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EmbeddedBoundaryFormula.cpp
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EmbeddedBoundaryFormula.cpp
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/************************************************************************
* Copyright © 2020 The Multiphysics Modeling and Computation (M2C) Lab
* <kevin.wgy@gmail.com> <kevinw3@vt.edu>
************************************************************************/
#include<EmbeddedBoundaryFormula.h>
#include<cassert>
//if the verification script is activated, turn following line on
//#include<trilinear_interpolation.h>
//-----------------------------------------------------------------------------
EmbeddedBoundaryFormula::EmbeddedBoundaryFormula(Operation operation_, double eps_)
: operation(operation_), scenario(NODE), constant(0.0),
eps(eps_)
{ }
//-----------------------------------------------------------------------------
EmbeddedBoundaryFormula::~EmbeddedBoundaryFormula()
{ }
//-----------------------------------------------------------------------------
void
EmbeddedBoundaryFormula::SpecifyFormula(Operation op, ImageScenario sc, std::vector<Int3> &node_,
std::vector<double> &coeff_, double constant_)
{
assert(node_.size() == coeff_.size());
operation = op;
scenario = sc;
node = node_;
coeff = coeff_;
constant = constant_;
}
//-----------------------------------------------------------------------------
void
EmbeddedBoundaryFormula::BuildMirroringFormula(Int3& ghost, Int3& image, Vec3D& xi0, double constant_)
{
operation = MIRRORING;
constant = constant_;
node.clear();
coeff.clear();
//---------------------------------------------------------------------
// Step 1: Check xi0 to identify degenerate cases (node, edge, face)
//---------------------------------------------------------------------
int involved[2][2][2];
for(int k=0; k<2; k++)
for(int j=0; j<2; j++)
for(int i=0; i<2; i++)
involved[k][j][i] = 1; //by default, all the 8 nodes are involved
std::vector<double> xi;
if(fabs(xi0[0])<=eps || fabs(xi0[0]-1.0)<eps) {
int i = fabs(xi0[0])<=eps ? 1 : 0;
for(int k=0; k<2; k++)
for(int j=0; j<2; j++)
involved[k][j][i] = 0;
} else
xi.push_back(xi0[0]);
if(fabs(xi0[1])<=eps || fabs(xi0[1]-1.0)<eps) {
int j = fabs(xi0[1])<=eps ? 1 : 0;
for(int k=0; k<2; k++)
for(int i=0; i<2; i++)
involved[k][j][i] = 0;
} else
xi.push_back(xi0[1]);
if(fabs(xi0[2])<=eps || fabs(xi0[2]-1.0)<eps) {
int k = fabs(xi0[2])<=eps ? 1 : 0;
for(int j=0; j<2; j++)
for(int i=0; i<2; i++)
involved[k][j][i] = 0;
} else
xi.push_back(xi0[2]);
//---------------------------------------------------------------------
// Step 2: Deal with difference cases separately
//---------------------------------------------------------------------
std::vector<Int3> node_tmp;
for(int k=0; k<2; k++)
for(int j=0; j<2; j++)
for(int i=0; i<2; i++)
if(involved[k][j][i])
node_tmp.push_back(image + Int3(i,j,k));
switch(node_tmp.size()) {
case 1: //node
assert(xi.size() == 0);
node = node_tmp;
coeff.push_back(1.0);
scenario = NODE;
break;
case 2: //edge
assert(xi.size() == 1);
FinalizeMirroringFormulaEdge(ghost, node_tmp, xi);
break;
case 4: //face
assert(xi.size() == 2);
FinalizeMirroringFormulaFace(ghost, node_tmp, xi);
break;
case 8: //element (interior)
assert(xi.size() == 3);
FinalizeMirroringFormulaElem(ghost, node_tmp, xi);
break;
default:
fprintf(stdout,"*** Error: Detected error in the construction of mirroring formulas. Ghost node: %d %d %d.\n",
ghost[0], ghost[1], ghost[2]);
break;
}
}
//-----------------------------------------------------------------------------
void
EmbeddedBoundaryFormula::BuildLinearExtrapolationFormula(Int3& ghost, Int3& image, Vec3D& xi0,
double constant_)
{
//everything is the same as BuildMirroringFormula, except the "operation" type;
BuildMirroringFormula(ghost, image, xi0, constant_);
operation = LINEAR_EXTRAPOLATION;
}
//-----------------------------------------------------------------------------
//-----------------------------------------------------------------------------
void
EmbeddedBoundaryFormula::FinalizeMirroringFormulaEdge(Int3 &ghost, std::vector<Int3> &node_tmp,
std::vector<double>& xi)
{
if(ghost != node_tmp[0] && ghost != node_tmp[1]) {
scenario = EDGE_REMOTE;
node = node_tmp;
coeff.push_back(1-xi[0]);
coeff.push_back(xi[0]);
//Formula: v(ghost) = coeff[0]*v(node[0]) + coeff[1]*v(node[1])
}
else {
scenario = EDGE_SHARED;
if(ghost == node_tmp[0])
node.push_back(node_tmp[1]);
else
node.push_back(node_tmp[0]);
coeff.push_back(1.0);
//Formula: v(ghost) = coeff[0]*v(node[0]) (where coeff[0] = 1.0)
}
}
//-----------------------------------------------------------------------------
void
EmbeddedBoundaryFormula::FinalizeMirroringFormulaFace(Int3 &ghost, std::vector<Int3> &node_tmp,
std::vector<double>& xi)
{
std::vector<double> coeff_tmp;
coeff_tmp.push_back((1-xi[1])*(1-xi[0]));
coeff_tmp.push_back((1-xi[1])*xi[0]);
coeff_tmp.push_back(xi[1]*(1-xi[0]));
coeff_tmp.push_back(xi[1]*xi[0]);
scenario = FACE_REMOTE;
double denom = 0;
for(int i=0; i<(int)node_tmp.size(); i++) {
if(node_tmp[i] != ghost) {
node.push_back(node_tmp[i]);
coeff.push_back(coeff_tmp[i]);
} else {
denom = 1.0 - coeff_tmp[i];
scenario = FACE_SHARED;
}
}
if(scenario == FACE_SHARED) {
assert(denom != 0.0);
for(int i=0; i<(int)coeff.size(); i++)
coeff[i] /= denom;
}
//Formula: v(ghost) = sum ( coeff[i]*v(node[i]) )
}
//-----------------------------------------------------------------------------
void
EmbeddedBoundaryFormula::FinalizeMirroringFormulaElem(Int3 &ghost, std::vector<Int3> &node_tmp,
std::vector<double>& xi)
{
std::vector<double> coeff_tmp(8, 0.0);
coeff_tmp[0] = (1-xi[0])*(1-xi[1])*(1-xi[2]);
coeff_tmp[1] = xi[0]*(1-xi[1])*(1-xi[2]);
coeff_tmp[2] = (1-xi[0])*xi[1]*(1-xi[2]);
coeff_tmp[3] = xi[0]*xi[1]*(1-xi[2]);
coeff_tmp[4] = (1-xi[0])*(1-xi[1])*xi[2];
coeff_tmp[5] = xi[0]*(1-xi[1])*xi[2];
coeff_tmp[6] = (1-xi[0])*xi[1]*xi[2];
coeff_tmp[7] = xi[0]*xi[1]*xi[2];
scenario = ELEMENT_REMOTE;
double denom = 0;
for(int i=0; i<(int)node_tmp.size(); i++) {
if(node_tmp[i] != ghost) {
node.push_back(node_tmp[i]);
coeff.push_back(coeff_tmp[i]);
} else {
denom = 1.0 - coeff_tmp[i];
scenario = ELEMENT_SHARED;
}
}
if(scenario == ELEMENT_SHARED) {
assert(denom != 0.0);
for(int i=0; i<(int)coeff.size(); i++)
coeff[i] /= denom;
}
//Formula: v(ghost) = sum ( coeff[i]*v(node[i]) )
/*
//verification
std::vector<double> coeff2(8, 0.0);
coeff2[0] = MathTools::trilinear_interpolation<double>(1,0,0,0,0,0,0,0,xi.data());
coeff2[1] = MathTools::trilinear_interpolation<double>(0,1,0,0,0,0,0,0,xi.data());
coeff2[2] = MathTools::trilinear_interpolation<double>(0,0,1,0,0,0,0,0,xi.data());
coeff2[3] = MathTools::trilinear_interpolation<double>(0,0,0,1,0,0,0,0,xi.data());
coeff2[4] = MathTools::trilinear_interpolation<double>(0,0,0,0,1,0,0,0,xi.data());
coeff2[5] = MathTools::trilinear_interpolation<double>(0,0,0,0,0,1,0,0,xi.data());
coeff2[6] = MathTools::trilinear_interpolation<double>(0,0,0,0,0,0,1,0,xi.data());
coeff2[7] = MathTools::trilinear_interpolation<double>(0,0,0,0,0,0,0,1,xi.data());
for(int i=0; i<8; i++)
assert(fabs(coeff2[i]-coeff_tmp[i])<1.0e-14);
*/
}
//-----------------------------------------------------------------------------
double
EmbeddedBoundaryFormula::Evaluate(double*** v, double vin)
{
double res = 0.0;
if(operation==MIRRORING) {
assert(vin==0.0); //should be specified as "constant"
res = constant;
for(int i=0; i<(int)node.size(); i++)
res += coeff[i]*v[node[i][2]/*k*/][node[i][1]/*j*/][node[i][0]/*i*/];
}
else if(operation==LINEAR_EXTRAPOLATION) {
for(int i=0; i<(int)node.size(); i++)
res += coeff[i]*v[node[i][2]/*k*/][node[i][1]/*j*/][node[i][0]/*i*/];
res = (vin - constant*res)/(1.0-constant); //constant should be at most 0.5.
}
return res;
}
//-----------------------------------------------------------------------------
Vec3D
EmbeddedBoundaryFormula::Evaluate3D(Vec3D*** v, Vec3D vin)
{
Vec3D res(0.0);
if(operation==MIRRORING) {
assert(vin[0]==vin[1] && vin[1]==vin[2] && vin[2]==0.0); //should be specified as "constant"
res = constant;
for(int i=0; i<(int)node.size(); i++)
res += coeff[i]*v[node[i][2]/*k*/][node[i][1]/*j*/][node[i][0]/*i*/];
}
else if(operation==LINEAR_EXTRAPOLATION) {
for(int i=0; i<(int)node.size(); i++)
res += coeff[i]*v[node[i][2]/*k*/][node[i][1]/*j*/][node[i][0]/*i*/];
res = (vin - constant*res)/(1.0-constant); //constant should be at most 0.5.
}
return res;
}
//-----------------------------------------------------------------------------
double
EmbeddedBoundaryFormula::Evaluate(std::vector<double>& v, double vin)
{
assert(v.size() == node.size());
double res = 0.0;
if(operation==MIRRORING) {
assert(vin==0.0); //should be specified as "constant"
res = constant;
for(int i=0; i<(int)v.size(); i++)
res += coeff[i]*v[i];
}
else if(operation==LINEAR_EXTRAPOLATION) {
for(int i=0; i<(int)v.size(); i++)
res += coeff[i]*v[i];
res = (vin - constant*res)/(1.0-constant); //constant should be at most 0.5.
}
return res;
}
//-----------------------------------------------------------------------------
Vec3D
EmbeddedBoundaryFormula::Evaluate3D(std::vector<Vec3D>& v, Vec3D vin)
{
assert(v.size() == node.size());
Vec3D res(0.0);
if(operation==MIRRORING) {
assert(vin[0]==vin[1] && vin[1]==vin[2] && vin[2]==0.0); //should be specified as "constant"
res = constant;
for(int i=0; i<(int)v.size(); i++)
res += coeff[i]*v[i];
}
else if(operation==LINEAR_EXTRAPOLATION) {
for(int i=0; i<(int)v.size(); i++)
res += coeff[i]*v[i];
res = (vin - constant*res)/(1.0-constant); //constant should be at most 0.5.
}
return res;
}
//-----------------------------------------------------------------------------
//-----------------------------------------------------------------------------