File: step_db.cpp

package info (click to toggle)
meep-mpich2 1.7.0-3
  • links: PTS, VCS
  • area: main
  • in suites: bullseye, buster, sid
  • size: 25,824 kB
  • sloc: cpp: 27,370; python: 10,574; lisp: 1,213; makefile: 440; sh: 28
file content (418 lines) | stat: -rw-r--r-- 17,534 bytes parent folder | download | duplicates (5)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
/* Copyright (C) 2005-2015 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, 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 <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>

#include "meep.hpp"
#include "meep_internals.hpp"

#define RESTRICT

using namespace std;

namespace meep {

void fields::step_db(field_type ft) {
  for (int i=0;i<num_chunks;i++)
    if (chunks[i]->is_mine())
      if (chunks[i]->step_db(ft))
      	chunk_connections_valid = false;

  /* synchronize to avoid deadlocks in connect_the_chunks */
  chunk_connections_valid = and_to_all(chunk_connections_valid);
}

bool fields_chunk::step_db(field_type ft) {
  bool allocated_u = false;

  if (ft != B_stuff && ft != D_stuff)
    abort("bug - step_db should only be called for B or D");

  DOCMP FOR_FT_COMPONENTS(ft, cc)
    if (f[cc][cmp]) {
      const component c_p=plus_component[cc], c_m=minus_component[cc];
      const direction d_deriv_p = plus_deriv_direction[cc];
      const direction d_deriv_m = minus_deriv_direction[cc];
      const direction d_c = component_direction(cc);
      const bool have_p = have_plus_deriv[cc];
      const bool have_m = have_minus_deriv[cc];
      const direction dsig0 = cycle_direction(gv.dim,d_c,1);
      const direction dsig = s->sigsize[dsig0] > 1 ? dsig0 : NO_DIRECTION;
      const direction dsigu0 = cycle_direction(gv.dim,d_c,2);
      const direction dsigu = s->sigsize[dsigu0] > 1 ? dsigu0 : NO_DIRECTION;
      ptrdiff_t stride_p = have_p?gv.stride(d_deriv_p):0;
      ptrdiff_t stride_m = have_m?gv.stride(d_deriv_m):0;
      realnum *f_p = have_p?f[c_p][cmp]:NULL;
      realnum *f_m = have_m?f[c_m][cmp]:NULL;
      realnum *the_f = f[cc][cmp];

      if (dsig != NO_DIRECTION
	  && s->conductivity[cc][d_c] && !f_cond[cc][cmp]) {
	f_cond[cc][cmp] = new realnum[gv.ntot()];
	memset(f_cond[cc][cmp], 0, sizeof(realnum) * gv.ntot());
      }
      if (dsigu != NO_DIRECTION && !f_u[cc][cmp]) {
	f_u[cc][cmp] = new realnum[gv.ntot()];
	memcpy(f_u[cc][cmp], the_f, gv.ntot() * sizeof(realnum));
	allocated_u = true;
      }

      if (ft == D_stuff) { // strides are opposite sign for H curl
	stride_p = -stride_p;
	stride_m = -stride_m;
      }

      if (gv.dim == Dcyl) switch (d_c) {
      case R:
	f_p = NULL; // im/r Fz term will be handled separately
	break;
      case P:
	break; // curl works normally for phi component
      case Z: {
	f_m = NULL; // im/r Fr term will be handled separately

	/* Here we do a somewhat cool hack: the update of the z
	   component gives a 1/r d(r Fp)/dr term, rather than
	   just the derivative dg/dr expected in step_curl.
	   Rather than duplicating all of step_curl to handle
	   this bloody derivative, however, we define a new
	   array f_rderiv_int which is the integral of 1/r d(r Fp)/dr,
	   so that we can pass it to the unmodified step_curl
	   and get the correct derivative.  (More precisely,
	   the derivative and integral are replaced by differences
	   and sums, but you get the idea). */
	if (!f_rderiv_int) f_rderiv_int = new realnum[gv.ntot()];
	double ir0 = gv.origin_r() * gv.a
	  + 0.5 * gv.iyee_shift(c_p).in_direction(R);
	for (int iz = 0; iz <= gv.nz(); ++iz) f_rderiv_int[iz] = 0;
	int sr = gv.nz() + 1;
	for (int ir = 1; ir <= gv.nr(); ++ir) {
	  double rinv = 1.0 / ((ir+ir0)-0.5);
	  for (int iz = 0; iz <= gv.nz(); ++iz) {
	    ptrdiff_t idx = ir*sr + iz;
	    f_rderiv_int[idx] = f_rderiv_int[idx - sr] +
	      rinv * (f_p[idx] * (ir+ir0) - f_p[idx - sr] * ((ir-1)+ir0));
	  }
	}
	f_p = f_rderiv_int;
	break;
      }
      default: abort("bug - non-cylindrical field component in Dcyl");
      }

      STEP_CURL(the_f, cc, f_p, f_m, stride_p, stride_m, gv, Courant,
		dsig, s->sig[dsig], s->kap[dsig], s->siginv[dsig],
		f_u[cc][cmp], dsigu, s->sig[dsigu], s->kap[dsigu], s->siginv[dsigu],
		dt,
		s->conductivity[cc][d_c], s->condinv[cc][d_c],f_cond[cc][cmp]);
    }

  /* In 2d with beta != 0, add beta terms.  This is a trick to model
     an exp(i beta z) z-dependence but without requiring a "3d"
     calculation and without requiring complex fields.  Looking at the
     z=0 2d cross-section, the exp(i beta z) term adds an i \beta
     \hat{z} \times cross-product to the curls, which couples the TE
     and TM polarizations.  However, to avoid complex fields, in the
     case of real fields we implicitly store i*(TM fields) rather than
     the TM fields, in which case the i's cancel in the update
     equations.  (Mathematically, this is equivalent to looking at the
     superposition of the fields at beta and the timereversed fields
     at -beta.)  The nice thing about this is that most calculations
     of flux, energy, etcetera, are insensitive to this implicit "i"
     factor.   For complex fields, we implement i*beta directly. */
  if (gv.dim == D2 && beta != 0) DOCMP for (direction d_c=X; d_c <= Y;
					   d_c = direction(d_c + 1)) {
    component cc = direction_component(first_field_component(ft), d_c);
    component c_g = direction_component(ft == D_stuff ? Hx : Ex,
					d_c == X ? Y : X);
    realnum *the_f = f[cc][cmp];
    const realnum *g = f[c_g][1-cmp] ? f[c_g][1-cmp] : f[c_g][cmp];
    const direction dsig0 = cycle_direction(gv.dim,d_c,1);
    const direction dsig = s->sigsize[dsig0] > 1 ? dsig0 : NO_DIRECTION;
    const direction dsigu0 = cycle_direction(gv.dim,d_c,2);
    const direction dsigu = s->sigsize[dsigu0] > 1 ? dsigu0 : NO_DIRECTION;
    const double betadt = 2 * pi * beta * dt * (d_c == X ? +1 : -1)
      * (f[c_g][1-cmp] ? (ft == D_stuff ? -1 : +1) * (2*cmp-1) : 1);
    STEP_BETA(the_f, cc, g, gv, betadt,
	      dsig, s->siginv[dsig],
	      f_u[cc][cmp], dsigu, s->siginv[dsigu],
	      s->condinv[cc][d_c], f_cond[cc][cmp]);
  }

  // in cylindrical coordinates, we now have to add the i*m/r terms... */
  if (gv.dim == Dcyl && m != 0) DOCMP FOR_FT_COMPONENTS(ft, cc) {
    const direction d_c = component_direction(cc);
    if (f[cc][cmp] && (d_c == R || d_c == Z)) {
      const component c_g = d_c==R ? plus_component[cc] : minus_component[cc];
      const realnum *g = f[c_g][1-cmp];
      realnum *the_f = f[cc][cmp];
      const realnum *cndinv = s->condinv[cc][d_c];
      realnum *fcnd = f_cond[cc][cmp];
      realnum *fu = f_u[cc][cmp];
      const direction dsig = cycle_direction(gv.dim,d_c,1);
      const double *siginv = s->sigsize[dsig] > 1 ? s->siginv[dsig] : 0;
      const int dk = gv.iyee_shift(cc).in_direction(dsig);
      const direction dsigu = cycle_direction(gv.dim,d_c,2);
      const double *siginvu = s->sigsize[dsigu] > 1 ? s->siginv[dsigu] : 0;
      const int dku = gv.iyee_shift(cc).in_direction(dsigu);
      const double the_m =
      	m * (1-2*cmp) * (1-2*(ft==B_stuff)) * (1-2*(d_c==R)) * Courant;
      const double ir0 = gv.origin_r() * gv.a
      	+ 0.5 * gv.iyee_shift(cc).in_direction(R);
      int sr = gv.nz() + 1;

      // 8 special cases of the same loop (sigh):
      if (siginv) { // PML in f update
      	if (siginvu) { // PML + fu
      	  if (cndinv) // PML + fu + conductivity
      	    //////////////////// MOST GENERAL CASE //////////////////////
      	    for (int ir = ir0 == 0; ir <= gv.nr(); ++ir) {
      	      double rinv = the_m / (ir+ir0);
      	      for (int iz = 0; iz <= gv.nz(); ++iz) {
            		ptrdiff_t idx = ir*sr + iz;
            		int k = dk + 2*(dsig==Z ? iz : ir);
            		int ku = dku + 2*(dsigu==Z ? iz : ir);
            		double df, dfcnd = rinv * g[idx] * cndinv[idx];
            		fcnd[idx] += dfcnd;
            		fu[idx] += (df = dfcnd * siginv[k]);
            		the_f[idx] += siginvu[ku] * df;
      	      }
      	    }
      	    /////////////////////////////////////////////////////////////
      	  else // PML + fu - conductivity
      	    for (int ir = ir0 == 0; ir <= gv.nr(); ++ir) {
      	      double rinv = the_m / (ir+ir0);
      	      for (int iz = 0; iz <= gv.nz(); ++iz) {
            		ptrdiff_t idx = ir*sr + iz;
            		int k = dk + 2*(dsig==Z ? iz : ir);
            		int ku = dku + 2*(dsigu==Z ? iz : ir);
            		double df, dfcnd = rinv * g[idx];
            		fu[idx] += (df = dfcnd * siginv[k]);
            		the_f[idx] += siginvu[ku] * df;
      	      }
      	    }
      	}
      	else { // PML - fu
      	  if (cndinv) // PML - fu + conductivity
      	    for (int ir = ir0 == 0; ir <= gv.nr(); ++ir) {
      	      double rinv = the_m / (ir+ir0);
      	      for (int iz = 0; iz <= gv.nz(); ++iz) {
            		ptrdiff_t idx = ir*sr + iz;
            		int k = dk + 2*(dsig==Z ? iz : ir);
            		double dfcnd = rinv * g[idx] * cndinv[idx];
            		fcnd[idx] += dfcnd;
            		the_f[idx] += dfcnd * siginv[k];
      	      }
      	    }
      	  else // PML - fu - conductivity
      	    for (int ir = ir0 == 0; ir <= gv.nr(); ++ir) {
      	      double rinv = the_m / (ir+ir0);
      	      for (int iz = 0; iz <= gv.nz(); ++iz) {
            		ptrdiff_t idx = ir*sr + iz;
            		int k = dk + 2*(dsig==Z ? iz : ir);
            		double dfcnd = rinv * g[idx];
            		the_f[idx] += dfcnd * siginv[k];
      	      }
      	    }
      	}
      }
      else { // no PML in f update
      	if (siginvu) { // no PML + fu
      	  if (cndinv) // no PML + fu + conductivity
      	    for (int ir = ir0 == 0; ir <= gv.nr(); ++ir) {
      	      double rinv = the_m / (ir+ir0);
      	      for (int iz = 0; iz <= gv.nz(); ++iz) {
            		ptrdiff_t idx = ir*sr + iz;
            		int ku = dku + 2*(dsigu==Z ? iz : ir);
            		double df = rinv * g[idx] * cndinv[idx];
            		fu[idx] += df;
            		the_f[idx] += siginvu[ku] * df;
      	      }
      	    }
      	  else // no PML + fu - conductivity
      	    for (int ir = ir0 == 0; ir <= gv.nr(); ++ir) {
      	      double rinv = the_m / (ir+ir0);
      	      for (int iz = 0; iz <= gv.nz(); ++iz) {
            		ptrdiff_t idx = ir*sr + iz;
            		int ku = dku + 2*(dsigu==Z ? iz : ir);
            		double df = rinv * g[idx];
            		fu[idx] += df;
            		the_f[idx] += siginvu[ku] * df;
      	      }
      	    }
      	}
      	else { // no PML - fu
      	  if (cndinv) // no PML - fu + conductivity
      	    for (int ir = ir0 == 0; ir <= gv.nr(); ++ir) {
      	      double rinv = the_m / (ir+ir0);
      	      for (int iz = 0; iz <= gv.nz(); ++iz) {
            		ptrdiff_t idx = ir*sr + iz;
            		the_f[idx] += rinv * g[idx] * cndinv[idx];
      	      }
      	    }
      	  else // no PML - fu - conductivity
      	    for (int ir = ir0 == 0; ir <= gv.nr(); ++ir) {
      	      double rinv = the_m / (ir+ir0);
      	      for (int iz = 0; iz <= gv.nz(); ++iz) {
            		ptrdiff_t idx = ir*sr + iz;
            		the_f[idx] += rinv * g[idx];
      	      }
      	    }
      	}
      }
    }
  }

#define ZERO_Z(array) memset(array, 0, sizeof(realnum)*(nz+1));

  // deal with annoying r=0 boundary conditions for m=0 and m=1
  if (gv.dim == Dcyl && gv.origin_r() == 0.0) DOCMP {
    const int nz = gv.nz();
    if (m == 0 && ft == D_stuff && f[Dz][cmp]) {
      // d(Dz)/dt = (1/r) * d(r*Hp)/dr
      const realnum *g = f[Hp][cmp];
      const realnum *cndinv = s->condinv[Dz][Z];
      realnum *fcnd = f_cond[Dz][cmp];
      const direction dsig = cycle_direction(gv.dim,Z,1);
      const double *siginv = s->sigsize[dsig] > 1 ? s->siginv[dsig] : 0;
      const int dk = gv.iyee_shift(Dz).in_direction(dsig);
      const direction dsigu = cycle_direction(gv.dim,Z,2);
      const double *siginvu = s->sigsize[dsigu] > 1 ? s->siginv[dsigu] : 0;
      const int dku = gv.iyee_shift(Dz).in_direction(dsigu);
      realnum *fu = siginvu && f_u[Dz][cmp] ? f[Dz][cmp] : 0;
      realnum *the_f = fu ? f_u[Dz][cmp] : f[Dz][cmp];
      for (int iz = 0; iz < nz; ++iz) {
      	// Note: old code (prior to Meep 0.2) was missing factor of 4??
      	double df, dfcnd = g[iz] * (Courant * 4) * (cndinv ? cndinv[iz] : 1);
      	if (fcnd) fcnd[iz] += dfcnd;
      	the_f[iz] += (df = dfcnd * (siginv ? siginv[dk + 2*(dsig==Z)*iz] : 1));
      	if (fu) fu[iz] += siginvu[dku + 2*(dsigu==Z)*iz] * df;
      }
      ZERO_Z(f[Dp][cmp]);
      if (f_cond[Dp][cmp]) ZERO_Z(f_cond[Dp][cmp]);
      if (f_u[Dp][cmp]) ZERO_Z(f_u[Dp][cmp]);
    }
    else if (m == 0 && ft == B_stuff && f[Br][cmp]) {
      ZERO_Z(f[Br][cmp]);
      if (f_cond[Br][cmp]) ZERO_Z(f_cond[Br][cmp]);
      if (f_u[Br][cmp]) ZERO_Z(f_u[Br][cmp]);
    }
    else if (fabs(m) == 1) {
      // D_stuff: d(Dp)/dt = d(Hr)/dz - d(Hz)/dr
      // B_stuff: d(Br)/dt = d(Ep)/dz - i*m*Ez/r
      component cc = ft == D_stuff ? Dp : Br;
      direction d_c = component_direction(cc);
      if (!f[cc][cmp]) continue;
      const realnum *f_p = f[ft == D_stuff ? Hr : Ep][cmp];
      const realnum *f_m = ft == D_stuff ? f[Hz][cmp]
      	: (f[Ez][1-cmp] + (nz+1));
      const realnum *cndinv = s->condinv[cc][d_c];
      realnum *fcnd = f_cond[cc][cmp];
      const direction dsig = cycle_direction(gv.dim,d_c,1);
      const double *siginv = s->sigsize[dsig] > 1 ? s->siginv[dsig] : 0;
      const int dk = gv.iyee_shift(cc).in_direction(dsig);
      const direction dsigu = cycle_direction(gv.dim,d_c,2);
      const double *siginvu = s->sigsize[dsigu] > 1 ? s->siginv[dsigu] : 0;
      const int dku = gv.iyee_shift(cc).in_direction(dsigu);
      realnum *fu = siginvu && f_u[cc][cmp] ? f[cc][cmp] : 0;
      realnum *the_f = fu ? f_u[cc][cmp] : f[cc][cmp];
      int sd = ft == D_stuff ? +1 : -1;
      double f_m_mult = ft == D_stuff ? 2 : (1-2*cmp);

      for (int iz = (ft == D_stuff); iz < nz + (ft == D_stuff); ++iz) {
      	double df;
      	double dfcnd = (sd*Courant) * (f_p[iz]-f_p[iz-sd] - f_m_mult*f_m[iz])
      	  * (cndinv ? cndinv[iz] : 1);
      	if (fcnd) fcnd[iz] += dfcnd;
      	the_f[iz] += (df = dfcnd * (siginv ? siginv[dk + 2*(dsig==Z)*iz] : 1));
      	if (fu) fu[iz] += siginvu[dku + 2*(dsigu==Z)*iz] * df;
      }
      if (ft == D_stuff) {
      	ZERO_Z(f[Dz][cmp]);
      	if (f_cond[Dz][cmp]) ZERO_Z(f_cond[Dz][cmp]);
      	if (f_u[Dz][cmp]) ZERO_Z(f_u[Dz][cmp]);
      }
    }
    else if (m != 0) { // m != {0,+1,-1}
      if (zero_fields_near_cylorigin) { /* default behavior */
      	/* I seem to recall David telling me that this was for numerical
      	   stability of some sort - the larger m is, the farther from
      	   the origin we need to be before we can use nonzero fields
      	   ... note that this is a fixed number of pixels for a given m,
      	   so it should still converge.  Still, this is weird...

      	   Update: experimentally, this seems to indeed be important
      	   for stability.  Setting these fields to zero, it seems to be
      	   stable with a Courant number < 0.62 or so for all m.  Without
      	   this, it becomes unstable unless we set the Courant number to
      	   about 1 / (|m| + 0.5) or less.

      	   Cons: setting fields near the origin to identically zero is
      	   somewhat unexpected for users, and probably spoils 2nd-order
      	   accuracy, and may not fix all stability issues anyway (based
      	   on anecdotal evidence from Alex M. of having to reduce Courant
      	   for large m). */
      	double rmax = fabs(m) - int(gv.origin_r()*gv.a+0.5);
      	if (ft == D_stuff)
      	  for (int r = 0; r <= gv.nr() && r < rmax; r++) {
      	    const int ir = r*(nz+1);
      	    ZERO_Z(f[Dp][cmp]+ir);
      	    ZERO_Z(f[Dz][cmp]+ir);
      	    if (f_cond[Dp][cmp]) ZERO_Z(f_cond[Dp][cmp]+ir);
      	    if (f_cond[Dz][cmp]) ZERO_Z(f_cond[Dz][cmp]+ir);
      	    if (f_u[Dp][cmp]) ZERO_Z(f_u[Dp][cmp]+ir);
      	    if (f_u[Dz][cmp]) ZERO_Z(f_u[Dz][cmp]+ir);
      	  }
      	else
      	  for (int r = 0; r <= gv.nr() && r < rmax; r++) {
      	    const int ir = r*(nz+1);
      	    ZERO_Z(f[Br][cmp]+ir);
      	    if (f_cond[Br][cmp]) ZERO_Z(f_cond[Br][cmp]+ir);
      	    if (f_u[Br][cmp]) ZERO_Z(f_u[Br][cmp]+ir);
      	  }
      }
      else {
      	/* Without David's hack: just set boundary conditions at r=0.
      	   This seems to be unstable unless we make the Courant number
      	   around 1 / (|m| + 0.5) or smaller.  Pros: probably maintains
      	   2nd-order accuracy, is more sane for r near zero.  Cons:
      	   1/(|m|+0.5) is purely empirical (no theory yet), and I'm not
      	   sure how universal it is.  Makes higher m's more expensive. */
      	if (ft == D_stuff) {
      	  ZERO_Z(f[Dp][cmp]);
      	  ZERO_Z(f[Dz][cmp]);
      	  if (f_cond[Dp][cmp]) ZERO_Z(f_cond[Dp][cmp]);
      	  if (f_cond[Dz][cmp]) ZERO_Z(f_cond[Dz][cmp]);
      	  if (f_u[Dp][cmp]) ZERO_Z(f_u[Dp][cmp]);
      	  if (f_u[Dz][cmp]) ZERO_Z(f_u[Dz][cmp]);
      	}
      	else {
      	  ZERO_Z(f[Br][cmp]);
      	  if (f_cond[Br][cmp]) ZERO_Z(f_cond[Br][cmp]);
      	  if (f_u[Br][cmp]) ZERO_Z(f_u[Br][cmp]);
      	}
      }
    }
  }

  return allocated_u;
}

} // namespace meep