newton.hh

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#pragma once
 
// standard library
#include <functional>
 
// external libraries
#include <deal.II/base/config.h>
#include <deal.II/base/timer.h>
#include <deal.II/lac/vector_memory.h>
 
namespace DiFfRG
{
  using namespace dealii;
 
  template <typename VectorType_> class Newton
  {
  public:
    using VectorType = VectorType_;
 
    Newton(double abstol_ = 1e-10, double reltol_ = 1e-6, double assemble_threshold_ = 0., uint max_steps_ = 21,
           uint n_stepsize_iterations_ = 21)
        : abstol(abstol_), reltol(reltol_), assemble_threshold(assemble_threshold_), max_steps(max_steps_),
          n_stepsize_iterations(n_stepsize_iterations_), ignore_nonconv(false)
    {
    }
 
    void reinit(const VectorType &u) { update_jacobian(u); }
 
    void operator()(VectorType &iterate)
    {
      Timer timer;
 
      converged = false;
      step = 0;
      resnorm = 1.;
      jacobians = 0;
 
      initial_vector = iterate;
      iterate_vector = iterate;
      VectorType &u = iterate_vector;
 
      GrowingVectorMemory<VectorType> mem;
      typename VectorMemory<VectorType>::Pointer Du(mem);
 
      Du->reinit(u);
      residual_vector.reinit(u);
 
      // fill res with (f(u), v)
      residual(residual_vector, u);
      if (!std::isfinite(residual_vector.l2_norm())) throw std::runtime_error("Initial residual non-finite!");
      resnorm = get_EEst();
      double old_residual = 0.;
      double assembly_time = 0.;
 
      while (check()) {
        step++;
 
        // assemble (Df(u), v)
        if ((step > 1) && (resnorm / old_residual >= assemble_threshold)) {
          Timer timer_assembly;
          update_jacobian(u);
          assembly_time += timer_assembly.wall_time();
          jacobians++;
        }
 
        Du->reinit(u);
        try {
          lin_solve(*Du.get(), residual_vector);
        } catch (std::exception &) {
          throw std::runtime_error("Linear solve failed!");
        }
 
        u.add(-1., *Du);
        old_residual = resnorm;
 
        residual(residual_vector, u);
        resnorm = get_EEst();
        if (!std::isfinite(residual_vector.l2_norm())) {
          std::cerr << "Residual non-finite!" << std::endl;
          throw std::runtime_error("Residual non-finite!");
        }
 
        // Simple line search: decrease the step size until the residual is smaller than the one in the step before
        uint step_size = 0;
        while (resnorm >= old_residual) {
          ++step_size;
          if (step_size > n_stepsize_iterations) {
            break;
          }
          u.add(1. / double(1 << step_size), *Du);
          residual(residual_vector, u);
          resnorm = get_EEst();
        }
      }
 
      timings_newton.push_back(timer.wall_time() - assembly_time);
 
      // in case of failure: throw exception
      if (!(converged || ignore_nonconv) || !std::isfinite(resnorm)) {
        throw std::runtime_error("Newton did not converge!");
      }
      // otherwise exit as normal
      else
        iterate = iterate_vector;
    }
 
    double threshold(const double thr)
    {
      const double t = assemble_threshold;
      assemble_threshold = thr;
      return t;
    }
 
    const VectorType &get_residual() const { return residual_vector; }
    const VectorType &get_initial() const { return initial_vector; }
    const VectorType &get_iterate() const { return iterate_vector; }
 
    double average_time_newton() const
    {
      double t = 0.;
      double n = timings_newton.size();
      for (const auto &t_ : timings_newton)
        t += t_ / n;
      return t;
    }
    uint num_newton_calls() const { return timings_newton.size(); }
 
    void set_ignore_nonconv(bool x) { ignore_nonconv = x; }
 
    std::function<void(VectorType &, const VectorType &)> residual;
    std::function<void(VectorType &, const VectorType &)> lin_solve;
    std::function<void(const VectorType &)> update_jacobian;
 
    double get_error() { return resnorm; }
 
    uint get_step() { return step; }
 
    uint get_jacobians() { return jacobians; }
 
  private:
    VectorType residual_vector;
    VectorType initial_vector;
    VectorType iterate_vector;
    double abstol, reltol, assemble_threshold;
    uint max_steps, n_stepsize_iterations;
 
    bool converged;
    bool ignore_nonconv;
    double resnorm;
    uint step, jacobians;
 
    std::vector<double> timings_newton;
 
    double get_EEst()
    {
      const VectorType &err = residual_vector;
      const VectorType &u_prev = initial_vector;
      const VectorType &u = iterate_vector;
 
      GrowingVectorMemory<VectorType> mem;
      typename VectorMemory<VectorType>::Pointer tmp(mem);
      tmp->reinit(u, true);
 
      using std::abs, std::max, std::sqrt;
      tbb::parallel_for(tbb::blocked_range<uint>(0, tmp->size()), [&](tbb::blocked_range<uint> r) {
        for (uint n = r.begin(); n < r.end(); ++n) {
          (*tmp)[n] = abs(err[n]) / (abstol + max(abs(u_prev[n]), abs(u[n])) * reltol);
        }
      });
      return tmp->l2_norm() / sqrt(tmp->size());
      return tmp->linfty_norm(); // tmp->l2_norm() / sqrt(tmp->size());
    }
 
    bool check()
    {
      if (step > max_steps) return false;
      if (step == 0) return true;
      double err = get_EEst();
      converged = err <= 1.;
      return !converged;
    }
  };
} // namespace DiFfRG