Hello all
I wrote a semi-lagrangian code for advection which requires tracing
characteristics back in time and locating cell where it lies at previous time.
The simplest scheme would be like this
xf = x - a(x,t)*dt
u(x,t+dt) = u(xf, t)
My solution is in FE_Q<dim>(2). For each dof (x), I make a list of neighboring
cells
std::vector<std::set<typename DoFHandler<dim>::active_cell_iterator>> cells;
Then for each dof (x), I search for xf in this list. Here is a piece of the code
Functions::FEFieldFunction<dim> fe_fun (dof_handler, solution0);
for(auto v : interior_vertices) // update only interior dofs
{
Tensor<1,dim> vel1 = velocity1.value(support_points[v]);
Point<dim> p1 = support_points[v] - dt * vel1; // locate backward
characteristic
typename DoFHandler<dim>::active_cell_iterator cell1 = dof_handler.end();
for(auto cell : cells[v]) // Loop over cells around current dof
{
CellAccessor<dim> cell_accessor = CellAccessor<dim>(&triangulation,
cell->level(),
cell->index());
bool inside = cell_accessor.point_inside(p1);
if(inside)
{
cell1 = cell;
break;
}
}
AssertThrow(cell1 != dof_handler.end(),
ExcMessage("Did not find cell for p0"));
fe_fun.set_active_cell (cell1);
solution1(v) = fe_fun.value (p1);
}
This code works but it seems to be terribly slow even though I am setting the
active cell FEFieldFunction. Also, when I run it on my quad-core macbook pro,
the cpu usage is at 500% due to the call to FEFieldFunction.value() function !!!
Is there a way to make this faster, for locating the characteristic and
evaluating function ?
Thanks
praveen
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