Algorithm

In Samurai, two different algorithms are implemented to browse all the cells of the mesh in order to apply some operator on them. The choice depends on whether one has a local operator, that is, utilizing information belonging only to one cell without interaction with the neighbors; or an operator encoding some interaction with the surrounding cells.

If the operator is local, one can use samurai::for_each_cell(), otherwise, when the operator has an extended stencil, one can employ samurai::for_each_interval().

Note

samurai::for_each_interval() can be easily used in every situation.

Apply a function on all cells

In the previous section, we have seen that we can access the data field using Cell. The algorithm in samurai::for_each_cell() browses all the cells of the mesh and applies a lambda function on them. It can be useful, for example, when one wants to initialize a field.

Let us give an example

auto u = samurai::make_field<double, 1>("my_field", mesh);

samurai::for_each_cell(mesh, [&](auto cell)
{
    auto x = cell.center(0);
    auto y = cell.center(1);

    u[cell] = cos(x)*sin(y);
});

The first parameter is the mesh we want to navigate through and the second parameter is a lambda function with one parameter: the cell. We have used the procedure center() of the Cell class to recover the spatial coordinates of the cell center.

Apply a function using intervals

As suggested before, we can also evaluate a function on a given interval using samurai::for_each_interval() as illustrated in the following example

auto u = samurai::make_field<double, 1>("my_field", mesh);

samurai::for_each_interval(mesh, [&](std::size_t level, const auto& interval, const auto& index)
{
    auto i = interval;
    auto j = index[0];
    u(level, i, j) = i;
});

The first parameter is the mesh where we want to browse all the intervals and the second parameter is again a lambda function. This function takes three parameters: the level of the intervals we want to pick, the interval in the x-direction, and index[dim-1] an array with the index for the other dimensions.