TPZMatCombinedSpaces

This class is a fundamental part of the TPZMaterial group.

It contains the interfaces that multiphysics materials should implement. It is noteworthy to observe that this definition does not depend on the definition of the approximation spaces.

Note

Materials should derive from TPZMatBase class.

tparam TVar

State variable type (CSTATE/STATE)

Subclassed by TPZMatCombinedSpacesBC< TVar >

Contribute

virtual void Contribute(const TPZVec<TPZMaterialDataT<TVar>> &datavec, REAL weight, TPZFMatrix<TVar> &ek, TPZFMatrix<TVar> &ef) = 0

It computes a contribution to the stiffness matrix and load vector at one integration point.

Parameters

  • datavec – [in] stores all input data

  • weight – [in] is the weight of the integration rule

  • ek – [out] is the element matrix

  • ef – [out] is the rhs vector

virtual void Contribute(const TPZVec<TPZMaterialDataT<TVar>> &datavec, REAL weight, TPZFMatrix<TVar> &ef)

It computes a contribution to the residual vector at one integration point.

Parameters

  • datavec – [in] stores all input data

  • weight – [in] is the weight of the integration rule

  • ef – [out] is the residual vector

ContributeBC

virtual void ContributeBC(const TPZVec<TPZMaterialDataT<TVar>> &datavec, REAL weight, TPZFMatrix<TVar> &ek, TPZFMatrix<TVar> &ef, TPZBndCondT<TVar> &bc) = 0

It computes a contribution to the stiffness matrix and load vector at one BC integration point.

Parameters

  • datavec – [in] stores all input data

  • weight – [in] is the weight of the integration rule

  • ek – [out] is the element matrix

  • ef – [out] is the rhs vector

  • bc – [in] is the boundary condition material

virtual void ContributeBC(const TPZVec<TPZMaterialDataT<TVar>> &datavec, REAL weight, TPZFMatrix<TVar> &ef, TPZBndCondT<TVar> &bc)

It computes a contribution to the stiffness matrix and load vector at one BC integration point.

Parameters

  • datavec – [in] stores all input data

  • weight – [in] is the weight of the integration rule

  • ef – [out] is the rhs vector

  • bc – [in] is the boundary condition material

Public Functions

TPZMatCombinedSpacesT() = default

Default constructor.

virtual void FillDataRequirements(TPZVec<TPZMaterialDataT<TVar>> &datavec) const

Fill material data parameter with necessary requirements for the Contribute method.

Here, in base class, all requirements are considered as not necessary.

virtual void FillDataRequirements(std::map<int, TPZMaterialDataT<TVar>> &datavec) const

Fill material data parameter with necessary requirements for the Contribute method.

Here, in base class, all requirements are considered as not necessary.

virtual void FillBoundaryConditionDataRequirements(int type, TPZVec<TPZMaterialDataT<TVar>> &datavec) const

This method defines which parameters need to be initialized in order to compute the contribution of the boundary condition.

virtual void Solution(const TPZVec<TPZMaterialDataT<TVar>> &datavec, int var, TPZVec<TVar> &sol) = 0

Returns the solution associated with a given index based on the finite element approximation.

Parameters

  • datavec – [in] Stores all the input data.

  • var – [in] Index of the queried solution

  • sol – [out] FEM Solution at the integration point

virtual int IntegrationRuleOrder(const TPZVec<int> &elPMaxOrder) const override

Gets the order of the integration rule necessary to integrate an element with polynomial order p taking the forcing function order into account.

Parameters

elPMaxOrder – [in] maximum element order for each space

Returns

adjusted integration rule order

virtual int ClassId() const override

Unique identifier for each class.

Combined Spaces Boundary Conditions

As discussed in Material Interfaces, each interface shall also define a boundary condition counterpart. In this case, it is the TPZMatCombinedSpacesBC. This class mostly forwards any TPZMatCombinedSpacesBC::Contribute calls to the appropriate TPZMatCombinedSpacesT::ContributeBC.

template<class TVar>
class TPZMatCombinedSpacesBC : public TPZMatCombinedSpacesT<TVar>

Boundary condition interface for TPZMatCombinedSpacesT.

Public Functions

TPZMatCombinedSpacesBC() = default

Default constructor.

virtual void Contribute(const TPZVec<TPZMaterialDataT<TVar>> &datavec, REAL weight, TPZFMatrix<TVar> &ek, TPZFMatrix<TVar> &ef) override

Forward the call to TPZMatCombinedSpacesT::ContributeBC.

virtual void Contribute(const TPZVec<TPZMaterialDataT<TVar>> &datavec, REAL weight, TPZFMatrix<TVar> &ef) override

Forward the call to TPZMatCombinedSpacesT::ContributeBC.

virtual void ContributeBC(const TPZVec<TPZMaterialDataT<TVar>> &datavec, REAL weight, TPZFMatrix<TVar> &ek, TPZFMatrix<TVar> &ef, TPZBndCondT<TVar> &bc) override

This method should never be called.

Throws.

virtual void Solution(const TPZVec<TPZMaterialDataT<TVar>> &datavec, int var, TPZVec<TVar> &sol) override

This method should never be called.

Throws.

virtual void FillDataRequirements(TPZVec<TPZMaterialDataT<TVar>> &datavec) const override

Fill material data parameter with necessary requirements for the Contribute method.

Here, in base class, all requirements are considered as not necessary.

virtual int ClassId() const override

Unique identifier for each class.

Protected Attributes

TPZMatCombinedSpacesT<TVar> *fMatCombinedSpaces = {nullptr}

Pointer to material which created this BC.

Available Interfaces

Interface

Interface for discontinuous materials

template<class TVar>
class TPZMatInterfaceCombinedSpaces : public virtual TPZSavable

Interface for discontinuous materials using combined approximation spaces.

This material allows contribution of the FEM matrix using the interface between elements. It should be used as a template parameter of TPZMatBase.

Subclassed by TPZMatInterfaceCombinedSpacesBC< TVar >

Interface

virtual int GetIntegrationOrder(const TPZVec<int> &porder_left, const TPZVec<int> &porder_right) const

returns the integration order as a function of interpolation orders of the left and right elements

virtual void ContributeInterface(const TPZMaterialDataT<TVar> &data, const std::map<int, TPZMaterialDataT<TVar>> &dataleft, const std::map<int, TPZMaterialDataT<TVar>> &dataright, REAL weight, TPZFMatrix<TVar> &ek, TPZFMatrix<TVar> &ef) = 0

Computes a contribution to the stiffness matrix and load vector at one integration point to multiphysics simulation.

Since

June 5, 2012

Parameters

  • data – [in]

  • dataleft – [in]

  • dataright – [in]

  • weight – [in]

  • ek – [out] is the stiffness matrix

  • ef – [out] is the load vector

virtual void ContributeInterface(const TPZMaterialDataT<TVar> &data, const std::map<int, TPZMaterialDataT<TVar>> &dataleft, const std::map<int, TPZMaterialDataT<TVar>> &dataright, REAL weight, TPZFMatrix<TVar> &ef)

Computes a contribution to residual vector at one integration point.

Since

June 5, 2012

Parameters

  • data – [in]

  • dataleft – [in]

  • dataright – [in]

  • weight – [in]

  • ef – [out] is the load vector

virtual void ContributeBCInterface(const TPZMaterialDataT<TVar> &data, const std::map<int, TPZMaterialDataT<TVar>> &dataleft, REAL weight, TPZFMatrix<TVar> &ek, TPZFMatrix<TVar> &ef, TPZBndCondT<TVar> &bc) = 0

It computes a contribution to stiffness matrix and load vector at one BC integration point to multiphysics simulation.

Since

February 21, 2013

Parameters

  • data – [in]

  • dataleft – [in]

  • weight – [in]

  • ek – [out] is the stiffness matrix

  • ef – [out] is the load vector

  • bc – [in] is the boundary condition object

virtual void ContributeBCInterface(const TPZMaterialDataT<TVar> &data, const std::map<int, TPZMaterialDataT<TVar>> &dataleft, REAL weight, TPZFMatrix<TVar> &ef, TPZBndCondT<TVar> &bc)

It computes a contribution to the load vector at one BC integration point to multiphysics simulation.

Since

February 21, 2013

Parameters

  • data – [in]

  • dataleft – [in]

  • weight – [in]

  • ef – [out] is the load vector

  • bc – [in] is the boundary condition object

virtual void FillDataRequirementsInterface(TPZMaterialDataT<TVar> &data, std::map<int, TPZMaterialDataT<TVar>> &datavec_left, std::map<int, TPZMaterialDataT<TVar>> &datavec_right) = 0

This method defines which parameters need to be initialized in order to compute the contribution of interface elements.

virtual void SolutionInterface(const TPZMaterialDataT<TVar> &data, const std::map<int, TPZMaterialDataT<TVar>> &dataleftvec, const std::map<int, TPZMaterialDataT<TVar>> &datarightvec, int var, TPZVec<TVar> &Solout) = 0

Returns the solution associated with the var index based on the finite element approximation around one interface element.

virtual void SolutionInterface(const TPZMaterialDataT<TVar> &data, const std::map<int, TPZMaterialDataT<TVar>> &dataleftvec, const std::map<int, TPZMaterialDataT<TVar>> &datarightvec, int var, TPZVec<TVar> &Solout, TPZCompEl *left, TPZCompEl *right) = 0

Returns the solution associated with the var index based on the finite element approximation around one interface element.

Error

Interface for computing the error of the FEM solution based on an exact solution.

template<class TVar>
class TPZMatErrorCombinedSpaces : public virtual TPZMatError<TVar>

Interface for error computation of materials using combined approximation spaces.

This material allows the computation of error measures of the FEM approximation based on an exact solution. It should be used as a template parameter of TPZMatBase.

Subclassed by TPZMatErrorCombinedSpacesBC< TVar >

Error

virtual void Errors(const TPZVec<TPZMaterialDataT<TVar>> &data, TPZVec<REAL> &errors) = 0

Calculates the error at a given point x.

Parameters

  • datavec – [in] input data

  • errors – [out] The calculated errors.

Common

See also the Common Interfaces.