convergence_test.cpp

//
// Created by jstark on 27.05.21.
//
#define BOOST_TEST_DYN_LINK
//#define BOOST_TEST_MAIN  // in only one cpp file
#include <boost/test/unit_test.hpp>
 
// Include redistancing files
#include "util/PathsAndFiles.hpp"
#include "level_set/redistancing_Sussman/RedistancingSussman.hpp"
#include "level_set/redistancing_Sussman/NarrowBand.hpp"
// Include header files for testing
#include "Draw/DrawSphere.hpp"
#include "l_norms/LNorms.hpp"
#include "analytical_SDF/AnalyticalSDF.hpp"
 
 
 
BOOST_AUTO_TEST_SUITE(ConvergenceTestSuite)
    typedef double phi_type;
    typedef double space_type;
    const phi_type EPSILON = std::numeric_limits<phi_type>::epsilon();
    
    space_type get_min_required_time_step(size_t Nmax, space_type b_low, space_type b_up, int dims)
    {
        space_type dx = (b_up - b_low) / (space_type) Nmax;
        space_type sum = 0;
        for (int d = 0; d < dims; d++)
        {
            sum += 1 / dx;
        }
        return 0.1 / sum;
    }
 
    BOOST_AUTO_TEST_CASE(RedistancingSussman_convergence_test_1D)
    {
        // CFL dt in 1D for N=64 and c=1 is 0.000503905
        
        const size_t grid_dim = 1;
        // some indices
        const size_t x = 0;
        
        const size_t Phi_0_grid = 0;
        const size_t SDF_sussman_grid = 1;
        const size_t SDF_exact_grid = 2;
        const size_t Error_grid = 3;
        
        const space_type box_lower = -1.0;
        const space_type box_upper = 1.0;
        Box<grid_dim, space_type> box({box_lower}, {box_upper});
        Ghost<grid_dim, long int> ghost(0);
        typedef aggregate<phi_type, phi_type, phi_type, phi_type> props;
        typedef grid_dist_id<grid_dim, space_type, props> grid_in_type;
        
//      space_type dt = 0.000503905;
        size_t Nmin = 32;
        size_t Nmax = 4096;
        space_type dt = get_min_required_time_step(Nmax, box_lower, box_upper, grid_dim);
        for (size_t N = Nmin; N <= Nmax; N*=2)
        {
            const size_t sz[grid_dim] = {N};
            grid_in_type g_dist(sz, box, ghost);
            g_dist.setPropNames({"Phi_0", "SDF_sussman", "SDF_exact", "Relative error"});
            
            // Now we initialize the grid with the indicator function and the analytical solution
            auto dom = g_dist.getDomainIterator();
            while(dom.isNext())
            {
                auto key = dom.get();
                Point<grid_dim, space_type> coords = g_dist.getPos(key);
                g_dist.template get<Phi_0_grid>(key) = sgn(coords.get(x));
                g_dist.template get<SDF_exact_grid>(key) = coords.get(x);
                ++dom;
            }
            
            {
                Redist_options<phi_type> redist_options;
                redist_options.min_iter = 1e3;
                redist_options.max_iter = 1e16;
                
                // set both convergence criteria to false s.t. termination only when max_iterations reached
                redist_options.convTolChange.check = true;    // define here which of the convergence criteria above should
                // be used. If both are true, termination only occurs when both are fulfilled or when iter > max_iter
                redist_options.convTolChange.value = EPSILON;
                
                redist_options.convTolResidual.check = false;    // (default: false)
                redist_options.interval_check_convergence = 1000;        // interval of #iterations at which
                // convergence is checked (default: 100)
                redist_options.width_NB_in_grid_points = 10;        // width of narrow band in number of grid points.
                // Must
                // be at least 4, in order to have at least 2 grid points on each side of the interface. (default: 4)
                redist_options.print_current_iterChangeResidual = true;     // if true, prints out every current iteration + corresponding change from the previous iteration + residual from SDF (default: false)
                redist_options.print_steadyState_iter = true;     // if true, prints out the final iteration number when steady state was reached + final change + residual (default: true)
                
                RedistancingSussman<grid_in_type, phi_type> redist_obj(g_dist,
                                                             redist_options);   // Instantiation of Sussman-redistancing class
                std::cout << "CFL dt = " << redist_obj.get_time_step() << std::endl;
                redist_obj.set_user_time_step(dt);
                std::cout << "dt set to = " << dt << std::endl;
                // Run the redistancing. in the <> brackets provide property-index where 1.) your initial Phi is stored and 2.) where the resulting SDF should be written to.
                redist_obj.run_redistancing<Phi_0_grid, SDF_sussman_grid>();
                
                // Compute the absolute error between analytical and numerical solution at each grid point
                get_absolute_error<SDF_sussman_grid, SDF_exact_grid, Error_grid>(g_dist);
//              g_dist.write("grid_postRedistancing", FORMAT_BINARY);
                //  Get narrow band: Place particles on interface (narrow band width e.g. 4 grid points on each side of the
                //  interface)
                size_t bc[grid_dim] = {NON_PERIODIC};
                typedef aggregate<phi_type> props_nb;
                typedef vector_dist<grid_dim, space_type, props_nb> vd_type;
                Ghost<grid_dim, space_type> ghost_vd(0);
                vd_type vd_narrow_band(0, box, bc, ghost_vd);
                vd_narrow_band.setPropNames({"error"});
                const size_t Error_vd = 0;
                // Compute the L_2- and L_infinity-norm and save to file
                NarrowBand<grid_in_type, phi_type> narrowBand_points(g_dist, redist_options.width_NB_in_grid_points ); // Instantiation of
                // NarrowBand class
                narrowBand_points.get_narrow_band_copy_specific_property<SDF_sussman_grid, Error_grid, Error_vd>(g_dist,
                                                                                                                 vd_narrow_band);
//              vd_narrow_band.write("vd_error_N" + std::to_string(N), FORMAT_BINARY);
//              vd_narrow_band.save("test_data/output/vd_nb8p_error" + std::to_string(N) + ".bin");
                // Compute the L_2- and L_infinity-norm and save to file
                LNorms<phi_type> lNorms_vd;
                lNorms_vd.get_l_norms_vector<Error_vd>(vd_narrow_band);
                lNorms_vd.write_to_file(N, 6, "l_norms_", "./");
            }
            
        }
    }
    
    BOOST_AUTO_TEST_CASE(RedistancingSussman_convergence_test_3D)
    {
        const size_t grid_dim = 3;
        // some indices
        const size_t x                      = 0;
        const size_t y                      = 1;
        const size_t z                      = 2;
        
        const size_t Phi_0_grid             = 0;
        const size_t SDF_sussman_grid       = 1;
        const size_t SDF_exact_grid         = 2;
        const size_t Error_grid             = 3;
        
        for (size_t N=32; N <=128; N*=2)
        {
            const size_t sz[grid_dim] = {N, N, N};
            const space_type radius = 1.0;
            const space_type box_lower = 0.0;
            const space_type box_upper = 4.0 * radius;
            Box<grid_dim, space_type> box({box_lower, box_lower, box_lower}, {box_upper, box_upper, box_upper});
            Ghost<grid_dim, long int> ghost(0);
            typedef aggregate<phi_type, phi_type, phi_type, phi_type> props;
            typedef grid_dist_id<grid_dim, space_type, props > grid_in_type;
            grid_in_type g_dist(sz, box, ghost);
            g_dist.setPropNames({"Phi_0", "SDF_sussman", "SDF_exact", "Relative error"});
            
            const space_type center[grid_dim] = {0.5*(box_upper+box_lower), 0.5*(box_upper+box_lower), 0.5*(box_upper+box_lower)};
            init_grid_with_sphere<Phi_0_grid>(g_dist, radius, center[x], center[y], center[z]); // Initialize sphere onto grid
            
            int order = 1;
            {
                Redist_options<phi_type> redist_options;
                redist_options.min_iter                             = 1e3;
                redist_options.max_iter                             = 1e3;
                
                // set both convergence criteria to false s.t. termination only when max_iterations reached
                redist_options.convTolChange.check                  = false;    // define here which of the convergence criteria above should be used. If both are true, termination only occurs when both are fulfilled or when iter > max_iter
                redist_options.convTolResidual.check                = false;    // (default: false)
                
                redist_options.interval_check_convergence           = 100;        // interval of #iterations at which
                // convergence is checked (default: 100)
                redist_options.width_NB_in_grid_points              = 4;        // width of narrow band in number of
                // grid points. Must be at least 4, in order to have at least 2 grid points on each side of the interface. (default: 4)
                redist_options.print_current_iterChangeResidual     = true;     // if true, prints out every current iteration + corresponding change from the previous iteration + residual from SDF (default: false)
                redist_options.print_steadyState_iter               = true;     // if true, prints out the final iteration number when steady state was reached + final change + residual (default: true)
                
                RedistancingSussman<grid_in_type, phi_type> redist_obj(g_dist, redist_options);   // Instantiation of
                // Sussman-redistancing class
                //redist_obj.set_user_time_step(dt);
                //std::cout << "dt set to = " << dt << std::endl;
                // Run the redistancing. in the <> brackets provide property-index where 1.) your initial Phi is stored and 2.) where the resulting SDF should be written to.
                redist_obj.run_redistancing<Phi_0_grid, SDF_sussman_grid>();
                
                // Compute exact signed distance function at each grid point
                init_analytic_sdf_sphere<SDF_exact_grid>(g_dist, radius, center[x], center[y], center[z]);
                
                // Compute the absolute error between analytical and numerical solution at each grid point
                get_absolute_error<SDF_sussman_grid, SDF_exact_grid, Error_grid>(g_dist);
                
                
                //  Get narrow band: Place particles on interface (narrow band width e.g. 4 grid points on each side of the
                //  interface)
                size_t bc[grid_dim] = {PERIODIC, PERIODIC, PERIODIC};
                typedef aggregate<phi_type> props_nb;
                typedef vector_dist<grid_dim, space_type, props_nb> vd_type;
                Ghost<grid_dim, space_type> ghost_vd(0);
                vd_type vd_narrow_band(0, box, bc, ghost_vd);
                vd_narrow_band.setPropNames({"error"});
                const size_t Error_vd = 0;
                // Compute the L_2- and L_infinity-norm and save to file
                NarrowBand<grid_in_type, phi_type> narrowBand_points(g_dist, redist_options.width_NB_in_grid_points); // Instantiation of NarrowBand class
                narrowBand_points.get_narrow_band_copy_specific_property<SDF_sussman_grid, Error_grid, Error_vd>(g_dist,
                                                                                                                 vd_narrow_band);
                vd_narrow_band.write("vd_nb4p_error_N" + std::to_string(N) + "_order" +
                std::to_string(order), FORMAT_BINARY);
//              vd_narrow_band.save("test_data/output/vd_nb8p_error" + std::to_string(N) + ".bin");
                // Compute the L_2- and L_infinity-norm and save to file
                LNorms<phi_type> lNorms_vd;
                lNorms_vd.get_l_norms_vector<Error_vd>(vd_narrow_band);
                lNorms_vd.write_to_file(N, 6, "l_norms_vd_absError_4p_order" + std::to_string(order), "./");
                
//              32,0.044692,0.066994
//              64,0.010542,0.018396
//              128,0.003301,0.009491
 
                switch(N)
                {
                    case 32:
                        BOOST_CHECK(lNorms_vd.l2   < 0.044693);
                        BOOST_CHECK(lNorms_vd.linf < 0.066995);
                        break;
                    case 64:
                        BOOST_CHECK(lNorms_vd.l2   < 0.010543);
                        BOOST_CHECK(lNorms_vd.linf < 0.018397);
                        break;
                    case 128:
                        BOOST_CHECK(lNorms_vd.l2   < 0.003302);
                        BOOST_CHECK(lNorms_vd.linf < 0.009492);
                        break;
                }
            
            }
        }
    }
    
BOOST_AUTO_TEST_SUITE_END()