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lammps/lib/atc/FE_Element.cpp

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// ATC header files
#include "ATC_Error.h"
#include "FE_Element.h"
#include "FE_Mesh.h"
// Other headers
#include "math.h"
namespace ATC {
// -------------------------------------------------------------
// -------------------------------------------------------------
// class FE_Element
// -------------------------------------------------------------
// -------------------------------------------------------------
FE_Element::FE_Element(FE_Mesh * feMesh,
int nSD,
int numEltNodes,
int numIPs,
int numFaces,
int numFaceNodes,
int numFaceIPs)
: feMesh_(feMesh),
nSD_(nSD),
numEltNodes_(numEltNodes),
numIPs_(numIPs),
numFaces_(numFaces),
numFaceNodes_(numFaceNodes),
numFaceIPs_(numFaceIPs),
localCoords_(nSD,numEltNodes),
ipCoords_(nSD,numIPs),
N_(numIPs,numEltNodes),
ipWeights_(numIPs),
localFaceConn_(numFaces,numFaceNodes),
ipFace2DCoords_(nSD-1,numFaceIPs),
ipFaceCoords_(numFaces),
// localFaceCoords_(nSD-1,numFaceNodes),
NFace_(numFaces),
ipFaceWeights_(numFaceIPs)
{
for (int f = 0; f < numFaces; f++) {
ipFaceCoords_[f].reset(nSD,numFaceIPs);
NFace_[f].reset(numFaceIPs,numEltNodes);
}
}
FE_Element::~FE_Element()
{
// Nothing else to do
}
// -------------------------------------------------------------
// -------------------------------------------------------------
// class FE_ElementHex
// -------------------------------------------------------------
// -------------------------------------------------------------
FE_ElementHex::FE_ElementHex(FE_Mesh * feMesh)
: FE_Element(feMesh, 3, 8, 8, 6, 4, 4)
{
// Matrix of local nodal coordinates
localCoords_(0,0) = -1; localCoords_(1,0) = -1; localCoords_(2,0) = -1;
localCoords_(0,1) = +1; localCoords_(1,1) = -1; localCoords_(2,1) = -1;
localCoords_(0,2) = +1; localCoords_(1,2) = +1; localCoords_(2,2) = -1;
localCoords_(0,3) = -1; localCoords_(1,3) = +1; localCoords_(2,3) = -1;
localCoords_(0,4) = -1; localCoords_(1,4) = -1; localCoords_(2,4) = +1;
localCoords_(0,5) = +1; localCoords_(1,5) = -1; localCoords_(2,5) = +1;
localCoords_(0,6) = +1; localCoords_(1,6) = +1; localCoords_(2,6) = +1;
localCoords_(0,7) = -1; localCoords_(1,7) = +1; localCoords_(2,7) = +1;
// 3 --- 2
// /| /|
// / 0 --/ 1 y
// 7 --- 6 / |
// | |/ |
// 4 --- 5 ---> x
// /
// /
// z
// Matrix of local face connectivity
// -x
localFaceConn_(0,0) = 0;
localFaceConn_(0,1) = 4;
localFaceConn_(0,2) = 7;
localFaceConn_(0,3) = 3;
// +x
localFaceConn_(1,0) = 1;
localFaceConn_(1,1) = 2;
localFaceConn_(1,2) = 6;
localFaceConn_(1,3) = 5;
// -y
localFaceConn_(2,0) = 0;
localFaceConn_(2,1) = 1;
localFaceConn_(2,2) = 5;
localFaceConn_(2,3) = 4;
// +y
localFaceConn_(3,0) = 2;
localFaceConn_(3,1) = 3;
localFaceConn_(3,2) = 7;
localFaceConn_(3,3) = 6;
// -z
localFaceConn_(4,0) = 0;
localFaceConn_(4,1) = 3;
localFaceConn_(4,2) = 2;
localFaceConn_(4,3) = 1;
// +z
localFaceConn_(5,0) = 4;
localFaceConn_(5,1) = 5;
localFaceConn_(5,2) = 6;
localFaceConn_(5,3) = 7;
/*
localFaceCoords_(0,0) = -1; localFaceCoords_(1,0) = -1;
localFaceCoords_(0,1) = +1; localFaceCoords_(1,1) = -1;
localFaceCoords_(0,2) = +1; localFaceCoords_(1,2) = +1;
localFaceCoords_(0,3) = -1; localFaceCoords_(1,3) = +1;
*/
set_quadrature(GAUSSIAN_QUADRATURE);
}
//-----------------------------------------------------------------
void FE_ElementHex::set_quadrature(int quadrature)
{
double a = 1./sqrt(3.);
if (quadrature == NODAL_QUADRATURE) {
a = 1.0;
}
// Matrix of integration point locations (Gaussian) & follows local conn
ipCoords_(0,0) = -a; ipCoords_(1,0) = -a; ipCoords_(2,0) = -a;
ipCoords_(0,1) = +a; ipCoords_(1,1) = -a; ipCoords_(2,1) = -a;
ipCoords_(0,2) = +a; ipCoords_(1,2) = +a; ipCoords_(2,2) = -a;
ipCoords_(0,3) = -a; ipCoords_(1,3) = +a; ipCoords_(2,3) = -a;
ipCoords_(0,4) = -a; ipCoords_(1,4) = -a; ipCoords_(2,4) = +a;
ipCoords_(0,5) = +a; ipCoords_(1,5) = -a; ipCoords_(2,5) = +a;
ipCoords_(0,6) = +a; ipCoords_(1,6) = +a; ipCoords_(2,6) = +a;
ipCoords_(0,7) = -a; ipCoords_(1,7) = +a; ipCoords_(2,7) = +a;
// Compute shape functions at ip's
for (int ip = 0; ip < numIPs_; ip++) {
double r = ipCoords_(0, ip);
double s = ipCoords_(1, ip);
double t = ipCoords_(2, ip);
for (int iNode = 0; iNode < numEltNodes_; iNode++) {
double rI = localCoords_(0, iNode);
double sI = localCoords_(1, iNode);
double tI = localCoords_(2, iNode);
N_(ip, iNode) = 0.125 * (1 + r*rI) * (1 + s*sI) * (1 + t*tI);
}
}
// Integration point weights
ipWeights_ = 1.0;
// integration points by face
ipFace2DCoords_(0,0)=-a; ipFace2DCoords_(1,0)=-a;
ipFace2DCoords_(0,1)= a; ipFace2DCoords_(1,1)=-a;
ipFace2DCoords_(0,2)= a; ipFace2DCoords_(1,2)= a;
ipFace2DCoords_(0,3)=-a; ipFace2DCoords_(1,3)= a;
ipFaceCoords_[0](0,0)=-1;ipFaceCoords_[0](1,0)=-a;ipFaceCoords_[0](2,0)=-a;
ipFaceCoords_[0](0,1)=-1;ipFaceCoords_[0](1,1)= a;ipFaceCoords_[0](2,1)=-a;
ipFaceCoords_[0](0,2)=-1;ipFaceCoords_[0](1,2)= a;ipFaceCoords_[0](2,2)= a;
ipFaceCoords_[0](0,3)=-1;ipFaceCoords_[0](1,3)=-a;ipFaceCoords_[0](2,3)= a;
ipFaceCoords_[1](0,0)= 1;ipFaceCoords_[1](1,0)=-a;ipFaceCoords_[1](2,0)=-a;
ipFaceCoords_[1](0,1)= 1;ipFaceCoords_[1](1,1)= a;ipFaceCoords_[1](2,1)=-a;
ipFaceCoords_[1](0,2)= 1;ipFaceCoords_[1](1,2)= a;ipFaceCoords_[1](2,2)= a;
ipFaceCoords_[1](0,3)= 1;ipFaceCoords_[1](1,3)=-a;ipFaceCoords_[1](2,3)= a;
ipFaceCoords_[2](0,0)=-a;ipFaceCoords_[2](1,0)=-1;ipFaceCoords_[2](2,0)=-a;
ipFaceCoords_[2](0,1)=-a;ipFaceCoords_[2](1,1)=-1;ipFaceCoords_[2](2,1)= a;
ipFaceCoords_[2](0,2)= a;ipFaceCoords_[2](1,2)=-1;ipFaceCoords_[2](2,2)= a;
ipFaceCoords_[2](0,3)= a;ipFaceCoords_[2](1,3)=-1;ipFaceCoords_[2](2,3)=-a;
ipFaceCoords_[3](0,0)=-a;ipFaceCoords_[3](1,0)= 1;ipFaceCoords_[3](2,0)=-a;
ipFaceCoords_[3](0,1)=-a;ipFaceCoords_[3](1,1)= 1;ipFaceCoords_[3](2,1)= a;
ipFaceCoords_[3](0,2)= a;ipFaceCoords_[3](1,2)= 1;ipFaceCoords_[3](2,2)= a;
ipFaceCoords_[3](0,3)= a;ipFaceCoords_[3](1,3)= 1;ipFaceCoords_[2](2,3)=-a;
ipFaceCoords_[4](0,0)=-a;ipFaceCoords_[4](1,0)=-a;ipFaceCoords_[4](2,0)=-1;
ipFaceCoords_[4](0,1)= a;ipFaceCoords_[4](1,1)=-a;ipFaceCoords_[4](2,1)=-1;
ipFaceCoords_[4](0,2)= a;ipFaceCoords_[4](1,2)= a;ipFaceCoords_[4](2,2)=-1;
ipFaceCoords_[4](0,3)=-a;ipFaceCoords_[4](1,3)= a;ipFaceCoords_[4](2,3)=-1;
ipFaceCoords_[5](0,0)=-a;ipFaceCoords_[5](1,0)=-a;ipFaceCoords_[5](2,0)= 1;
ipFaceCoords_[5](0,1)= a;ipFaceCoords_[5](1,1)=-a;ipFaceCoords_[5](2,1)= 1;
ipFaceCoords_[5](0,2)= a;ipFaceCoords_[5](1,2)= a;ipFaceCoords_[5](2,2)= 1;
ipFaceCoords_[5](0,3)=-a;ipFaceCoords_[5](1,3)= a;ipFaceCoords_[5](2,3)= 1;
// Compute shape functions at ip's
for (int f = 0; f < numFaces_; f++) {
for (int ip = 0; ip < numFaceIPs_; ip++) {
double r = ipFaceCoords_[f](0, ip);
double s = ipFaceCoords_[f](1, ip);
double t = ipFaceCoords_[f](2, ip);
for (int iNode = 0; iNode < numEltNodes_; iNode++) {
double rI = localCoords_(0, iNode);
double sI = localCoords_(1, iNode);
double tI = localCoords_(2, iNode);
NFace_[f](ip, iNode) = 0.125 * (1 + r*rI) * (1 + s*sI) * (1 + t*tI);
}
}
}
// integration points
ipFaceWeights_ = 1.0;
}
FE_ElementHex::~FE_ElementHex()
{
// Nothing to do here
}
// -------------------------------------------------------------
// shape_function
// -------------------------------------------------------------
void FE_ElementHex::shape_function(const int eltID,
DENS_MAT &N,
vector<DENS_MAT> &dN,
DIAG_MAT &weights)
{
// Get element node coordinates from mesh
DENS_MAT xCoords;
feMesh_->element_coordinates(eltID, xCoords);
// Transpose xCoords
DENS_MAT xCoordsT(transpose(xCoords));
// Shape functions are simply the canonical element values
N = N_;
// Set sizes of matrices and vectors
if ((int)dN.size() != nSD_) dN.resize(nSD_);
for (int isd = 0; isd < nSD_; isd++) dN[isd].resize(numIPs_, numEltNodes_);
weights.resize(numIPs_,numIPs_);
// Create some temporary matrices:
// Shape function deriv.'s w.r.t. element coords
DENS_MAT dNdr(nSD_, numEltNodes_, false);
// Jacobian matrix: [dx/dr dy/ds dz/dt | dx/ds ... ]
DENS_MAT dxdr, drdx, dNdx;
// Loop over integration points
for (int ip = 0; ip < numIPs_; ip++) {
const double &r = ipCoords_(0,ip);
const double &s = ipCoords_(1,ip);
const double &t = ipCoords_(2,ip);
// Fill dNdr
for (int inode = 0; inode < numEltNodes_; inode++) {
const double &rI = localCoords_(0,inode);
const double &sI = localCoords_(1,inode);
const double &tI = localCoords_(2,inode);
dNdr(0,inode) = 0.125 * rI * (1 + s*sI) * (1 + t*tI);
dNdr(1,inode) = 0.125 * sI * (1 + r*rI) * (1 + t*tI);
dNdr(2,inode) = 0.125 * tI * (1 + r*rI) * (1 + s*sI);
}
// Compute dx/dxi matrix
dxdr = dNdr * xCoordsT;
drdx = inv(dxdr);
// Compute dNdx and fill dN matrix
dNdx = drdx*dNdr;
for (int isd = 0; isd < nSD_; isd++)
for (int inode = 0; inode < numEltNodes_; inode++)
dN[isd](ip,inode) = dNdx(isd,inode);
// Compute jacobian determinant of dxdr at this ip
double J = dxdr(0,0) * ( dxdr(1,1)*dxdr(2,2) - dxdr(2,1)*dxdr(1,2) )
- dxdr(0,1) * ( dxdr(1,0)*dxdr(2,2) - dxdr(1,2)*dxdr(2,0) )
+ dxdr(0,2) * ( dxdr(1,0)*dxdr(2,1) - dxdr(1,1)*dxdr(2,0) );
// Compute ip weight
weights(ip,ip) = ipWeights_(ip)*J;
}
}
//-----------------------------------------------------------------
void FE_ElementHex::shape_function(const int eltID,
const VECTOR &xi,
DENS_VEC &N)
{
N.resize(numEltNodes_);
for (int inode = 0; inode < numEltNodes_; ++inode)
{
double shp = 0.125;
for (int i = 0; i < nSD_; ++i) shp *= (1 + xi(i)*localCoords_(i, inode));
N(inode) = shp;
}
}
//-----------------------------------------------------------------
void FE_ElementHex::shape_function(const int eltID,
const VECTOR &xi,
DENS_VEC &N,
DENS_MAT &dNdx)
{
N.resize(numEltNodes_);
// Get element node coordinates from mesh
DENS_MAT xCoords;
feMesh_->element_coordinates(eltID, xCoords);
DENS_MAT xCoordsT = transpose(xCoords);
DENS_MAT dNdr(3,8,false), dxdr(3,3,false), drdx;
double r = xi(0);
double s = xi(1);
double t = xi(2);
for (int inode = 0; inode < numEltNodes_; ++inode)
{
double rI = localCoords_(0,inode);
double sI = localCoords_(1,inode);
double tI = localCoords_(2,inode);
// Shape function
N(inode) = 0.125 * (1.0 + r*rI) * (1.0 + s*sI) * (1.0 + t*tI);
// Shape function derivative wrt (r,s,t)
dNdr(0,inode) = 0.125 * rI * (1.0 + s*sI) * (1.0 + t*tI);
dNdr(1,inode) = 0.125 * sI * (1.0 + r*rI) * (1.0 + t*tI);
dNdr(2,inode) = 0.125 * tI * (1.0 + r*rI) * (1.0 + s*sI);
}
// Derivatives wrt (x,y,z)
dxdr = dNdr * xCoordsT;
drdx = inv(dxdr);
dNdx = drdx*dNdr;
}
//-----------------------------------------------------------------
void FE_ElementHex::face_shape_function(const PAIR & face,
DENS_MAT &N,
vector<DENS_MAT> &dN,
vector<DENS_MAT> &Nn,
DIAG_MAT &weights)
{
int eltID = face.first;
int local_faceID = face.second;
// const double * face_normal = face.normal();
// double * normal = face_normal;
DENS_VEC normal(nSD_);
// Get element node coordinates from mesh
DENS_MAT xCoords;
feMesh_->element_coordinates(eltID, xCoords);
// Transpose xCoords
DENS_MAT xCoordsT = transpose(xCoords);
// Shape functions are simply the canonical element values
N.reset(numFaceIPs_, numEltNodes_);
N = NFace_[local_faceID];
// Set sizes of matrices and vectors
if ((int)dN.size() != nSD_) dN.resize(nSD_);
for (int isd = 0; isd < nSD_; isd++) dN[isd].reset(numFaceIPs_, numEltNodes_);
weights.reset(numFaceIPs_,numFaceIPs_);
// Create some temporary matrices:
// Shape function deriv.'s w.r.t. element coords
DENS_MAT dNdr(nSD_, numEltNodes_);
// Jacobian matrix: [dx/dr dy/ds dz/dt | dx/ds ... ]
DENS_MAT dxdr, drdx, dNdx;
// Loop over integration points
for (int ip = 0; ip < numFaceIPs_; ip++) {
double r = ipFaceCoords_[local_faceID](0,ip);
double s = ipFaceCoords_[local_faceID](1,ip);
double t = ipFaceCoords_[local_faceID](2,ip);
// Fill dNdr
for (int inode = 0; inode < numEltNodes_; inode++) {
double rI = localCoords_(0,inode);
double sI = localCoords_(1,inode);
double tI = localCoords_(2,inode);
dNdr(0,inode) = 0.125 * rI * (1 + s*sI) * (1 + t*tI);
dNdr(1,inode) = 0.125 * sI * (1 + r*rI) * (1 + t*tI);
dNdr(2,inode) = 0.125 * tI * (1 + r*rI) * (1 + s*sI);
}
// Compute dx/dxi matrix
dxdr = dNdr * xCoordsT;
drdx = inv(dxdr);
// Compute 2d jacobian determinant of dxdr at this ip
double J = face_normal(face, ip, normal);
// Compute dNdx and fill dN matrix
dNdx = drdx*dNdr;
for (int isd = 0; isd < nSD_; isd++) {
for (int inode = 0; inode < numEltNodes_; inode++) {
dN[isd](ip,inode) = dNdx(isd,inode);
Nn[isd](ip,inode) = N(ip,inode)*normal(isd);
}
}
// Compute ip weight
weights(ip,ip) = ipFaceWeights_(ip)*J;
}
}
//-----------------------------------------------------------------
void FE_ElementHex::face_shape_function(const PAIR & face,
DENS_MAT &N,
DENS_MAT &n,
DIAG_MAT &weights)
{
int eltID = face.first;
int local_faceID = face.second;
// const double * face_normal = face.normal();
// double * normal = face_normal;
DENS_VEC normal(nSD_);
// Get element node coordinates from mesh
DENS_MAT xCoords;
feMesh_->element_coordinates(eltID, xCoords);
// Transpose xCoords
DENS_MAT xCoordsT = transpose(xCoords);
// Shape functions are simply the canonical element values
N.reset(numFaceIPs_, numEltNodes_);
N = NFace_[local_faceID];
weights.reset(numFaceIPs_,numFaceIPs_);
// Create some temporary matrices:
// Shape function deriv.'s w.r.t. element coords
DENS_MAT dNdr(nSD_, numEltNodes_);
// Jacobian matrix: [dx/dr dy/ds dz/dt | dx/ds ... ]
DENS_MAT dxdr, drdx, dNdx;
// Loop over integration points
for (int ip = 0; ip < numFaceIPs_; ip++) {
double r = ipFaceCoords_[local_faceID](0,ip);
double s = ipFaceCoords_[local_faceID](1,ip);
double t = ipFaceCoords_[local_faceID](2,ip);
// Compute 2d jacobian determinant of dxdr at this ip
double J = face_normal(face, ip, normal);
// Copy normal at integration point
for (int isd = 0; isd < nSD_; isd++) {
n(isd,ip) = normal(isd);
}
// Compute ip weight
weights(ip,ip) = ipFaceWeights_(ip)*J;
}
}
// -------------------------------------------------------------
// face_normal
// -------------------------------------------------------------
double FE_ElementHex::face_normal(const PAIR & face,
int ip,
DENS_VEC &normal)
{
// Get element node coordinates from mesh
DENS_MAT xCoords;
feMesh_->face_coordinates(face, xCoords);
// Transpose xCoords
DENS_MAT xCoordsT = transpose(xCoords);
double r = ipFace2DCoords_(0,ip);
double s = ipFace2DCoords_(1,ip);
DENS_MAT dNdr(nSD_-1, numFaceNodes_);
for (int inode = 0; inode < numFaceNodes_; inode++) {
double rI = localCoords_(0,inode); // NOTE a little dangerous
double sI = localCoords_(1,inode);
dNdr(0,inode) = 0.25 * rI * (1 + s*sI);
dNdr(1,inode) = 0.25 * sI * (1 + r*rI);
}
DENS_MAT dxdr(2,3);
// Compute dx/dxi matrix
dxdr = dNdr * xCoordsT;
normal(0) = dxdr(0,1)*dxdr(1,2) - dxdr(0,2)*dxdr(1,1) ;
normal(1) = dxdr(0,2)*dxdr(1,0) - dxdr(0,0)*dxdr(1,2) ;
normal(2) = dxdr(0,0)*dxdr(1,1) - dxdr(0,1)*dxdr(1,0) ;
double J = sqrt(normal(0)*normal(0)+normal(1)*normal(1)+normal(2)*normal(2));
// double inv_J = normal_sense(face)/J;
double inv_J = 1.0/J;
normal(0) *= inv_J;
normal(1) *= inv_J;
normal(2) *= inv_J;
return J;
}
}; // namespace ATC_Transfer
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