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HArD::Core3D
Hybrid Arbitrary Degree::Core 3D - Library to implement 3D schemes with vertex, edge, face and cell polynomials as unknowns
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Assemble a YangMills problem. More...
#include <laddr-yangmills-lm.hpp>
Public Types | |
| typedef Eigen::SparseMatrix< double > | SystemMatrixType |
| typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)> | ForcingTermType |
| Base functions. | |
| typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)> | ElectricFieldType |
| typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)> | MagneticFieldType |
| typedef std::function< Eigen::Vector3d(const double &, const Eigen::Vector3d &)> | TForcingTermType |
| Base functions with time component. | |
| typedef std::function< Eigen::Vector3d(const double &, const Eigen::Vector3d &)> | TElectricFieldType |
| typedef std::function< Eigen::Vector3d(const double &, const Eigen::Vector3d &)> | TMagneticFieldType |
| typedef std::vector< ForcingTermType > | LAForcingTermType |
| Lie algebra valued functions (vector of dim Lie algebra) | |
| typedef std::vector< ElectricFieldType > | LAElectricFieldType |
| typedef std::vector< MagneticFieldType > | LAMagneticFieldType |
| typedef std::vector< TForcingTermType > | TLAForcingTermType |
| Lie algebra valued functions with time component. | |
| typedef std::vector< TElectricFieldType > | TLAElectricFieldType |
| typedef std::vector< TMagneticFieldType > | TLAMagneticFieldType |
| typedef Eigen::SparseMatrix< double > | SystemMatrixType |
| typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)> | ForcingTermType |
| Base functions. | |
| typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)> | ElectricFieldType |
| typedef std::function< Eigen::Vector3d(const Eigen::Vector3d &)> | MagneticFieldType |
| typedef std::function< Eigen::Vector3d(const double &, const Eigen::Vector3d &)> | TForcingTermType |
| Base functions with time component. | |
| typedef std::function< Eigen::Vector3d(const double &, const Eigen::Vector3d &)> | TElectricFieldType |
| typedef std::function< Eigen::Vector3d(const double &, const Eigen::Vector3d &)> | TMagneticFieldType |
| typedef std::vector< ForcingTermType > | LAForcingTermType |
| Lie algebra valued functions (vector of dim Lie algebra) | |
| typedef std::vector< ElectricFieldType > | LAElectricFieldType |
| typedef std::vector< MagneticFieldType > | LAMagneticFieldType |
| typedef std::vector< TForcingTermType > | TLAForcingTermType |
| Lie algebra valued functions with time component. | |
| typedef std::vector< TElectricFieldType > | TLAElectricFieldType |
| typedef std::vector< TMagneticFieldType > | TLAMagneticFieldType |
Public Member Functions | |
| YangMills (const DDRCore &ddrcore, const LieAlgebra &liealgebra, bool use_threads, std::ostream &output=std::cout) | |
| Constructor. | |
| void | assembleLinearSystem (double dt) |
| Assemble the global system | |
| void | setSystemVector (const Eigen::VectorXd &interp_f, const Eigen::VectorXd &interp_dE, const Eigen::VectorXd &interp_A, const Eigen::VectorXd &E_old, const Eigen::VectorXd &A_old, double dt, double theta, double nonlinear_coeff) |
| Sets system vector for the nonlinear problem. | |
| void | assembleSystemNewton (const Eigen::VectorXd &E_i, const Eigen::VectorXd &A_i, const Eigen::VectorXd &Elambdac_k, const Eigen::VectorXd &sysVec, double dt, double theta, double nonlinear_coeff) |
| Assembles the system for Newton iterations. | |
| double | stoppingCrit (const Eigen::VectorXd &v, const Eigen::VectorXd &u) |
| Stops once changes become small. | |
| double | stoppingCrit2 (const Eigen::VectorXd &Elambda_k, const Eigen::VectorXd &E_i, const Eigen::VectorXd &A_i, const Eigen::VectorXd &sysVec, double dt, double theta, double nonlinear_coeff) |
| Stops once close enough to system vector for nonlinear problem. | |
| void | addBoundaryConditions (const LAMagneticFieldType &curl_A, double dt) |
| Adds boundary condition for chosen solution to the system vector. | |
| Eigen::VectorXd | computeInitialConditions (const Eigen::MatrixXd &Eh, const Eigen::MatrixXd &Ah, const double nonlinear_coeff, const size_t solver) |
| Computes the projected initial conditions that satisfy the constraint. | |
| Eigen::MatrixXd | epsBkt_v (size_t iT, boost::multi_array< double, 3 > &ebkt_T, const Eigen::VectorXd &v) const |
| Calculates the matrix of *[v,.]^div in element index iT. | |
| Eigen::MatrixXd | L2v_Bkt (size_t iT, boost::multi_array< double, 3 > &intPciPcjPgk, const Eigen::VectorXd &v, const size_t &entry) const |
| Wrapper to plug vector into L2 integral product: int (Pcurl 1,[Pcurl 2, Pgrad 3]) | |
| Eigen::MatrixXd | L2v_epsBkt (size_t iT, boost::multi_array< double, 3 > &ebkt_T, const Eigen::VectorXd &v_T, const Eigen::MatrixXd &L2prod) const |
| Calculates the bracket inside the L2prod with v. | |
| size_t | dimension () const |
| Returns the global problem dimension. | |
| size_t | sizeSystem () const |
| Returns the size of the system. | |
| const LieAlgebra & | lieAlg () const |
| Returns the Lie algebra. | |
| const LAXGrad & | laXGrad () const |
| Returns the space LAXGrad. | |
| const LAXCurl & | laXCurl () const |
| Returns the space LAXCurl. | |
| const LAXDiv & | laXDiv () const |
| Returns the space LAXCurl. | |
| const XGrad & | xGrad () const |
| Returns the space XDiv. | |
| const XCurl & | xCurl () const |
| Returns the space XDiv. | |
| const XDiv & | xDiv () const |
| Returns the space XDiv. | |
| const SystemMatrixType & | systemMatrix () const |
| Returns the linear system matrix. | |
| SystemMatrixType & | systemMatrix () |
| Returns the linear system matrix. | |
| const Eigen::VectorXd & | systemVector () const |
| Returns the linear system right-hand side vector. | |
| Eigen::VectorXd & | systemVector () |
| Returns the linear system right-hand side vector. | |
| const double & | stabilizationParameter () const |
| Returns the stabilization parameter. | |
| double & | stabilizationParameter () |
| Returns the stabilization parameter. | |
| std::vector< YangMillsNorms > | computeYangMillsNorms (const std::vector< Eigen::VectorXd > &list_dofs) const |
| Compute the discrete L2 norms, for a family of Eigen::VectorXd representing the electric field and potential. | |
| template<typename outValue , typename TFct > | |
| std::function< outValue(const Eigen::Vector3d &)> | contractPara (const TFct &F, double t) const |
| Takes a two parameter function and a value and returns a function with the first parameter fixed to value. | |
| template<typename outValue , typename Fct , typename TFct > | |
| std::vector< Fct > | contractParaLA (const std::vector< TFct > &TF, double t) const |
| Takes a vector of two parameter functions and a value and returns a function with the first parameter fixed to value. | |
| double | computeResidual (const Eigen::VectorXd &x) const |
| Calculates residual with current matrix and rhs from given x (m_A*x = m_b) | |
| Eigen::VectorXd | computeConstraint (const Eigen::VectorXd &E, const Eigen::VectorXd &A, const double nonlinear_coeff) |
| Computes the constraint [E, grad P'] + int <E, [A, P']> for the DOFs. | |
| double | computeConstraintNorm (const Eigen::VectorXd &Ch, const size_t itersolver) const |
| Solves a system to calculate the norm of the constraint (in the dual space of LaXgrad) | |
| std::pair< double, double > | computeConditionNum () const |
| YangMills (const DDRCore &ddrcore, const LADDRCore &laddrcore, const LieAlgebra &liealgebra, size_t nonlinear_discretisation, bool use_threads, std::ostream &output=std::cout) | |
| Constructor. | |
| void | assembleLinearSystem (double dt) |
| Assemble the global system | |
| void | setSystemVector (const Eigen::VectorXd &interp_f, const Eigen::VectorXd &interp_dE, const Eigen::VectorXd &interp_A, const Eigen::VectorXd &E_i, const Eigen::VectorXd &A_i, double dt, double theta, double nonlinear_coeff) |
| Sets system vector for the nonlinear problem. | |
| void | assembleSystemNewton (const Eigen::VectorXd &E_i, const Eigen::VectorXd &A_i, const Eigen::VectorXd &Elambda_k, double dt, double theta, double nonlinear_coeff) |
| Assembles the system for Newton iterations. | |
| double | stoppingCrit (const Eigen::VectorXd &v, const Eigen::VectorXd &u) |
| Stops once changes become small. | |
| void | setNonlinearRes (const Eigen::VectorXd &Elambda_k, const Eigen::VectorXd &E_i, const Eigen::VectorXd &A_i, double dt, double theta, double nonlinear_coeff) |
| Sets the nonlinear residual vector b-F(x_k) in m_b_k. | |
| void | addBoundaryConditions (const LAMagneticFieldType &curl_A, double dt) |
| Adds boundary condition for chosen solution to the system vector. | |
| Eigen::VectorXd | computeInitialConditions (const Eigen::MatrixXd &Eh, const Eigen::MatrixXd &Ah, const double nonlinear_coeff, const size_t solver) |
| Computes the projected initial conditions that satisfy the constraint. | |
| std::vector< Eigen::MatrixXd > | epsBkt_v (size_t iT, boost::multi_array< double, 3 > &crossij_Pot_T, const std::vector< Eigen::VectorXd > &vec_list) const |
| std::vector< Eigen::MatrixXd > | L2v_Bkt (size_t iT, boost::multi_array< double, 3 > &intPciPcjPgk, const std::vector< Eigen::VectorXd > &vec_list, const size_t &entry) const |
| Wrapper to plug vector into L2 integral product: int (Pcurl 1,[Pcurl 2, Pgrad 3]) | |
| std::vector< Eigen::MatrixXd > | L2v_epsBkt (size_t iT, boost::multi_array< double, 3 > &crossij_Pot_T, const std::vector< Eigen::VectorXd > &v_L2prod) const |
| size_t | dimensionSpace () const |
| Returns the global problem dimension. | |
| size_t | nbSCDOFs_E () const |
| Returns the number of statically condensed DOFs (Electric field) | |
| size_t | nbSCDOFs_lambda () const |
| Returns the number of statically condensed DOFs (lambda) | |
| size_t | nbSCDOFs () const |
| Returns the number of statically condensed DOFs (both velocity and pressure) | |
| size_t | sizeSystem () const |
| Returns the size of the system. | |
| const LieAlgebra & | lieAlg () const |
| Returns the Lie algebra. | |
| const LASXGrad & | laSXGrad () const |
| Returns the space LAXGrad. | |
| const LASXCurl & | laSXCurl () const |
| Returns the space LAXCurl. | |
| const LASXDiv & | laSXDiv () const |
| Returns the space LAXCurl. | |
| const SXGrad & | xSGrad () const |
| Returns the space XDiv. | |
| const SXCurl & | xSCurl () const |
| Returns the space XDiv. | |
| const SXDiv & | xSDiv () const |
| Returns the space XDiv. | |
| const SystemMatrixType & | systemMatrix () const |
| Returns the linear system matrix. | |
| SystemMatrixType & | systemMatrix () |
| Returns the linear system matrix. | |
| const Eigen::VectorXd & | systemVectorNewton () const |
| Returns the linear system right-hand side vector. | |
| Eigen::VectorXd & | systemVectorNewton () |
| Returns the linear system right-hand side vector. | |
| const Eigen::VectorXd & | systemVector () const |
| Returns the right-hand side to the nonlinear problem. | |
| Eigen::VectorXd & | systemVector () |
| Returns the right-hand side to the nonlinear problem. | |
| const Eigen::VectorXd & | nonlinearRes () const |
| Returns the right-hand side to the nonlinear problem. | |
| Eigen::VectorXd & | nonlinearRes () |
| Returns the right-hand side to the nonlinear problem. | |
| const SystemMatrixType & | scMatrix () const |
| Returns the static condensation recovery operator. | |
| Eigen::VectorXd & | scVector () |
| Returns the static condensation rhs. | |
| const double & | stabilizationParameter () const |
| Returns the stabilization parameter. | |
| double & | stabilizationParameter () |
| Returns the stabilization parameter. | |
| std::vector< YangMillsNorms > | computeYangMillsNorms (const std::vector< Eigen::VectorXd > &list_dofs) const |
| Compute the discrete L2 norms, for a family of Eigen::VectorXd representing the electric field and potential. | |
| template<typename outValue , typename TFct > | |
| std::function< outValue(const Eigen::Vector3d &)> | contractPara (const TFct &F, double t) const |
| Takes a two parameter function and a value and returns a function with the first parameter fixed to value. | |
| template<typename outValue , typename Fct , typename TFct > | |
| std::vector< Fct > | contractParaLA (const std::vector< TFct > &TF, double t) const |
| Takes a vector of two parameter functions and a value and returns a function with the first parameter fixed to value. | |
| double | computeResidual (const Eigen::VectorXd &x) const |
| Calculates residual with current matrix and rhs from given x (m_A*x = m_b) | |
| Eigen::VectorXd | computeConstraint (const Eigen::VectorXd &E, const Eigen::VectorXd &A, const double nonlinear_coeff) |
| Computes the constraint [E, grad P'] + int <E, [A, P']> for the DOFs. | |
| double | computeConstraintNorm (const Eigen::VectorXd &Ch, const size_t itersolver) const |
| Solves a system to calculate the norm of the constraint (in the dual space of LaXgrad) | |
| std::pair< double, double > | computeConditionNum () const |
Assemble a YangMills problem.
1.9.8