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customtest.h
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customtest.h
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// ==== from CIM paper
double dbc_custom(double *x, int thedim, double thetime){
double value = 0.0;
for (int j = 0; j < thedim; j++)
value += x[j]*x[j];
value = -1.0/(1.0+value);
return value;
}
double getf_custom(double *x, double thesign, PBData &pb, GridData &grid){
double value = 0.0;
double radius2 = 0.0;
for (int r = 0; r < grid.dim; r++)
radius2 += x[r]*x[r];
if (thesign < 0.0)
{
for (int r = 0; r < grid.dim; r++)
value -= pb.epsilonm*
(8.0*x[r]*x[r]/((1.0+radius2)*(1.0+radius2)*(1.0+radius2))-
2.0/((1.0+radius2)*(1.0+radius2)));
}
else
{
for (int r = 0; r < grid.dim; r++)
value -= pb.epsilonp*
(-8.0*x[r]*x[r]/((1.0+radius2)*(1.0+radius2)*(1.0+radius2))+
2.0/((1.0+radius2)*(1.0+radius2)));
}
return value;
}
double gettau_custom(double *x, GridData &grid){
int r;
double valuep, valuem, radius2;
radius2 = 0.0;
for (int r = 0; r < grid.dim; r++)
radius2 += x[r]*x[r];
valuep = -1.0/(1.0+radius2);
valuem = 1.0/(1.0+radius2);
return valuep-valuem;
}
void getDtau_custom(double *Dtau, double *x, GridData &grid){
double valuep, valuem, radius2;
radius2 = 0.0;
for (int r = 0; r < grid.dim; r++)
radius2 += x[r]*x[r];
for (int s = 0; s < grid.dim; s++)
{
valuep = 2.0*x[s]/((1.0+radius2)*(1.0+radius2));
valuem = -2.0*x[s]/((1.0+radius2)*(1.0+radius2));
Dtau[s] = valuep-valuem;
}
}
void getD2tau_custom(double **D2tau, double *x, GridData &grid){
double valuep, valuem, radius2;
radius2 = 0.0;
for (int r = 0; r < grid.dim; r++)
radius2 += x[r]*x[r];
for (int r = 0; r < grid.dim; r++)
for (int s = r; s < grid.dim; s++)
{
valuep = -8.0*x[r]*x[s]/((1.0+radius2)*(1.0+radius2)*(1.0+radius2));
valuem = 8.0*x[r]*x[s]/((1.0+radius2)*(1.0+radius2)*(1.0+radius2));
if (s == r)
{
valuep += 2.0/((1.0+radius2)*(1.0+radius2));
valuem += -2.0/((1.0+radius2)*(1.0+radius2));
}
D2tau[r][s] = valuep-valuem;
D2tau[s][r] = D2tau[r][s];
}
}
double getsigma_custom(double *x, double *normal, PBData &pb, GridData &grid){
int r, s;
double sigma, gradp[grid.dim], gradm[grid.dim], radius2;
sigma = 0.0;
radius2 = 0.0;
for (r = 0; r < grid.dim; r++)
radius2 += x[r]*x[r];
for (r = 0; r < grid.dim; r++)
{
gradp[r] = 2.0*x[r]/((1.0+radius2)*(1.0+radius2));
gradm[r] = -2.0*x[r]/((1.0+radius2)*(1.0+radius2));
sigma += (pb.epsilonp*gradp[r]-pb.epsilonm*gradm[r])*normal[r];
}
return sigma;
}
void getDsigma_custom(double *Dsigma, double *x, double *normal, double **Dnormal, PBData &pb, GridData &grid)
{
int r, s;
double gradp[grid.dim], gradm[grid.dim], D2p[grid.dim][grid.dim],
D2m[grid.dim][grid.dim], radius2;
radius2 = 0.0;
for (r = 0; r < grid.dim; r++)
radius2 += x[r]*x[r];
for (r = 0; r < grid.dim; r++)
{
gradp[r] = 2.0*x[r]/((1.0+radius2)*(1.0+radius2));//grad(u+)
gradm[r] = -2.0*x[r]/((1.0+radius2)*(1.0+radius2));//grad(u-)
for (s = 0; s < grid.dim; s++)
{
D2p[r][s] = -8.0*x[r]*x[s]/((1.0+radius2)*(1.0+radius2)*(1.0+radius2));
D2m[r][s] = 8.0*x[r]*x[s]/((1.0+radius2)*(1.0+radius2)*(1.0+radius2));
if (s == r)
{
D2p[r][s] += 2.0/((1.0+radius2)*(1.0+radius2));
D2m[r][s] += -2.0/((1.0+radius2)*(1.0+radius2));
}
}
}
for (r = 0; r < grid.dim; r++)
{
Dsigma[r] = 0.0;
for (s = 0; s < grid.dim; s++)
Dsigma[r] += (pb.epsilonp*gradp[s]-pb.epsilonm*gradm[s])*Dnormal[s][r]+
(pb.epsilonp*D2p[r][s]-pb.epsilonm*D2m[r][s])*normal[s];
}
}