public SecondDerivativeOp(int direction, FdmMesher mesher)
: base(direction, mesher)
{
FdmLinearOpLayout layout = mesher.layout();
FdmLinearOpIterator endIter = layout.end();
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter; ++iter)
{
int i = iter.index();
double?hm = mesher.dminus(iter, direction_);
double?hp = mesher.dplus(iter, direction_);
double?zetam1 = hm * (hm + hp);
double?zeta0 = hm * hp;
double?zetap1 = hp * (hm + hp);
int co = iter.coordinates()[direction_];
if (co == 0 || co == layout.dim()[direction] - 1)
{
lower_[i] = diag_[i] = upper_[i] = 0.0;
}
else
{
lower_[i] = 2.0 / zetam1.Value;
diag_[i] = -2.0 / zeta0.Value;
upper_[i] = 2.0 / zetap1.Value;
}
}
}
public FirstDerivativeOp(int direction, FdmMesher mesher)
: base(direction, mesher)
{
FdmLinearOpLayout layout = mesher.layout();
FdmLinearOpIterator endIter = layout.end();
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter; ++iter)
{
int i = iter.index();
double?hm = mesher.dminus(iter, direction_);
double?hp = mesher.dplus(iter, direction_);
double?zetam1 = hm * (hm + hp);
double?zeta0 = hm * hp;
double?zetap1 = hp * (hm + hp);
if (iter.coordinates()[direction_] == 0)
{
//upwinding scheme
lower_[i] = 0.0;
diag_[i] = -(upper_[i] = 1 / hp.Value);
}
else if (iter.coordinates()[direction_]
== layout.dim()[direction] - 1)
{
// downwinding scheme
lower_[i] = -(diag_[i] = 1 / hm.Value);
upper_[i] = 0.0;
}
else
{
lower_[i] = -hp.Value / zetam1.Value;
diag_[i] = (hp.Value - hm.Value) / zeta0.Value;
upper_[i] = hm.Value / zetap1.Value;
}
}
}
public SecondOrderMixedDerivativeOp(int d0, int d1, FdmMesher mesher)
: base(d0, d1, mesher)
{
FdmLinearOpLayout layout = mesher.layout();
FdmLinearOpIterator endIter = layout.end();
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter; ++iter)
{
int i = iter.index();
double?hm_d0 = mesher.dminus(iter, d0_);
double?hp_d0 = mesher.dplus(iter, d0_);
double?hm_d1 = mesher.dminus(iter, d1_);
double?hp_d1 = mesher.dplus(iter, d1_);
double?zetam1 = hm_d0 * (hm_d0 + hp_d0);
double?zeta0 = hm_d0 * hp_d0;
double?zetap1 = hp_d0 * (hm_d0 + hp_d0);
double?phim1 = hm_d1 * (hm_d1 + hp_d1);
double?phi0 = hm_d1 * hp_d1;
double?phip1 = hp_d1 * (hm_d1 + hp_d1);
int c0 = iter.coordinates()[d0_];
int c1 = iter.coordinates()[d1_];
if (c0 == 0 && c1 == 0)
{
// lower left corner
a00_[i] = a01_[i] = a02_[i] = a10_[i] = a20_[i] = 0.0;
a11_[i] = a22_[i] = 1.0 / (hp_d0.Value * hp_d1.Value);
a21_[i] = a12_[i] = -a11_[i];
}
else if (c0 == layout.dim()[d0_] - 1 && c1 == 0)
{
// upper left corner
a22_[i] = a21_[i] = a20_[i] = a10_[i] = a00_[i] = 0.0;
a01_[i] = a12_[i] = 1.0 / (hm_d0.Value * hp_d1.Value);
a11_[i] = a02_[i] = -a01_[i];
}
else if (c0 == 0 && c1 == layout.dim()[d1_] - 1)
{
// lower right corner
a00_[i] = a01_[i] = a02_[i] = a12_[i] = a22_[i] = 0.0;
a10_[i] = a21_[i] = 1.0 / (hp_d0.Value * hm_d1.Value);
a20_[i] = a11_[i] = -a10_[i];
}
else if (c0 == layout.dim()[d0_] - 1 && c1 == layout.dim()[d1_] - 1)
{
// upper right corner
a20_[i] = a21_[i] = a22_[i] = a12_[i] = a02_[i] = 0.0;
a00_[i] = a11_[i] = 1.0 / (hm_d0.Value * hm_d1.Value);
a10_[i] = a01_[i] = -a00_[i];
}
else if (c0 == 0)
{
// lower side
a00_[i] = a01_[i] = a02_[i] = 0.0;
a10_[i] = hp_d1.Value / (hp_d0.Value * phim1.Value);
a20_[i] = -a10_[i];
a21_[i] = (hp_d1.Value - hm_d1.Value) / (hp_d0.Value * phi0.Value);
a11_[i] = -a21_[i];
a22_[i] = hm_d1.Value / (hp_d0.Value * phip1.Value);
a12_[i] = -a22_[i];
}
else if (c0 == layout.dim()[d0_] - 1)
{
// upper side
a20_[i] = a21_[i] = a22_[i] = 0.0;
a00_[i] = hp_d1.Value / (hm_d0.Value * phim1.Value);
a10_[i] = -a00_[i];
a11_[i] = (hp_d1.Value - hm_d1.Value) / (hm_d0.Value * phi0.Value);
a01_[i] = -a11_[i];
a12_[i] = hm_d1.Value / (hm_d0.Value * phip1.Value);
a02_[i] = -a12_[i];
}
else if (c1 == 0)
{
// left side
a00_[i] = a10_[i] = a20_[i] = 0.0;
a01_[i] = hp_d0.Value / (zetam1.Value * hp_d1.Value);
a02_[i] = -a01_[i];
a12_[i] = (hp_d0.Value - hm_d0.Value) / (zeta0.Value * hp_d1.Value);
a11_[i] = -a12_[i];
a22_[i] = hm_d0.Value / (zetap1.Value * hp_d1.Value);
a21_[i] = -a22_[i];
}
else if (c1 == layout.dim()[d1_] - 1)
{
// right side
a22_[i] = a12_[i] = a02_[i] = 0.0;
a00_[i] = hp_d0.Value / (zetam1.Value * hm_d1.Value);
a01_[i] = -a00_[i];
a11_[i] = (hp_d0.Value - hm_d0.Value) / (zeta0.Value * hm_d1.Value);
a10_[i] = -a11_[i];
a21_[i] = hm_d0.Value / (zetap1.Value * hm_d1.Value);
a20_[i] = -a21_[i];
}
else
{
a00_[i] = hp_d0.Value * hp_d1.Value / (zetam1.Value * phim1.Value);
a10_[i] = -(hp_d0.Value - hm_d0.Value) * hp_d1.Value / (zeta0.Value * phim1.Value);
a20_[i] = -hm_d0.Value * hp_d1.Value / (zetap1.Value * phim1.Value);
a01_[i] = -hp_d0.Value * (hp_d1.Value - hm_d1.Value) / (zetam1.Value * phi0.Value);
a11_[i] = (hp_d0.Value - hm_d0.Value) * (hp_d1.Value - hm_d1.Value) / (zeta0.Value * phi0.Value);
a21_[i] = hm_d0.Value * (hp_d1.Value - hm_d1.Value) / (zetap1.Value * phi0.Value);
a02_[i] = -hp_d0.Value * hm_d1.Value / (zetam1.Value * phip1.Value);
a12_[i] = hm_d1.Value * (hp_d0.Value - hm_d0.Value) / (zeta0.Value * phip1.Value);
a22_[i] = hm_d0.Value * hm_d1.Value / (zetap1.Value * phip1.Value);
}
}
}