/
ref_metric.c
3431 lines (3086 loc) · 121 KB
/
ref_metric.c
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/* Copyright 2014 United States Government as represented by the
* Administrator of the National Aeronautics and Space
* Administration. No copyright is claimed in the United States under
* Title 17, U.S. Code. All Other Rights Reserved.
*
* The refine platform is licensed under the Apache License, Version
* 2.0 (the "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0.
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
* implied. See the License for the specific language governing
* permissions and limitations under the License.
*/
#include "ref_metric.h"
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "ref_cell.h"
#include "ref_dict.h"
#include "ref_edge.h"
#include "ref_egads.h"
#include "ref_grid.h"
#include "ref_interp.h"
#include "ref_malloc.h"
#include "ref_math.h"
#include "ref_matrix.h"
#include "ref_meshlink.h"
#include "ref_node.h"
#include "ref_phys.h"
#include "ref_sort.h"
#define REF_METRIC_MAX_DEGREE (1000)
REF_STATUS ref_metric_show(REF_DBL *m) {
printf(" %18.10e %18.10e %18.10e\n", m[0], m[1], m[2]);
printf(" %18.10e %18.10e %18.10e\n", m[1], m[3], m[4]);
printf(" %18.10e %18.10e %18.10e\n", m[2], m[4], m[5]);
return REF_SUCCESS;
}
REF_STATUS ref_metric_inspect(REF_NODE ref_node) {
REF_INT node;
REF_DBL m[6];
each_ref_node_valid_node(ref_node, node) {
RSS(ref_node_metric_get(ref_node, node, m), "get");
RSS(ref_metric_show(m), "show it");
}
return REF_SUCCESS;
}
REF_STATUS ref_metric_from_node(REF_DBL *metric, REF_NODE ref_node) {
REF_INT node;
each_ref_node_valid_node(ref_node, node) {
RSS(ref_node_metric_get(ref_node, node, &(metric[6 * node])), "get");
}
return REF_SUCCESS;
}
REF_STATUS ref_metric_to_node(REF_DBL *metric, REF_NODE ref_node) {
REF_INT node;
each_ref_node_valid_node(ref_node, node) {
RSS(ref_node_metric_set(ref_node, node, &(metric[6 * node])), "set");
}
return REF_SUCCESS;
}
REF_STATUS ref_metric_olympic_node(REF_NODE ref_node, REF_DBL h) {
REF_INT node;
REF_DBL hh;
each_ref_node_valid_node(ref_node, node) {
hh = h + (0.1 - h) * ABS(ref_node_xyz(ref_node, 2, node) - 0.5) / 0.5;
RSS(ref_node_metric_form(ref_node, node, 1.0 / (0.1 * 0.1), 0, 0,
1.0 / (0.1 * 0.1), 0, 1.0 / (hh * hh)),
"set node met");
}
return REF_SUCCESS;
}
REF_STATUS ref_metric_side_node(REF_NODE ref_node) {
REF_INT node;
REF_DBL h0 = 0.1;
REF_DBL h = 0.01;
REF_DBL hh;
each_ref_node_valid_node(ref_node, node) {
hh = h + (h0 - h) * ABS(ref_node_xyz(ref_node, 2, node));
RSS(ref_node_metric_form(ref_node, node, 1.0 / (0.1 * 0.1), 0, 0,
1.0 / (0.1 * 0.1), 0, 1.0 / (hh * hh)),
"set node met");
}
return REF_SUCCESS;
}
REF_STATUS ref_metric_ring_node(REF_NODE ref_node) {
REF_INT node;
REF_DBL hh;
REF_DBL h = 0.01;
REF_DBL x;
each_ref_node_valid_node(ref_node, node) {
x = ref_node_xyz(ref_node, 0, node);
hh = h + (0.1 - h) * MIN(2 * ABS(x - 1.0), 1);
RSS(ref_node_metric_form(ref_node, node, 1.0 / (hh * hh), 0, 0,
1.0 / (0.1 * 0.1), 0, 1.0 / (0.1 * 0.1)),
"set node met");
}
return REF_SUCCESS;
}
REF_STATUS ref_metric_twod_analytic_node(REF_NODE ref_node,
const char *version) {
REF_INT node;
REF_DBL x = 0, y = 0, r, t;
REF_DBL h_z = 1, h_t = 1, h_r = 1, h0, h, hh, hy, hx, c, k1, d0;
REF_DBL d[12], m[6];
REF_BOOL metric_recognized = REF_FALSE;
each_ref_node_valid_node(ref_node, node) {
if (strcmp(version, "iso01") == 0) {
metric_recognized = REF_TRUE;
h = 0.1;
RSS(ref_node_metric_form(ref_node, node, 1.0 / (h * h), 0, 0,
1.0 / (h * h), 0, 1.0),
"set node met");
continue;
}
if (strcmp(version, "isorad") == 0) {
metric_recognized = REF_TRUE;
r = sqrt(pow(ref_node_xyz(ref_node, 0, node), 2) +
pow(ref_node_xyz(ref_node, 1, node), 2) +
pow(ref_node_xyz(ref_node, 2, node), 2));
h = 0.1 + 0.1 * r;
RSS(ref_node_metric_form(ref_node, node, 1.0 / (h * h), 0, 0,
1.0 / (h * h), 0, 1.0),
"set node met");
continue;
}
if (strcmp(version, "masabl-1") == 0) {
metric_recognized = REF_TRUE;
hx = 0.01 +
0.2 * cos(ref_math_pi * (ref_node_xyz(ref_node, 0, node) - 0.5));
c = 0.001;
k1 = 6.0;
hy = c * exp(k1 * ref_node_xyz(ref_node, 1, node));
RSS(ref_node_metric_form(ref_node, node, 1.0 / (hx * hx), 0, 0,
1.0 / (hy * hy), 0, 1.0),
"set node met");
continue;
}
if (strcmp(version, "side") == 0) {
metric_recognized = REF_TRUE;
h0 = 0.1;
h = 0.01;
hh = h + (h0 - h) * ref_node_xyz(ref_node, 1, node);
RSS(ref_node_metric_form(ref_node, node, 1.0 / (0.1 * 0.1), 0, 0,
1.0 / (hh * hh), 0, 1.0),
"set node met");
continue;
}
if (strcmp(version, "linear-0001") == 0) {
metric_recognized = REF_TRUE;
h0 = 0.1;
h = 0.0001;
hh = h + (0.1 - h) * ABS(ref_node_xyz(ref_node, 1, node) - 0.5) / 0.5;
RSS(ref_node_metric_form(ref_node, node, 1.0 / (0.1 * 0.1), 0, 0,
1.0 / (hh * hh), 0, 1.0),
"set node met");
continue;
}
if (strcmp(version, "linear-01") == 0) {
metric_recognized = REF_TRUE;
h0 = 0.1;
h = 0.01;
hh = h + (0.1 - h) * ABS(ref_node_xyz(ref_node, 1, node) - 0.5) / 0.5;
RSS(ref_node_metric_form(ref_node, node, 1.0 / (0.1 * 0.1), 0, 0,
1.0 / (hh * hh), 0, 1.0),
"set node met");
continue;
}
if (strcmp(version, "polar-2") == 0) {
metric_recognized = REF_TRUE;
x = ref_node_xyz(ref_node, 0, node);
y = ref_node_xyz(ref_node, 1, node);
r = sqrt(x * x + y * y);
h_z = 1.0;
h_t = 0.1;
h0 = 0.001;
h_r = h0 + 2 * (0.1 - h0) * ABS(r - 0.5);
d0 = MIN(10.0 * ABS(r - 0.5), 1.0);
h_t = 0.1 * d0 + 0.025 * (1.0 - d0);
}
if (strcmp(version, "radial-1") == 0) {
metric_recognized = REF_TRUE;
x = ref_node_xyz(ref_node, 0, node) + 0.5;
y = ref_node_xyz(ref_node, 1, node) - 0.5;
t = atan2(y, x);
h_z = 1.0;
h_t = 0.1;
h_r = 0.01;
}
if (strcmp(version, "circle-1") == 0) {
metric_recognized = REF_TRUE;
x = ref_node_xyz(ref_node, 0, node) + 0.5;
y = ref_node_xyz(ref_node, 1, node) - 0.5;
r = sqrt(x * x + y * y);
t = atan2(y, x);
h_z = 1.0;
h_r = 0.0005 + 1.5 * ABS(1.0 - r);
h_t = 0.1 * r + 1.5 * ABS(1.0 - r);
}
t = atan2(y, x);
ref_matrix_eig(d, 0) = 1.0 / (h_r * h_r);
ref_matrix_eig(d, 1) = 1.0 / (h_t * h_t);
ref_matrix_eig(d, 2) = 1.0 / (h_z * h_z);
ref_matrix_vec(d, 0, 0) = cos(t);
ref_matrix_vec(d, 1, 0) = sin(t);
ref_matrix_vec(d, 2, 0) = 0.0;
ref_matrix_vec(d, 0, 1) = -sin(t);
ref_matrix_vec(d, 1, 1) = cos(t);
ref_matrix_vec(d, 2, 1) = 0.0;
ref_matrix_vec(d, 0, 2) = 0.0;
ref_matrix_vec(d, 1, 2) = 0.0;
ref_matrix_vec(d, 2, 2) = 1.0;
ref_matrix_form_m(d, m);
RSS(ref_node_metric_set(ref_node, node, m), "set node met");
}
RAS(metric_recognized, "metric unknown");
return REF_SUCCESS;
}
REF_STATUS ref_metric_ugawg_node(REF_NODE ref_node, REF_INT version) {
REF_INT node;
REF_DBL x, y, r, t;
REF_DBL h_z, h_t, h_r, h0, d0;
REF_DBL d[12], m[6];
if (1 == version || 2 == version) {
each_ref_node_valid_node(ref_node, node) {
x = ref_node_xyz(ref_node, 0, node);
y = ref_node_xyz(ref_node, 1, node);
r = sqrt(x * x + y * y);
t = atan2(y, x);
h_z = 0.1;
h_t = 0.1;
h0 = 0.001;
h_r = h0 + 2 * (0.1 - h0) * ABS(r - 0.5);
if (2 == version) {
d0 = MIN(10.0 * ABS(r - 0.5), 1.0);
h_t = 0.1 * d0 + 0.025 * (1.0 - d0);
}
ref_matrix_eig(d, 0) = 1.0 / (h_r * h_r);
ref_matrix_eig(d, 1) = 1.0 / (h_t * h_t);
ref_matrix_eig(d, 2) = 1.0 / (h_z * h_z);
ref_matrix_vec(d, 0, 0) = cos(t);
ref_matrix_vec(d, 1, 0) = sin(t);
ref_matrix_vec(d, 2, 0) = 0.0;
ref_matrix_vec(d, 0, 1) = -sin(t);
ref_matrix_vec(d, 1, 1) = cos(t);
ref_matrix_vec(d, 2, 1) = 0.0;
ref_matrix_vec(d, 0, 2) = 0.0;
ref_matrix_vec(d, 1, 2) = 0.0;
ref_matrix_vec(d, 2, 2) = 1.0;
ref_matrix_form_m(d, m);
RSS(ref_node_metric_set(ref_node, node, m), "set node met");
}
return REF_SUCCESS;
}
return REF_IMPLEMENT;
}
REF_STATUS ref_metric_masabl_node(REF_NODE ref_node) {
REF_INT node;
REF_DBL hx, hz, c, k1;
each_ref_node_valid_node(ref_node, node) {
hx =
0.01 + 0.2 * cos(ref_math_pi * (ref_node_xyz(ref_node, 0, node) - 0.5));
c = 0.001;
k1 = 6.0;
hz = c * exp(k1 * ref_node_xyz(ref_node, 2, node));
RSS(ref_node_metric_form(ref_node, node, 1.0 / (hx * hx), 0, 0,
1.0 / (0.1 * 0.1), 0, 1.0 / (hz * hz)),
"set node met");
}
return REF_SUCCESS;
}
REF_STATUS ref_metric_circle_node(REF_NODE ref_node) {
REF_INT node;
REF_DBL x, z, r, t;
REF_DBL hy, h1, h2;
REF_DBL d[12], m[6];
each_ref_node_valid_node(ref_node, node) {
x = ref_node_xyz(ref_node, 0, node);
z = ref_node_xyz(ref_node, 2, node);
r = sqrt(x * x + z * z);
t = atan2(z, x);
hy = 1.0;
h1 = 0.0005 + 1.5 * ABS(1.0 - r);
h2 = 0.1 * r + 1.5 * ABS(1.0 - r);
ref_matrix_eig(d, 0) = 1.0 / (h1 * h1);
ref_matrix_eig(d, 1) = 1.0 / (h2 * h2);
ref_matrix_eig(d, 2) = 1.0 / (hy * hy);
ref_matrix_vec(d, 0, 0) = cos(t);
ref_matrix_vec(d, 1, 0) = 0.0;
ref_matrix_vec(d, 2, 0) = sin(t);
ref_matrix_vec(d, 0, 1) = -sin(t);
ref_matrix_vec(d, 1, 1) = 0.0;
ref_matrix_vec(d, 2, 1) = cos(t);
ref_matrix_vec(d, 0, 2) = 0.0;
ref_matrix_vec(d, 1, 2) = 1.0;
ref_matrix_vec(d, 2, 2) = 0.0;
ref_matrix_form_m(d, m);
RSS(ref_node_metric_set(ref_node, node, m), "set node met");
}
return REF_SUCCESS;
}
REF_STATUS ref_metric_twod_node(REF_NODE ref_node) {
REF_INT node;
REF_DBL m[6];
each_ref_node_valid_node(ref_node, node) {
RSS(ref_node_metric_get(ref_node, node, m), "get");
m[2] = 0.0;
m[4] = 0.0;
m[5] = 1.0;
RSS(ref_node_metric_set(ref_node, node, m), "set");
}
return REF_SUCCESS;
}
REF_STATUS ref_metric_delta_box_node(REF_GRID ref_grid) {
REF_NODE ref_node = ref_grid_node(ref_grid);
REF_INT node;
REF_DBL m[6], m_int[6], m_target[6];
REF_DBL radius, h;
REF_DBL factor = 1.0;
REF_DBL n[3], dot;
each_ref_node_valid_node(ref_node, node) {
RSS(ref_node_metric_get(ref_node, node, m), "get");
n[0] = 0.90631;
n[1] = 0.42262;
n[2] = 0.0;
dot = ref_math_dot(n, ref_node_xyz_ptr(ref_node, node));
radius = sqrt(pow(ref_node_xyz(ref_node, 0, node) - dot * n[0], 2) +
pow(ref_node_xyz(ref_node, 1, node) - dot * n[1], 2) +
pow(ref_node_xyz(ref_node, 2, node) - dot * n[2], 2));
h = MIN(0.0003 + 0.002 * radius / (0.15 * 0.42262), 0.007);
h *= factor;
m_target[0] = 1.0 / (h * h);
m_target[1] = 0;
m_target[2] = 0;
m_target[3] = 1.0 / (h * h);
m_target[4] = 0;
m_target[5] = 1.0 / (h * h);
if (ref_node_xyz(ref_node, 0, node) > 1.1) {
REF_DBL ht, s, hx;
ht = 0.007;
s = (ref_node_xyz(ref_node, 0, node) - 1.1) / 3.9;
s = MIN(1.0, MAX(0.0, s));
hx = ht * (1.0 - s) + 10 * ht * s;
hx *= factor;
ht *= factor;
m_target[0] = 1.0 / (hx * hx);
m_target[1] = 0;
m_target[2] = 0;
m_target[3] = 1.0 / (ht * ht);
m_target[4] = 0;
m_target[5] = 1.0 / (ht * ht);
}
if (0.1 < ref_node_xyz(ref_node, 2, node) ||
-0.1 > ref_node_xyz(ref_node, 2, node) ||
1.0 < ref_node_xyz(ref_node, 1, node) ||
-0.1 > ref_node_xyz(ref_node, 0, node)) {
h = 0.1 + ABS(ref_node_xyz(ref_node, 2, node)) / 5.0 +
ABS(ref_node_xyz(ref_node, 1, node)) / 5.0 +
ABS(ref_node_xyz(ref_node, 0, node)) / 5.0;
h *= factor;
m_target[0] = 1.0 / (h * h);
m_target[1] = 0;
m_target[2] = 0;
m_target[3] = 1.0 / (h * h);
m_target[4] = 0;
m_target[5] = 1.0 / (h * h);
}
RSS(ref_matrix_intersect(m_target, m, m_int), "intersect");
RSS(ref_node_metric_set(ref_node, node, m_int), "set node met");
}
return REF_SUCCESS;
}
REF_STATUS ref_metric_interpolate_node(REF_GRID ref_grid, REF_INT node) {
REF_MPI ref_mpi = ref_grid_mpi(ref_grid);
REF_INTERP ref_interp;
REF_GRID from_grid;
REF_NODE from_node;
REF_CELL from_cell;
REF_DBL log_parent_m[4][6], log_m[6], bary[4];
REF_INT ibary, im;
REF_INT nodes[REF_CELL_MAX_SIZE_PER];
if (NULL == ref_grid_interp(ref_grid)) {
return REF_SUCCESS;
}
ref_interp = ref_grid_interp(ref_grid);
from_grid = ref_interp_from_grid(ref_interp);
from_node = ref_grid_node(from_grid);
if (ref_grid_twod(from_grid)) {
from_cell = ref_interp_from_tri(ref_interp);
} else {
from_cell = ref_interp_from_tet(ref_interp);
}
if (!ref_interp_continuously(ref_interp)) {
ref_interp_cell(ref_interp, node) = REF_EMPTY; /* mark moved */
return REF_SUCCESS;
}
RAISE(ref_interp_locate_node(ref_interp, node));
/* location unsuccessful */
if (REF_EMPTY == ref_interp_cell(ref_interp, node) ||
ref_mpi_rank(ref_mpi) != ref_interp->part[node])
return REF_SUCCESS;
RSS(ref_cell_nodes(from_cell, ref_interp_cell(ref_interp, node), nodes),
"node needs to be localized");
RSS(ref_node_clip_bary4(&ref_interp_bary(ref_interp, 0, node), bary), "clip");
for (ibary = 0; ibary < ref_cell_node_per(from_cell); ibary++)
RSS(ref_node_metric_get_log(from_node, nodes[ibary], log_parent_m[ibary]),
"log(parentM)");
for (im = 0; im < 6; im++) log_m[im] = 0.0;
for (im = 0; im < 6; im++) {
for (ibary = 0; ibary < ref_cell_node_per(from_cell); ibary++) {
log_m[im] += bary[ibary] * log_parent_m[ibary][im];
}
}
RSS(ref_node_metric_set_log(ref_grid_node(ref_grid), node, log_m),
"set interp log met");
return REF_SUCCESS;
}
REF_STATUS ref_metric_interpolate_between(REF_GRID ref_grid, REF_INT node0,
REF_INT node1, REF_INT new_node) {
REF_MPI ref_mpi = ref_grid_mpi(ref_grid);
REF_INTERP ref_interp;
REF_GRID from_grid;
REF_NODE from_node;
REF_CELL from_cell;
REF_NODE to_node;
REF_DBL log_parent_m[4][6], log_m[6], bary[4];
REF_INT ibary, im;
REF_INT nodes[REF_CELL_MAX_SIZE_PER];
/* skip null interp */
if (NULL == ref_grid_interp(ref_grid)) return REF_SUCCESS;
ref_interp = ref_grid_interp(ref_grid);
from_grid = ref_interp_from_grid(ref_interp);
from_node = ref_grid_node(from_grid);
from_node = ref_grid_node(from_grid);
if (ref_grid_twod(from_grid)) {
from_cell = ref_interp_from_tri(ref_interp);
} else {
from_cell = ref_interp_from_tet(ref_interp);
}
to_node = ref_grid_node(ref_interp_to_grid(ref_interp));
if (new_node >= ref_interp_max(ref_interp)) {
RSS(ref_interp_resize(ref_interp, ref_node_max(to_node)), "resize");
}
if (!ref_interp_continuously(ref_interp)) {
ref_interp->cell[new_node] = REF_EMPTY; /* initialize new_node locate */
return REF_SUCCESS;
}
RAISE(ref_interp_locate_between(ref_interp, node0, node1, new_node));
/* location unsuccessful or off-part don't interpolate */
if (REF_EMPTY == ref_interp_cell(ref_interp, new_node) ||
ref_mpi_rank(ref_mpi) != ref_interp_part(ref_interp, new_node))
return REF_SUCCESS;
RSS(ref_cell_nodes(from_cell, ref_interp_cell(ref_interp, new_node), nodes),
"new_node needs to be localized");
RSS(ref_node_clip_bary4(&ref_interp_bary(ref_interp, 0, new_node), bary),
"clip");
for (ibary = 0; ibary < ref_cell_node_per(from_cell); ibary++)
RSS(ref_node_metric_get_log(from_node, nodes[ibary], log_parent_m[ibary]),
"log(parentM)");
for (im = 0; im < 6; im++) log_m[im] = 0.0;
for (im = 0; im < 6; im++) {
for (ibary = 0; ibary < ref_cell_node_per(from_cell); ibary++) {
log_m[im] += bary[ibary] * log_parent_m[ibary][im];
}
}
RSS(ref_node_metric_set_log(ref_grid_node(ref_grid), new_node, log_m),
"set interp log met");
return REF_SUCCESS;
}
REF_STATUS ref_metric_interpolate(REF_INTERP ref_interp) {
REF_GRID to_grid = ref_interp_to_grid(ref_interp);
REF_GRID from_grid = ref_interp_from_grid(ref_interp);
REF_NODE to_node = ref_grid_node(to_grid);
REF_NODE from_node = ref_grid_node(from_grid);
REF_CELL from_cell;
REF_MPI ref_mpi = ref_interp_mpi(ref_interp);
REF_INT node, ibary, im;
REF_INT nodes[REF_CELL_MAX_SIZE_PER];
REF_DBL log_parent_m[4][6];
REF_INT receptor, n_recept, donation, n_donor;
REF_DBL *recept_log_m, *donor_log_m, *recept_bary, *donor_bary;
REF_INT *donor_node, *donor_ret, *donor_cell;
REF_INT *recept_proc, *recept_ret, *recept_node, *recept_cell;
if (ref_grid_twod(from_grid)) {
from_cell = ref_interp_from_tri(ref_interp);
} else {
from_cell = ref_interp_from_tet(ref_interp);
}
n_recept = 0;
each_ref_node_valid_node(to_node, node) {
if (ref_node_owned(to_node, node)) {
n_recept++;
}
}
ref_malloc(recept_bary, 4 * n_recept, REF_DBL);
ref_malloc(recept_cell, n_recept, REF_INT);
ref_malloc(recept_node, n_recept, REF_INT);
ref_malloc(recept_ret, n_recept, REF_INT);
ref_malloc(recept_proc, n_recept, REF_INT);
n_recept = 0;
each_ref_node_valid_node(to_node, node) {
if (ref_node_owned(to_node, node)) {
RUS(REF_EMPTY, ref_interp->cell[node], "node needs to be localized");
RSS(ref_node_clip_bary4(&(ref_interp->bary[4 * node]),
&(recept_bary[4 * n_recept])),
"clip");
recept_proc[n_recept] = ref_interp->part[node];
recept_cell[n_recept] = ref_interp->cell[node];
recept_node[n_recept] = node;
recept_ret[n_recept] = ref_mpi_rank(ref_mpi);
n_recept++;
}
}
RSS(ref_mpi_blindsend(ref_mpi, recept_proc, (void *)recept_cell, 1, n_recept,
(void **)(&donor_cell), &n_donor, REF_INT_TYPE),
"blind send cell");
RSS(ref_mpi_blindsend(ref_mpi, recept_proc, (void *)recept_ret, 1, n_recept,
(void **)(&donor_ret), &n_donor, REF_INT_TYPE),
"blind send ret");
RSS(ref_mpi_blindsend(ref_mpi, recept_proc, (void *)recept_node, 1, n_recept,
(void **)(&donor_node), &n_donor, REF_INT_TYPE),
"blind send node");
RSS(ref_mpi_blindsend(ref_mpi, recept_proc, (void *)recept_bary, 4, n_recept,
(void **)(&donor_bary), &n_donor, REF_DBL_TYPE),
"blind send bary");
ref_free(recept_proc);
ref_free(recept_ret);
ref_free(recept_node);
ref_free(recept_cell);
ref_free(recept_bary);
ref_malloc(donor_log_m, 6 * n_donor, REF_DBL);
for (donation = 0; donation < n_donor; donation++) {
RSS(ref_cell_nodes(from_cell, donor_cell[donation], nodes),
"node needs to be localized");
for (ibary = 0; ibary < 4; ibary++)
RSS(ref_node_metric_get_log(from_node, nodes[ibary], log_parent_m[ibary]),
"log(parentM)");
for (im = 0; im < 6; im++) {
donor_log_m[im + 6 * donation] = 0.0;
for (ibary = 0; ibary < 4; ibary++) {
donor_log_m[im + 6 * donation] +=
donor_bary[ibary + 4 * donation] * log_parent_m[ibary][im];
}
}
}
ref_free(donor_cell);
ref_free(donor_bary);
RSS(ref_mpi_blindsend(ref_mpi, donor_ret, (void *)donor_log_m, 6, n_donor,
(void **)(&recept_log_m), &n_recept, REF_DBL_TYPE),
"blind send bary");
RSS(ref_mpi_blindsend(ref_mpi, donor_ret, (void *)donor_node, 1, n_donor,
(void **)(&recept_node), &n_recept, REF_INT_TYPE),
"blind send node");
ref_free(donor_log_m);
ref_free(donor_node);
ref_free(donor_ret);
for (receptor = 0; receptor < n_recept; receptor++) {
node = recept_node[receptor];
RSS(ref_node_metric_set_log(to_node, node, &(recept_log_m[6 * receptor])),
"set received log met");
}
ref_free(recept_node);
ref_free(recept_log_m);
return REF_SUCCESS;
}
REF_STATUS ref_metric_synchronize(REF_GRID to_grid) {
REF_INTERP ref_interp = ref_grid_interp(to_grid);
REF_MPI ref_mpi;
REF_INT node;
REF_DBL max_error, tol = 1.0e-8;
REF_BOOL report_interp_error = REF_FALSE;
if (NULL == ref_interp) return REF_SUCCESS;
ref_mpi = ref_interp_mpi(ref_interp);
if (ref_mpi_para(ref_mpi)) {
/* parallel can miss on partition boundaries, refresh interp */
RSS(ref_interp_locate_warm(ref_interp), "map from existing");
RSS(ref_metric_interpolate(ref_interp), "interp");
} else {
/* sequential should always localized unless mixed, assert */
each_ref_node_valid_node(ref_grid_node(to_grid), node) {
if (!ref_cell_node_empty(ref_grid_tri(to_grid), node) &&
!ref_cell_node_empty(ref_grid_tet(to_grid), node)) {
RUS(REF_EMPTY, ref_interp_cell(ref_interp, node), "should be located");
}
}
}
if (report_interp_error) {
RSS(ref_interp_max_error(ref_interp, &max_error), "err");
if (max_error > tol && ref_mpi_once(ref_mpi)) {
printf("warning: %e max_error greater than %e tol\n", max_error, tol);
}
}
return REF_SUCCESS;
}
REF_STATUS ref_metric_metric_space_gradation(REF_DBL *metric, REF_GRID ref_grid,
REF_DBL r) {
REF_NODE ref_node = ref_grid_node(ref_grid);
REF_EDGE ref_edge;
REF_DBL *metric_orig;
REF_DBL ratio, enlarge, log_r;
REF_DBL direction[3];
REF_DBL limit_metric[6], limited[6];
REF_INT node, i;
REF_INT edge, node0, node1;
log_r = log(r);
RSS(ref_edge_create(&ref_edge, ref_grid), "orig edges");
ref_malloc(metric_orig, 6 * ref_node_max(ref_grid_node(ref_grid)), REF_DBL);
each_ref_node_valid_node(ref_grid_node(ref_grid), node) {
for (i = 0; i < 6; i++) metric_orig[i + 6 * node] = metric[i + 6 * node];
}
/* F. Alauzet doi:10.1016/j.finel.2009.06.028 equation (9) */
each_ref_edge(ref_edge, edge) {
node0 = ref_edge_e2n(ref_edge, 0, edge);
node1 = ref_edge_e2n(ref_edge, 1, edge);
direction[0] =
(ref_node_xyz(ref_node, 0, node1) - ref_node_xyz(ref_node, 0, node0));
direction[1] =
(ref_node_xyz(ref_node, 1, node1) - ref_node_xyz(ref_node, 1, node0));
direction[2] =
(ref_node_xyz(ref_node, 2, node1) - ref_node_xyz(ref_node, 2, node0));
ratio = ref_matrix_sqrt_vt_m_v(&(metric_orig[6 * node1]), direction);
enlarge = pow(1.0 + ratio * log_r, -2.0);
for (i = 0; i < 6; i++)
limit_metric[i] = metric_orig[i + 6 * node1] * enlarge;
if (REF_SUCCESS != ref_matrix_intersect(&(metric_orig[6 * node0]),
limit_metric, limited)) {
REF_WHERE("limit m0 with enlarged m1");
ref_node_location(ref_node, node0);
printf("ratio %24.15e enlarge %24.15e \n", ratio, enlarge);
printf("RECOVER ref_metric_metric_space_gradation\n");
continue;
}
if (REF_SUCCESS != ref_matrix_intersect(&(metric[6 * node0]), limited,
&(metric[6 * node0]))) {
REF_WHERE("update m0");
ref_node_location(ref_node, node0);
printf("ratio %24.15e enlarge %24.15e \n", ratio, enlarge);
printf("RECOVER ref_metric_metric_space_gradation\n");
continue;
}
ratio = ref_matrix_sqrt_vt_m_v(&(metric_orig[6 * node0]), direction);
enlarge = pow(1.0 + ratio * log_r, -2.0);
for (i = 0; i < 6; i++)
limit_metric[i] = metric_orig[i + 6 * node0] * enlarge;
if (REF_SUCCESS != ref_matrix_intersect(&(metric_orig[6 * node1]),
limit_metric, limited)) {
REF_WHERE("limit m1 with enlarged m0");
ref_node_location(ref_node, node1);
printf("ratio %24.15e enlarge %24.15e \n", ratio, enlarge);
printf("RECOVER ref_metric_metric_space_gradation\n");
continue;
}
if (REF_SUCCESS != ref_matrix_intersect(&(metric[6 * node1]), limited,
&(metric[6 * node1]))) {
REF_WHERE("update m1");
ref_node_location(ref_node, node1);
printf("ratio %24.15e enlarge %24.15e \n", ratio, enlarge);
printf("RECOVER ref_metric_metric_space_gradation\n");
continue;
}
}
ref_free(metric_orig);
ref_edge_free(ref_edge);
RSS(ref_node_ghost_dbl(ref_grid_node(ref_grid), metric, 6), "update ghosts");
return REF_SUCCESS;
}
REF_STATUS ref_metric_mixed_space_gradation(REF_DBL *metric, REF_GRID ref_grid,
REF_DBL r, REF_DBL t) {
REF_NODE ref_node = ref_grid_node(ref_grid);
REF_EDGE ref_edge;
REF_DBL *metric_orig;
REF_DBL dist, ratio, enlarge, log_r;
REF_DBL direction[3];
REF_DBL limit_metric[6], limited[6];
REF_INT node, i;
REF_INT edge, node0, node1;
REF_DBL diag_system[12];
REF_DBL metric_space, phys_space;
if (r < 1.0) r = 1.5;
if (t < 0.0 || 1.0 > t) t = 1.0 / 8.0;
log_r = log(r);
RSS(ref_edge_create(&ref_edge, ref_grid), "orig edges");
ref_malloc(metric_orig, 6 * ref_node_max(ref_grid_node(ref_grid)), REF_DBL);
each_ref_node_valid_node(ref_grid_node(ref_grid), node) {
for (i = 0; i < 6; i++) metric_orig[i + 6 * node] = metric[i + 6 * node];
}
/* F. Alauzet doi:10.1016/j.finel.2009.06.028
* 6.2.1. Mixed-space homogeneous gradation */
each_ref_edge(ref_edge, edge) {
node0 = ref_edge_e2n(ref_edge, 0, edge);
node1 = ref_edge_e2n(ref_edge, 1, edge);
direction[0] =
(ref_node_xyz(ref_node, 0, node1) - ref_node_xyz(ref_node, 0, node0));
direction[1] =
(ref_node_xyz(ref_node, 1, node1) - ref_node_xyz(ref_node, 1, node0));
direction[2] =
(ref_node_xyz(ref_node, 2, node1) - ref_node_xyz(ref_node, 2, node0));
dist = sqrt(ref_math_dot(direction, direction));
ratio = ref_matrix_sqrt_vt_m_v(&(metric_orig[6 * node1]), direction);
RSB(ref_matrix_diag_m(&(metric_orig[6 * node1]), diag_system), "decomp",
{ ref_metric_show(&(metric_orig[6 * node1])); });
for (i = 0; i < 3; i++) {
metric_space = 1.0 + log_r * ratio;
phys_space = 1.0 + sqrt(ref_matrix_eig(diag_system, i)) * dist * log_r;
enlarge = pow(pow(phys_space, t) * pow(metric_space, 1.0 - t), -2.0);
ref_matrix_eig(diag_system, i) *= enlarge;
}
RSS(ref_matrix_form_m(diag_system, limit_metric), "reform limit");
if (REF_SUCCESS == ref_matrix_intersect(&(metric_orig[6 * node0]),
limit_metric, limited)) {
RSS(ref_matrix_intersect(&(metric[6 * node0]), limited,
&(metric[6 * node0])),
"update m0");
} else {
ref_node_location(ref_node, node0);
printf("dist %24.15e ratio %24.15e\n", dist, ratio);
printf("RECOVER ref_metric_mixed_space_gradation\n");
}
ratio = ref_matrix_sqrt_vt_m_v(&(metric_orig[6 * node0]), direction);
RSB(ref_matrix_diag_m(&(metric_orig[6 * node0]), diag_system), "decomp",
{ ref_metric_show(&(metric_orig[6 * node0])); });
for (i = 0; i < 3; i++) {
metric_space = 1.0 + log_r * ratio;
phys_space = 1.0 + sqrt(ref_matrix_eig(diag_system, i)) * dist * log_r;
enlarge = pow(pow(phys_space, t) * pow(metric_space, 1.0 - t), -2.0);
ref_matrix_eig(diag_system, i) *= enlarge;
}
RSS(ref_matrix_form_m(diag_system, limit_metric), "reform limit");
if (REF_SUCCESS == ref_matrix_intersect(&(metric_orig[6 * node1]),
limit_metric, limited)) {
RSS(ref_matrix_intersect(&(metric[6 * node1]), limited,
&(metric[6 * node1])),
"update m1");
} else {
ref_node_location(ref_node, node1);
printf("dist %24.15e ratio %24.15e\n", dist, ratio);
printf("RECOVER ref_metric_mixed_space_gradation\n");
}
}
ref_free(metric_orig);
ref_edge_free(ref_edge);
RSS(ref_node_ghost_dbl(ref_grid_node(ref_grid), metric, 6), "update ghosts");
return REF_SUCCESS;
}
REF_STATUS ref_metric_hessian_gradation(REF_DBL *metric, REF_GRID ref_grid) {
REF_NODE ref_node = ref_grid_node(ref_grid);
REF_MPI ref_mpi = ref_grid_mpi(ref_grid);
REF_DBL *min_h, *hess_min_h, *threshold;
REF_DBL temp, max_threshold, max_valid, eig;
REF_INT node;
ref_malloc(min_h, ref_node_max(ref_node), REF_DBL);
ref_malloc(hess_min_h, 6 * ref_node_max(ref_node), REF_DBL);
ref_malloc(threshold, ref_node_max(ref_node), REF_DBL);
each_ref_node_valid_node(ref_node, node) {
REF_DBL diag[12];
RSS(ref_matrix_diag_m(&(metric[6 * node]), diag), "decomp");
if (ref_grid_twod(ref_grid)) {
RSS(ref_matrix_ascending_eig_twod(diag), "2D ascend");
} else {
RSS(ref_matrix_ascending_eig(diag), "3D ascend");
}
min_h[node] = sqrt(MAX(0.0, ref_matrix_eig(diag, 0)));
if (ref_math_divisible(1.0, min_h[node])) {
min_h[node] = 1.0 / min_h[node];
} else {
min_h[node] = 1.0;
}
}
RSS(ref_recon_hessian(ref_grid, min_h, hess_min_h, REF_RECON_L2PROJECTION),
"hess");
max_threshold = 0.0;
each_ref_node_valid_node(ref_node, node) {
REF_DBL diag[12];
RSS(ref_matrix_diag_m(&(hess_min_h[6 * node]), diag), "decomp");
if (ref_grid_twod(ref_grid)) {
RSS(ref_matrix_ascending_eig_twod(diag), "2D ascend");
} else {
RSS(ref_matrix_ascending_eig(diag), "3D ascend");
}
threshold[node] = log(ABS(ref_matrix_eig(diag, 0)));
max_threshold = MAX(max_threshold, threshold[node]);
}
temp = max_threshold;
RSS(ref_mpi_max(ref_mpi, &temp, &max_threshold, REF_DBL_TYPE), "max");
max_threshold = exp(0.9 * log(max_threshold));
max_valid = 0.0;
each_ref_node_valid_node(ref_node, node) {
if (threshold[node] > max_threshold) {
eig = pow(min_h[node], -2);
max_valid = MAX(max_valid, eig);
}
}
each_ref_node_valid_node(ref_node, node) {
REF_DBL diag[12];
RSS(ref_matrix_diag_m(&(metric[6 * node]), diag), "decomp");
if (ref_grid_twod(ref_grid)) {
RSS(ref_matrix_ascending_eig_twod(diag), "2D ascend");
} else {
RSS(ref_matrix_ascending_eig(diag), "3D ascend");
}
ref_matrix_eig(diag, 0) = MIN(ref_matrix_eig(diag, 0), max_valid);
ref_matrix_eig(diag, 1) = MIN(ref_matrix_eig(diag, 1), max_valid);
if (!ref_grid_twod(ref_grid))
ref_matrix_eig(diag, 2) = MIN(ref_matrix_eig(diag, 2), max_valid);
RSS(ref_matrix_form_m(diag, &(metric[6 * node])), "reform");
}
ref_free(threshold);
ref_free(hess_min_h);
ref_free(min_h);
return REF_SUCCESS;
}
REF_STATUS ref_metric_interpolation_error(REF_DBL *metric, REF_DBL *hess,
REF_GRID ref_grid,
REF_DBL *interpolation_error) {
/* Corollary 3.4 CONTINUOUS MESH FRAMEWORK PART I DOI:10.1137/090754078 */
REF_NODE ref_node = ref_grid_node(ref_grid);
REF_INT node;
REF_DBL error[6], m1half[6], m1neghalf[6], det, sqrt_det;
REF_DBL constant = 1.0 / 10.0;
if (ref_grid_twod(ref_grid)) {
constant = 1.0 / 8.0;
}
each_ref_node_valid_node(ref_node, node) {
if (ref_node_owned(ref_node, node)) {
RSS(ref_matrix_sqrt_m(&(metric[6 * node]), m1half, m1neghalf), "m^-1/2");
RSS(ref_matrix_mult_m0m1m0(m1neghalf, &(hess[6 * node]), error),
"error=m1half*hess*m1half");
RSS(ref_matrix_det_m(&(metric[6 * node]), &det), "det");
if (ref_grid_twod(ref_grid)) {
interpolation_error[node] = constant * (error[0] + error[3]);
} else {
interpolation_error[node] = constant * (error[0] + error[3] + error[5]);
}
if (det >= 0.0) {
sqrt_det = sqrt(det);
if (ref_math_divisible(interpolation_error[node], sqrt_det)) {
interpolation_error[node] /= sqrt_det;
} else {
interpolation_error[node] = 0.0;
}
} else {
interpolation_error[node] = 0.0;
}
}
}
RSS(ref_node_ghost_dbl(ref_node, interpolation_error, 1), "update ghosts");
return REF_SUCCESS;
}
REF_STATUS ref_metric_integrate_error(REF_GRID ref_grid,
REF_DBL *interpolation_error,
REF_DBL *total_error) {
REF_NODE ref_node = ref_grid_node(ref_grid);
REF_CELL ref_cell;
REF_INT cell_node, cell, nodes[REF_CELL_MAX_SIZE_PER];
REF_DBL volume;
REF_BOOL have_tet;
REF_LONG ntet;
RSS(ref_cell_ncell(ref_grid_tet(ref_grid), ref_node, &ntet), "count");
have_tet = (0 < ntet);
if (have_tet) {
ref_cell = ref_grid_tet(ref_grid);
} else {
ref_cell = ref_grid_tri(ref_grid);
}
*total_error = 0.0;
each_ref_cell_valid_cell_with_nodes(ref_cell, cell, nodes) {
if (have_tet) {
RSS(ref_node_tet_vol(ref_node, nodes, &volume), "vol");
} else {
RSS(ref_node_tri_area(ref_node, nodes, &volume), "area");
}
for (cell_node = 0; cell_node < ref_cell_node_per(ref_cell); cell_node++) {
if (ref_node_owned(ref_node, nodes[cell_node])) {
(*total_error) += interpolation_error[nodes[cell_node]] * volume /
((REF_DBL)ref_cell_node_per(ref_cell));
}
}
}
RSS(ref_mpi_allsum(ref_grid_mpi(ref_grid), total_error, 1, REF_DBL_TYPE),