helmholtz_burton_miller_solver.hpp

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#ifndef NIHU_HELMHOLTZ_BURTON_MILLER_SOLVER_HPP_INCLUDED
#define NIHU_HELMHOLTZ_BURTON_MILLER_SOLVER_HPP_INCLUDED
 
#include "cluster_tree.hpp"
#include "elem_center_iterator.hpp"
#include "fmm_indexed.hpp"
#include "fmm_integrated.hpp"
#include "fmm_matrix.hpp"
#include "fmm_operator_collection.hpp"
#include "fmm_precompute.hpp"
#include "matrix_free.hpp"
#include "preconditioner.hpp"
 
#include "core/field.hpp"
#include "core/function_space.hpp"
#include "util/timer.h"
#include "util/type2tag.hpp"
 
#include <Eigen/IterativeLinearSolvers>
#include "GMRES.h"
 
#ifdef NIHU_FMM_PARALLEL
#include <omp.h>
#endif
 
namespace NiHu
{
namespace fmm
{
 
template <class Fmm, class TrialSpace>
class helmholtz_burton_miller_solver
{
public:
    typedef Fmm fmm_t;
    typedef TrialSpace trial_space_t;
 
    typedef dirac_space<trial_space_t> test_space_t;
    typedef Eigen::Matrix<std::complex<double>, Eigen::Dynamic, 1> excitation_t;
    typedef Eigen::Matrix<std::complex<double>, Eigen::Dynamic, 1> response_t;
 
    typedef typename fmm_t::cluster_t cluster_t;
    typedef cluster_tree<cluster_t> cluster_tree_t;
 
    typedef typename tmp::deref<
        typename tmp::begin<
        typename trial_space_t::field_type_vector_t
        >::type
    >::type trial_field_t;
 
    typedef type2tag<trial_field_t> trial_field_tag_t;
    typedef dirac_field<trial_field_t> test_field_t;
    typedef type2tag<test_field_t> test_field_tag_t;
 
    helmholtz_burton_miller_solver(trial_space_t const &trial_space)
        : m_trial_space(trial_space)
        , m_test_space(dirac(m_trial_space))
        , m_wave_number(0.0)
        , m_accuracy(3.0)
        , m_far_field_order(6)
        , m_iters(0)
        , m_restart(3000)
        , m_tolerance(1e-8)
    {
    }
 
    void set_restart(size_t restart)
    {
        m_restart = restart;
    }
 
    void set_tolerance(double tolerance)
    {
        m_tolerance = tolerance;
    }
 
    void set_wave_number(double k)
    {
        m_wave_number = k;
    }
 
    double get_wave_number() const
    {
        return m_wave_number;
    }
 
    response_t const &get_response() const
    {
        return m_response;
    }
 
    void set_excitation(excitation_t const &xct)
    {
        m_excitation = xct;
    }
 
    void set_accuracy(double accuracy)
    {
        m_accuracy = accuracy;
    }
 
    void set_far_field_order(size_t order)
    {
        m_far_field_order = order;
    }
 
    template <class DivideDerived>
    response_t const &solve(divide_base<DivideDerived> const &divide)
    {
        // build the cluster tree
        std::cout << "Building cluster tree ..." << std::endl;
        cluster_tree_t tree(
            create_field_center_iterator(m_trial_space.template field_begin<trial_field_t>()),
            create_field_center_iterator(m_trial_space.template field_end<trial_field_t>()),
            divide.derived());
 
        
        std::cout << "Tree:\n" << tree << std::endl;
        
        // instantiate the fmm object
        std::cout << "Instantiating fmm object ..." << std::endl;
        fmm_t fmm(m_wave_number);
        fmm.set_accuracy(m_accuracy);
 
        // initialize tree data
        std::cout << "Initializing tree data ..." << std::endl;
        fmm.init_level_data(tree);
        for (size_t c = 0; c < tree.get_n_clusters(); ++c)
            tree[c].set_p_level_data(&fmm.get_level_data(tree[c].get_level()));
 
#if NIHU_FMM_PARALLEL
        auto max_num_threads = omp_get_max_threads();
        std::cout << "Expanding to " << max_num_threads << " threads" << std::endl;
        for (size_t i = 0; i < tree.get_n_levels(); ++i)
            fmm.get_level_data(i).set_num_threads(max_num_threads);
#endif
 
        // create interaction lists
        std::cout << "Computing interaction lists..." << std::endl;
        interaction_lists lists(tree);
 
        // create functors
        auto int_fctr = create_integrated_functor(test_field_tag_t(), trial_field_tag_t(),
            m_far_field_order, true);
 
        auto idx_fctr = create_indexed_functor(
            m_test_space.template field_begin<test_field_t>(),
            m_test_space.template field_end<test_field_t>(),
            m_trial_space.template field_begin<trial_field_t>(),
            m_trial_space.template field_end<trial_field_t>(),
            tree);
 
        auto pre_fctr = create_precompute_functor(tree, lists);
 
        // Burton-Miller coupling constant
        std::complex<double> alpha(0.0, -1.0 / m_wave_number);
 
        // integration
        auto I = create_identity_p2p_integral(type2tag<test_field_t>(), type2tag<trial_field_t>());
        auto lhs_collection = create_fmm_operator_collection(
            int_fctr(fmm.template create_p2p<0, 1>())
                + alpha * int_fctr(fmm.template create_p2p<1, 1>())
                - 0.5 * I,
            int_fctr(fmm.template create_p2m<1>()),
            int_fctr(fmm.template create_p2l<1>()),
            int_fctr(fmm.template create_m2p<0>())
                + alpha * int_fctr(fmm.template create_m2p<1>()),
            int_fctr(fmm.template create_l2p<0>())
                + alpha * int_fctr(fmm.template create_l2p<1>()),
            fmm.create_m2m(),
            fmm.create_m2l(),
            fmm.create_l2l()
        );
 
        auto rhs_collection = create_fmm_operator_collection(
            int_fctr(fmm.template create_p2p<0, 0>())
                + alpha * int_fctr(fmm.template create_p2p<1, 0>())
                + (alpha / 2.0) * I,
            int_fctr(fmm.template create_p2m<0>()),
            int_fctr(fmm.template create_p2l<0>())
        );
 
        // indexing
        auto lhs_cix_collection = lhs_collection.transform(idx_fctr);
        auto rhs_cix_collection = rhs_collection.transform(idx_fctr);
 
        // precomputation
        std::cout << "Precomputing fmm operators ..." << std::endl;
        auto lhs_pre_collection = lhs_cix_collection.transform(pre_fctr);
 
        // create rhs matrix object
        std::cout << "Assembling rhs matrix ..." << std::endl;
        auto slp_matrix = create_fmm_matrix(
            pre_fctr(rhs_cix_collection.get(p2p_tag())),
            rhs_cix_collection.get(p2m_tag()),
            rhs_cix_collection.get(p2l_tag()),
            lhs_pre_collection.get(m2p_tag()),
            lhs_pre_collection.get(l2p_tag()),
            lhs_pre_collection.get(m2m_tag()),
            lhs_pre_collection.get(l2l_tag()),
            lhs_pre_collection.get(m2l_tag()),
            tree, lists);
 
        // compute rhs with fmbem
        std::cout << "Computing rhs ..." << std::endl;
        response_t rhs = slp_matrix * m_excitation;
 
        // create matrix object
        std::cout << "Assembling lhs matrix ..." << std::endl;
        auto dlp_matrix = create_fmm_matrix(
            lhs_pre_collection,
            tree, lists);
 
        // compute solution
        std::cout << "Starting iterative solution ..." << std::endl;
        auto M = create_matrix_free(dlp_matrix);
 
        Eigen::GMRES<decltype(M), Eigen::IdentityPreconditioner > solver(M);
        solver.setTolerance(m_tolerance);
        solver.set_restart(m_restart);
        m_response = solver.solve(rhs);
        m_iters = solver.iterations();
 
        return m_response;
    }
 
    size_t get_iterations() const
    {
        return m_iters;
    }
 
private:
    trial_space_t const &m_trial_space;
    test_space_t const &m_test_space;
 
    double m_wave_number;
    double m_accuracy;
    size_t m_far_field_order;
    excitation_t m_excitation;
    response_t m_response;
    size_t m_iters;
    size_t m_restart;
    double m_tolerance;
};
 
template <class FmmTag, class TrialSpace>
auto create_helmholtz_burton_miller_solver(FmmTag, TrialSpace const& trial_space)
{
    return helmholtz_burton_miller_solver<typename tag2type<FmmTag>::type, TrialSpace>(trial_space);
}
 
} // end of namespace fmm
} // end of namespace NiHu
 
#endif /* NIHU_HELMHOLTZ_BURTON_MILLER_SOLVER_HPP_INCLUDED */