Vortex in Cell 3D (Optimization)

Vortex in Cell 3D ring with ringlets optimization

In this example we solve the Navier-Stokes equation in the vortex formulation in 3D for an incompressible fluid. This example has the following changes compared to Vortex in Cell 3D

• Constructing grid is expensive in particular with a lot of cores. For this reason we create the grid in the main function rather than in the comp_vel function and helmotz_hodge_projection
• Constructing also FDScheme is expensive so we construct it once in the main. We set the left hand side to the poisson operator, and inside the functions comp_vel and helmotz_hodge_projection just write the right hand side with impose_dit_b

    grid_type g_vort(szu,domain,g,bc);
    grid_type g_vel(g_vort.getDecomposition(),szu,g);
    grid_type g_dvort(g_vort.getDecomposition(),szu,g);
    particles_type particles(g_vort.getDecomposition(),0);

    // Construct an FDScheme is heavy so we construct it here
    // We also construct distributed temporal grids here because
    // they are expensive

    // Here we create temporal distributed grid, create a distributed grid is expensive we do it once outside
    // And the vectorial phi_v
    grid_type_s psi(g_vort.getDecomposition(),g_vort.getGridInfo().getSize(),g);
    grid_type phi_v(g_vort.getDecomposition(),g_vort.getGridInfo().getSize(),g);

    // In order to create a matrix that represent the poisson equation we have to indicate
    // we have to indicate the maximum extension of the stencil and we we need an extra layer
    // of points in case we have to impose particular boundary conditions.
    Ghost<3,long int> stencil_max(2);

    // We define a field phi_f
    typedef Field<phi,poisson_nn_helm> phi_f;

    // We assemble the poisson equation doing the
    // poisson of the Laplacian of phi using Laplacian
    // central scheme (where the both derivative use central scheme, not
    // forward composed backward like usually)
    typedef Lap<phi_f,poisson_nn_helm,CENTRAL_SYM> poisson;

    FDScheme<poisson_nn_helm> fd(stencil_max, domain, psi);

    fd.template impose_dit<0>(poisson(),psi,psi.getDomainIterator());

    fd.new_b();
    fd.template impose_dit_b<0>(psi,psi.getDomainIterator());

Another optimization that we do is to use a Hilbert space-filling curve as sub-sub-domain distribution strategy