inline double
compute_linear_extrap(
D& patch_data,
const I& i,
const I& i_intr,
const IntVector<NDIM>& i_shft,
const int depth)
{
double ret_val = patch_data(i_intr,depth);
for (unsigned int d = 0; d < NDIM; ++d)
{
if (i_shft(d) != 0)
{
const I& i_intr0 = i_intr;
I i_intr1 = i_intr;
i_intr1(d) += i_shft(d);
const double& f0 = patch_data(i_intr0,depth);
const double& f1 = patch_data(i_intr1,depth);
const double du = f0-f1;
const double delta = std::abs(i(d)-i_intr(d));
ret_val += du*delta;
}
}
return ret_val;
}// compute_linear_extrap
inline double
compute_quadratic_extrap(D& patch_data,
const I& i,
const I& i_intr,
const IntVector<NDIM>& i_shft,
const int depth,
const int codim)
{
if (codim == 1)
{
for (unsigned int d = 0; d < NDIM; ++d)
{
if (i_shft(d) != 0)
{
const I& i_intr0 = i_intr;
I i_intr1 = i_intr;
i_intr1(d) += i_shft(d);
I i_intr2 = i_intr1;
i_intr2(d) += i_shft(d);
const double& f0 = patch_data(i_intr0, depth);
const double& f1 = patch_data(i_intr1, depth);
const double& f2 = patch_data(i_intr2, depth);
const double x = std::abs(i(d) - i_intr(d));
return (1.0 / 2.0 * f2 - f1 + 1.0 / 2.0 * f0) * x * x +
(-1.0 / 2.0 * f2 + 2.0 * f1 - 3.0 / 2.0 * f0) * x + f0;
}
}
}
else
{
return compute_linear_extrap(patch_data, i, i_intr, i_shft, depth);
}
return 0.0; // this statement should not be reached
} // compute_quadratic_extrap
inline double
compute_quadratic_extrap(
D& patch_data,
const I& i,
const I& i_intr,
const IntVector<NDIM>& i_shft,
const int depth,
const int codim)
{
if (codim == 1)
{
for (unsigned int d = 0; d < NDIM; ++d)
{
if (i_shft(d) != 0)
{
#if 1
const I& i_intr0 = i_intr;
I i_intr1 = i_intr;
i_intr1(d) += i_shft(d);
I i_intr2 = i_intr1;
i_intr2(d) += i_shft(d);
const double& f0 = patch_data(i_intr0,depth);
const double& f1 = patch_data(i_intr1,depth);
const double& f2 = patch_data(i_intr2,depth);
const double x = std::abs(i(d)-i_intr(d));
return (1.0/2.0*f2-f1+1.0/2.0*f0)*x*x+(-1.0/2.0*f2+2.0*f1-3.0/2.0*f0)*x+f0;
#endif
#if 0
// NOTE: The following only works in general for the case that
// the ghost cell width is >= 3.
const I& i_intr0 = i_intr;
I i_intr2 = i_intr;
i_intr2(d) += 2*i_shft(d);
I i_intr3 = i_intr2;
i_intr3(d) += i_shft(d);
const double& f0 = patch_data(i_intr0,depth);
const double& f2 = patch_data(i_intr2,depth);
const double& f3 = patch_data(i_intr3,depth);
const double x = std::abs(i(d)-i_intr(d));
return (1.0/3.0*f3-1.0/2.0*f2+1.0/6.0*f0)*x*x+(-2.0/3.0*f3+3.0/2.0*f2-5.0/6.0*f0)*x+f0;
#endif
}
}
}
else
{
return compute_linear_extrap(patch_data, i, i_intr, i_shft, depth);
}
return 0.0; // this statement should not be reached
}// compute_quadratic_extrap