cw_fields.cpp

/* Copyright (C) 2005-2020 Massachusetts Institute of Technology.
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#include "meep_internals.hpp"
#include "bicgstab.hpp"

using namespace std;

namespace meep {

static void fields_to_array(const fields &f, complex<realnum> *x) {
  size_t ix = 0;
  for (int i = 0; i < f.num_chunks; i++)
    if (f.chunks[i]->is_mine()) FOR_COMPONENTS(c) {
        if (is_D(c) || is_B(c)) {
          realnum *fr, *fi;
#define COPY_FROM_FIELD(fld)                                                                       \
  if ((fr = f.chunks[i]->fld[0]) && (fi = f.chunks[i]->fld[1]))                                    \
    LOOP_OVER_VOL_OWNED(f.chunks[i]->gv, c, idx)                                                   \
  x[ix++] = complex<double>(fr[idx], fi[idx]);
          COPY_FROM_FIELD(f[c]);
          COPY_FROM_FIELD(f_u[c]);
          COPY_FROM_FIELD(f_cond[c]);
          component c2 = field_type_component(is_D(c) ? E_stuff : H_stuff, c);
          COPY_FROM_FIELD(f_w[c2]);
          if (f.chunks[i]->f_w[c2][0]) COPY_FROM_FIELD(f[c2]);
#undef COPY_FROM_FIELD
        }
      }
}

static void array_to_fields(const complex<realnum> *x, fields &f) {
  size_t ix = 0;
  for (int i = 0; i < f.num_chunks; i++)
    if (f.chunks[i]->is_mine()) FOR_COMPONENTS(c) {
        if (is_D(c) || is_B(c)) {
          realnum *fr, *fi;
#define COPY_TO_FIELD(fld)                                                                         \
  if ((fr = f.chunks[i]->fld[0]) && (fi = f.chunks[i]->fld[1]))                                    \
    LOOP_OVER_VOL_OWNED(f.chunks[i]->gv, c, idx) {                                                 \
      fr[idx] = real(x[ix]);                                                                       \
      fi[idx] = imag(x[ix++]);                                                                     \
    }
          COPY_TO_FIELD(f[c]);
          COPY_TO_FIELD(f_u[c]);
          COPY_TO_FIELD(f_cond[c]);
          component c2 = field_type_component(is_D(c) ? E_stuff : H_stuff, c);
          COPY_TO_FIELD(f_w[c2]);
          if (f.chunks[i]->f_w[c2][0]) COPY_TO_FIELD(f[c2]);
#undef COPY_TO_FIELD
        }
      }

  f.step_boundaries(D_stuff);
  f.update_eh(E_stuff, true);
  f.step_boundaries(E_stuff);

  /* done in f.step before updating D:
  f.step_boundaries(B_stuff);
  f.update_eh(H_stuff);
  f.step_boundaries(H_stuff); */
}

typedef struct {
  size_t n;
  fields *f;
  complex<double> iomega;
} fieldop_data;

static void fieldop(const realnum *xr, realnum *yr, void *data_) {
  const complex<realnum> *x = reinterpret_cast<const complex<realnum> *>(xr);
  complex<realnum> *y = reinterpret_cast<complex<realnum> *>(yr);
  fieldop_data *data = (fieldop_data *)data_;
  array_to_fields(x, *data->f);
  data->f->step();
  fields_to_array(*data->f, y);
  size_t n = data->n;
  realnum dt_inv = 1.0 / data->f->dt;
  complex<realnum> iomega = complex<realnum>(real(data->iomega), imag(data->iomega));
  for (size_t i = 0; i < n; ++i)
    y[i] = (y[i] - x[i]) * dt_inv + iomega * x[i];
}

// Rayleigh-quotient estimate <x,Ax>/<x,x> for eigenfrequency given approximate eigenvector x (length n),
// overwriting x with Ax and b with x/|x|.
static complex<double> estimate_eigfreq(complex<realnum> *b, complex<realnum> *x, size_t n, fieldop_data *data) {
  memcpy(b, x, n * sizeof(complex<realnum>));
  fieldop(reinterpret_cast<realnum *>(b), reinterpret_cast<realnum *>(x), (void *) data);
  complex<double> bdotx(0,0);
  double bnorm2 = 0;
  for (size_t i = 0; i < n; ++i) {
    complex<realnum> bi = b[i];
    bnorm2 += real(bi)*real(bi) + imag(bi)*imag(bi);
    complex<realnum> bx = conj(bi) * x[i];
    bdotx += complex<double>(real(bx), imag(bx));
  }
  bnorm2 = sum_to_all(bnorm2);
  bdotx = sum_to_all(bdotx);
  double bnorminv = 1/sqrt(bnorm2);
  for (size_t i = 0; i < n; ++i) {
    b[i] *= bnorminv; // normalize b for subsequent shift-and-invert iterations
  }
  complex<double> iomega = data->iomega - bdotx/bnorm2; // unshifted eigenvalue
  // now, invert: iomega = (1 - exp(-i * (2 * pi * frequency) * dt)) / dt)
  // to get frequency = log(1 - iomega * dt) / (-2 pi i * dt)
  double dt = data->f->dt;
  return log(1.0 - iomega*dt) / complex<double>(0, -2*pi*dt);
}

/* Solve for the CW (constant frequency) field response at the given
   frequency to the sources (with amplitude given by the current sources
   at the current time).  The solver halts at a fractional convergence
   of tol, or when maxiters is reached, or when convergence fails;
   returns true if convergence succeeds and false if it fails.

   The parameter L determines the order of the iterative algorithm
   that is used.  L should always be positive and should normally be
   >= 2.  Larger values of L will often lead to faster convergence, at
   the expense of more memory and more work per iteration.

   If the optional argument eigfreq is non-NULL, then the solver is used for a
   shift-and-invert power iteration to find the closest eigenfrequency and
   eigenvector to frequency: the solver is iterated up to eigiters times,
   or until the estimated eigenfreq stops changing by <= eigtol (relative). */
bool fields::solve_cw(double tol, int maxiters, complex<double> frequency, int L, complex<double> *eigfreq, double eigtol, int eigiters) {
  if (is_real) abort("solve_cw is incompatible with use_real_fields()");
  if (L < 1) abort("solve_cw called with L = %d < 1", L);
  int tsave = t; // save time (gets incremented by iterations)
  int iters;

  set_solve_cw_omega(2 * pi * frequency);

  step(); // step once to make sure everything is allocated

  size_t N = 0; // size of linear system (on this processor, at least)
  for (int i = 0; i < num_chunks; i++)
    if (chunks[i]->is_mine()) {
      FOR_COMPONENTS(c) {
        if (chunks[i]->f[c][0] && (is_D(c) || is_B(c))) {
          component c2 = field_type_component(is_D(c) ? E_stuff : H_stuff, c);
          /* unknowns are just D and B in non-PML regions, but in PML
             regions the E, U, W, and C fields are also unknowns (in
             principle, we might be able to compute these extra fields
             in frequency domain via scalinb by the appropriate s
             factors, rather than storing them, but I had some
             problems getting that working) */
          N += 2 * chunks[i]->gv.nowned(c) *
               (1 + (chunks[i]->f_u[c][0] != NULL) + (chunks[i]->f_w[c2][0] != NULL) * 2 +
                (chunks[i]->f_cond[c][0] != NULL));
        }
      }
    }

  iters = maxiters;
  size_t nwork = (size_t)bicgstabL(L, N, 0, 0, 0, 0, tol, &iters, 0, true);
  realnum *work = new realnum[nwork + 2 * N];
  complex<realnum> *x = reinterpret_cast<complex<realnum> *>(work + nwork);
  complex<realnum> *b = reinterpret_cast<complex<realnum> *>(work + nwork + N);

  fields_to_array(*this, x); // initial guess = initial fields

  // get J amplitudes from current time step
  zero_fields(); // note that we've saved the fields in x above
  calc_sources(time());
  step_source(B_stuff, true);
  step_boundaries(B_stuff);
  update_eh(H_stuff);
  calc_sources(time() + 0.5 * dt);
  step_source(D_stuff, true);
  step_boundaries(D_stuff);
  update_eh(E_stuff);
  fields_to_array(*this, b);
  double mdt_inv = -1.0 / dt;
  for (size_t i = 0; i < N / 2; ++i)
    b[i] *= mdt_inv;
  {
    double bmax = 0;
    for (size_t i = 0; i < N / 2; ++i) {
      double babs = abs(b[i]);
      if (babs > bmax) bmax = babs;
    }
    if (max_to_all(bmax) == 0.0) abort("zero current amplitudes in solve_cw");
  }

  fieldop_data data;
  data.f = this;
  data.n = N / 2;
  data.iomega = ((1.0 - exp(complex<double>(0., -1.) * (2 * pi * frequency) * dt)) * (1.0 / dt));
  iters = maxiters;

  int ierr = (int)bicgstabL(L, N, reinterpret_cast<realnum *>(x), fieldop, &data,
                            reinterpret_cast<realnum *>(b), tol, &iters, work, verbosity == 0);

  if (verbosity > 0) {
    master_printf("Finished solve_cw after %d CG iters (~ %d timesteps).\n", iters, iters * 2*L);
    if (ierr) master_printf(" -- CONVERGENCE FAILURE (%d) in solve_cw!\n", ierr);
  }

  // do additional shift-and-invert iterations to find eigenfrequency
  if (eigfreq) {
    *eigfreq = estimate_eigfreq(b, x, data.n, &data);
    if (verbosity > 0) {
      master_printf("Initial eigen-frequency estimate = %g%+gi\n", real(*eigfreq), imag(*eigfreq));
    }
    for (int eigiter = 0; eigiter < eigiters; ++eigiter) {
        iters = maxiters;
        int ierr = (int)bicgstabL(L, N, reinterpret_cast<realnum *>(x), fieldop, &data,
                                  reinterpret_cast<realnum *>(b), tol, &iters, work, verbosity == 0);
        complex<double> newfreq = estimate_eigfreq(b, x, data.n, &data);
        complex<double> dfreq = newfreq - *eigfreq;
         if (verbosity > 0) {
          master_printf("Eigensolver step %d: %d CG iters, freq = %g%+gi (change = %g%+gi).\n",
                        eigiter+1, iters, real(newfreq), imag(newfreq), real(dfreq), imag(dfreq));
          if (ierr) master_printf(" -- CONVERGENCE FAILURE (%d) in solve_cw!\n", ierr);
        }
        *eigfreq = newfreq;
        if (abs(dfreq) <= eigtol * abs(newfreq)) break; // converged
    }
    memcpy(x, b, N * sizeof(realnum));
  }

  array_to_fields(x, *this);
  step(); // ensure H/B are updated and synced with E/D

  delete[] work;
  t = tsave;

  unset_solve_cw_omega();
  update_dfts();

  return !ierr;
}

/* as solve_cw, but infers frequency from sources */
bool fields::solve_cw(double tol, int maxiters, int L, complex<double> *eigfreq, double eigtol, int eigiters) {
  complex<double> freq = 0.0;
  for (src_time *s = sources; s; s = s->next) {
    complex<double> sf = s->frequency();
    if (sf != freq && freq != 0.0 && sf != 0.0)
      abort("must pass frequency to solve_cw if sources do not agree");
    if (sf != 0.0) freq = sf;
  }
  if (freq == 0.0) abort("must pass frequency to solve_cw if sources do not specify one");
  return solve_cw(tol, maxiters, freq, L, eigfreq, eigtol, eigiters);
}

} // namespace meep