/*!
Returns maximum norm if p == 0
*/
template<class Grid_T> double get_diff_lp_norm(
const std::vector<uint64_t>& cells,
const Grid_T& grid,
const double p,
const double cell_volume,
const size_t dimension
) {
double local_norm = 0, global_norm = 0;
for (const auto& cell: cells) {
const auto* const cell_data = grid[cell];
if (cell_data == NULL) {
std::cerr << __FILE__ << ":" << __LINE__
<< ": No data for cell " << cell
<< std::endl;
abort();
}
const auto center = grid.geometry.get_center(cell);
if (p == 0) {
local_norm = std::max(
local_norm,
std::fabs(
(*cell_data)[Gradient()][dimension]
- grad_of_function(center[dimension])
)
);
} else {
local_norm += std::pow(
std::fabs(
(*cell_data)[Gradient()][dimension]
- grad_of_function(center[dimension])
),
p
);
}
}
local_norm *= cell_volume;
if (p == 0) {
MPI_Comm comm = grid.get_communicator();
MPI_Allreduce(&local_norm, &global_norm, 1, MPI_DOUBLE, MPI_MAX, comm);
MPI_Comm_free(&comm);
return global_norm;
} else {
MPI_Comm comm = grid.get_communicator();
MPI_Allreduce(&local_norm, &global_norm, 1, MPI_DOUBLE, MPI_SUM, comm);
MPI_Comm_free(&comm);
return std::pow(global_norm, 1.0 / p);
}
}
/*!
Returns maximum norm
*/
template<class Grid_T> std::array<double, 3> get_max_norm(
const std::vector<uint64_t>& cells,
const Grid_T& grid
) {
std::array<double, 3>
local_norm{{0, 0, 0}},
global_norm{{0, 0, 0}};
for (const auto& cell: cells) {
const auto* const cell_data = grid[cell];
if (cell_data == NULL) {
std::cerr << __FILE__ << ":" << __LINE__
<< ": No data for cell " << cell
<< std::endl;
abort();
}
const auto center = grid.geometry.get_center(cell);
const auto grad_of = grad_of_function(center);
for (size_t i = 0; i < 3; i++) {
local_norm[i] = std::max(
local_norm[i],
std::fabs((*cell_data)[Gradient()][i] - grad_of[i])
);
}
}
MPI_Comm comm = grid.get_communicator();
MPI_Allreduce(
local_norm.data(),
global_norm.data(),
3,
MPI_DOUBLE,
MPI_MAX,
comm
);
MPI_Comm_free(&comm);
return global_norm;
}