PML3DHexa8.hpp

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//==============================================================================
//
//                       Seismo Virtual Laboratory
//             Module for Serial and Parallel Analysis of seismic 
//         wave propagation and soil-structure interaction simulation
//         Copyright (C) 2018-2021, The California Institute of Technology
//                         All Rights Reserved.
//
// Commercial use of this program without express permission of the California
// Institute of Technology, is strictly  prohibited. See  file "COPYRIGHT"  in
// main  directory  for  information on  usage  and  redistribution, and for a
// DISCLAIMER OF ALL WARRANTIES.
//
//==============================================================================
//
// Written by:
//   Danilo S. Kusanovic (dkusanov@caltech.edu)
//   Elnaz E. Seylabi    (elnaze@unr.edu)
//
// Supervised by:
//   Domniki M. Asimaki  (domniki@caltech.edu)
//
// References : 
//  [1] Fathi, A., Poursartip, B., & Kallivokas, L. F. (2015). Time‐domain hybrid 
//      formulations for wave simulations in three‐dimensional PML‐truncated 
//      heterogeneous media. International Journal for Numerical Methods in 
//      Engineering, 101(3), 165-198.
//
// Description:
//------------------------------------------------------------------------------

#ifndef _PML3DHEXA8_HPP_
#define _PML3DHEXA8_HPP_

#include <map>
#include <memory>
#include <string>
#include <Eigen/Dense>

#include "Node.hpp"
#include "Load.hpp"
#include "Material.hpp"
#include "Element.hpp"
#include "QuadratureRule.hpp"
#include "Damping.hpp"

class PML3DHexa8 : public Element{

    public:
        PML3DHexa8(const std::vector<unsigned int> nodes, std::unique_ptr<Material> &material, const std::vector<double> parameters, const std::string quadrature="GAUSS", const unsigned int nGauss=8);

        ~PML3DHexa8();

        void CommitState();

        void ReverseState();

        void InitialState();

        void UpdateState();

        void SetDomain(std::map<unsigned int, std::shared_ptr<Node> > &nodes);

        void SetDamping(const std::shared_ptr<Damping> &damping);

        std::vector<unsigned int> GetTotalDegreeOfFreedom() const;

        Eigen::MatrixXd GetStrain() const;

        Eigen::MatrixXd GetStress() const;

        Eigen::MatrixXd GetStrainRate() const;

        Eigen::MatrixXd GetStrainAt(double x3, double x2) const;

        Eigen::MatrixXd GetStressAt(double x3, double x2) const;

        Eigen::VectorXd GetVTKResponse(std::string response) const;

        double ComputeEnergy();

        Eigen::MatrixXd ComputeMassMatrix();

        Eigen::MatrixXd ComputeStiffnessMatrix();

        Eigen::MatrixXd ComputeDampingMatrix();

        Eigen::MatrixXd ComputePMLMatrix();

        Eigen::VectorXd ComputeInternalForces();

        Eigen::VectorXd ComputeInternalDynamicForces();

        Eigen::VectorXd ComputeSurfaceForces(const std::shared_ptr<Load> &surface, unsigned int face);

        Eigen::VectorXd ComputeBodyForces(const std::shared_ptr<Load> &body, unsigned int k=0);

        Eigen::VectorXd ComputeDomainReductionForces(const std::shared_ptr<Load> &drm, unsigned int k);

    private:
        double m_pml;

        double L_pml;

        double R_pml;

        double x0_pml;

        double y0_pml;

        double z0_pml;

        double nx_pml;

        double ny_pml;

        double nz_pml;

        std::shared_ptr<Damping> theDamping;

        std::vector<std::shared_ptr<Node> > theNodes;

        std::vector<std::unique_ptr<Material> > theMaterial;

        std::unique_ptr<QuadratureRule> QuadraturePoints;

        Eigen::VectorXd ComputeStrain(const Eigen::MatrixXd &Bij) const;

        Eigen::VectorXd ComputeStrainRate(const Eigen::MatrixXd &Bij) const;

        Eigen::MatrixXd ComputeJacobianMatrix(const double ri, const double si, const double ti) const;

        Eigen::MatrixXd ComputeShapeFunctionMatrix(const double ri, const double si, const double ti) const;

        Eigen::MatrixXd ComputeStrainDisplacementMatrix(const double ri, const double si, const double ti, const Eigen::MatrixXd &Jij) const;

        Eigen::VectorXd ComputePMLStretchingFactors(const double ri, const double si, const double ti, const double rho, const double mu, const double lambda) const;
};

#endif