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Nodal_mesh.c
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Nodal_mesh.c
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/*
Copyright (C) 2003 The GeoFramework Consortium
This file is part of Ellipsis3D.
Ellipsis3D is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License, version 2,
as published by the Free Software Foundation.
Ellipsis3D 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.
Authors:
Louis Moresi <[email protected]>
Richard Albert <[email protected]>
*/
/* Functions relating to the building and use of mesh locations ... */
#include "config.h"
#include <math.h>
#if HAVE_STRING_H
#include <string.h>
#endif
#if HAVE_STRINGS_H
#include <strings.h>
#endif
#if HAVE_STDLIB_H
#include <stdlib.h>
#endif
#include "element_definitions.h"
#include "global_defs.h"
int M_node_cols;
int *M_node_col_num[MAX_LEVELS];
int **M_node_col_list[MAX_LEVELS];
extern int Emergency_stop;
/* =================================================
Standard node positions including mesh refinement
================================================= */
void node_locations(
struct All_variables *E,
int step
)
{
int i,j,k,ijk[4],d,node,lv;
standard_precision *XX[4];
standard_precision smallest,this_space;
void set_spacing_functions();
void inject_node_values();
const int dims = E->mesh.nsd ;
const int dofs = E->mesh.dof ;
set_spacing_functions(E);
for(d=1;d<=dims;d++) {
if(E->control.verbose)
fprintf(stderr,"Computing nodes locations for dirn %d\n",d);
XX[d] = (standard_precision *)Malloc0((2+E->mesh.nnx[d])*sizeof(standard_precision));
}
/* First build nsd arrays along each edge & then convolve them (orthogonal)
Initially the coordinates are determined on the unit interval and then scaled/offset */
for(d=1;d<=dims;d++) {
XX[d][1] = 0.0;
for(i=2;i<=E->mesh.nnx[d];i++) {
XX[d][i] = XX[d][i-1] +
(E->node_space_function[d-1])(E,(i-1.5)/(E->mesh.nnx[d]-1),d,i); }
}
/* Correct for scaling errors. This is simpler than obtaining the integral of the
scaling function. */
for(d=1;d<=dims;d++) {
for(i=1;i<=E->mesh.nnx[d];i++) {
XX[d][i] = E->mesh.layer0[d] + XX[d][i] * (E->mesh.layer1[d]-E->mesh.layer0[d])/(XX[d][E->mesh.nnx[d]]);
}
}
/* find smallest spacing in each direction */
E->mesh.equiv_even_nodes[3] = 1; /* useful to define this when doing 2d */
for(d=1;d<=dims;d++) {
smallest=E->mesh.layer1[d];
for(i=1;i<E->mesh.nnx[d];i++) {
this_space = XX[d][i+1]-XX[d][i];
if(this_space < smallest)
smallest = this_space;
}
E->mesh.equiv_even_nodes[d] = (int)((E->mesh.layer1[d]-E->mesh.layer0[d])/smallest) + 1;
E->mesh.fine_spacing[d] = E->mesh.layer1[d] / (E->mesh.equiv_even_nodes[d]-1);
}
E->mesh.equiv_even_nsf = E->mesh.equiv_even_nodes[1] * E->mesh.equiv_even_nodes[3];
/* 1. If the problem is Cartesian, then this set of coordinates is
used as is. Define Cartesian mesh from point distributions on 3 orthogonal axes */
if (E->control.CART2D || E->control.CART2pt5D || E->control.CART3D || E->control.AXI) {
for(ijk[1]=1;ijk[1]<=E->mesh.nox;ijk[1]++)
for(ijk[2]=1;ijk[2]<=E->mesh.noz;ijk[2]++)
for(ijk[3]=1;ijk[3]<=E->mesh.noy;ijk[3]++) {
node = ijk[2]+(ijk[1]-1)*E->mesh.noz+(ijk[3]-1)*E->mesh.noz*E->mesh.nox;
for(d=1;d<=dims;d++) {
E->x[d][node] = XX[d][ijk[d]];
}
}
/* AD HOC adjustment for funnel problem */
#if 0
E->control.ORTHO = 0;
for(i=1;i<=E->mesh.nno;i++) {
if(E->x[2][i] > 2.76 && E->x[2][i] <= 3.375 )
E->x[1][i] += 1.0 * (E->x[2][i]-2.75) * (1.0 - E->x[1][i]);
if(E->x[2][i] > 3.375)
E->x[1][i] += 0.625 * (1.0 - E->x[1][i]);
}
#endif
/* AD HOC adjustment for interface problem */
#if 0
E->control.ORTHO = 0;
for(i=1;i<=E->mesh.nno;i++) {
if( fabs(E->x[2][i] - (0.5 + 0.01 * cos(2.*M_PI * E->x[1][i] / 1.284)) ) < 0.4999*fabs(E->x[2][1] - E->x[2][2])) {
E->x[2][i] = 0.5 + 0.01 * cos(2.*M_PI * E->x[1][i] / 1.284) ;
fprintf(stderr,"Node N0 %d has been moved to z = %.10e \n",i,E->x[2][i]) ;
}
}
#endif
/* AD HOC adjustment for Rayleigh-Taylor instability problem */
#if 0
E->control.ORTHO = 0;
for(i=1;i<=E->mesh.nno;i++) {
if(E->x[2][i] == 0.5) {
for(j=i-0.5*(sqrt(E->mesh.nno)-1);j<=i;j++)
E->x[2][j] += 0.01 * 0.5 * cos(2.*M_PI * E->x[1][i] / 1.284) * (E->x[2][j]/0.5) ;
for(j=i+1;j<=i+0.5*(sqrt(E->mesh.nno)-1);j++)
E->x[2][j] += 0.01 * 0.5 * cos(2.*M_PI * E->x[1][i] / 1.284) * ((1-E->x[2][j])/0.5) ;
fprintf(stderr,"Node N0 %d has been moved to z = %.10e \n",i,E->x[2][i]) ;
}
}
#endif
/* AD HOC adjustment for Buckling / Folding instability problem */
#if 0
/* Here you can put ad hoc modifications for specific problems !!! */
input_std_precision_vector("test_geometry_parameters",5,geom); /* What if fewer entries ?? */
E->control.secret_case_fl[1] = geom[0] ;
E->control.secret_case_fl[2] = geom[1] ;
E->control.secret_case_fl[3] = geom[2] ;
fprintf(stderr,"For buckling problem (nodes) w0 = %g k = %g and h = %g \n",geom[0],geom[1],geom[2]) ;
E->control.ORTHO = 0;
#if 1
/* All nodes are moved with a linear interpolation between the edge and the centered line */
for(i=1;i<=E->mesh.NOX[E->mesh.levmax];i++) {
for(j=(i-1)*E->mesh.NOZ[E->mesh.levmax]+1;j<=i*E->mesh.NOZ[E->mesh.levmax];j++) {
if(E->x[2][j]<=E->x[2][E->mesh.nno]*0.5) {
E->x[2][j] += (geom[0] * cos(geom[1]*M_PI/3.0*E->x[1][j])) * E->x[2][j] / (E->x[2][E->mesh.nno]*0.5) ;
}
else {
E->x[2][j] += (geom[0] * cos(geom[1]*M_PI/3.0*E->x[1][j])) * (E->x[2][E->mesh.nno] - E->x[2][j]) / (E->x[2][E->mesh.nno]*0.5) ;
}
}
}
#else
/* Only the node on the middle line are slightly moved */
for(i=1;i<=E->mesh.nno;i++) {
if(E->x[2][i] <= (0.5*E->x[2][E->mesh.nno]-geom[2]/2.+0.001) && E->x[2][i] >= (0.5*E->x[2][E->mesh.nno]-geom[2]/2.-0.001)) {
E->x[2][i] += geom[0] * cos(geom[1]*M_PI/3.0*E->x[1][i]) ;
}
else if(E->x[2][i] <= (0.5*E->x[2][E->mesh.nno]+geom[2]/2.+0.001) && E->x[2][i] >= (0.5*E->x[2][E->mesh.nno]+geom[2]/2.-0.001)) {
E->x[2][i] += geom[0] * cos(geom[1]*M_PI/3.0*E->x[1][i]) ;
}
}
#endif
#endif
/* Now inject to all levels of the multigrid formulation */
for(i=E->mesh.levmax;i>E->mesh.levmin;i--) {
inject_node_values(E,i,E->X[i][1],E->X[i-1][1]);
inject_node_values(E,i,E->X[i][2],E->X[i-1][2]);
if(dims==3)
inject_node_values(E,i,E->X[i][3],E->X[i-1][3]);
}
/* and alias the curvilinear mesh coords to the cartesian ones (for bc's etc) */
E->sx[1] = E->x[1];
E->sx[2] = E->x[2];
E->sx[3] = E->x[3];
for(i=E->mesh.levmin;i<=E->mesh.levmax;i++) {
E->SX[i][1] = E->X[i][1];
E->SX[i][2] = E->X[i][2];
E->SX[i][3] = E->X[i][3];
}
}
/* 2. If mesh is spherical or cylindrical then there are two sets of coordinates: the
curvilinear ones and a second representation in Cartesian geometry to use for
element computations */
else { /* Logical mesh coordinates are in phi,r,theta space (E->sx) */
for(ijk[1]=1;ijk[1]<=E->mesh.nox;ijk[1]++)
for(ijk[2]=1;ijk[2]<=E->mesh.noz;ijk[2]++)
for(ijk[3]=1;ijk[3]<=E->mesh.noy;ijk[3]++) {
node = ijk[2]+(ijk[1]-1)*E->mesh.noz+(ijk[3]-1)*E->mesh.noz*E->mesh.nox;
for(d=1;d<dims;d++) {
E->sx[d][node] = XX[d][ijk[d]];
}
}
/* inject to all levels */
for(i=E->mesh.levmax;i>E->mesh.levmin;i--) {
inject_node_values(E,i,E->SX[i][1],E->SX[i-1][1]);
inject_node_values(E,i,E->SX[i][2],E->SX[i-1][2]);
if(dims==3)
inject_node_values(E,i,E->SX[i][3],E->SX[i-1][3]);
}
/* Obtain cartesian coordinates from here */
/* SPHERICAL */
if(E->control.SPHERE) {
for(lv=E->mesh.levmin;lv<=E->mesh.levmax;lv++) {
for(i=1;i<=E->mesh.NOX[lv];i++) {
node = 1 + (i-1) * E->mesh.NOZ[lv];
E->curvilinear.cosph[lv][i] = cos(E->SX[lv][1][node]);
E->curvilinear.sinph[lv][i] = sin(E->SX[lv][1][node]);
}
for(k=1;k<=E->mesh.NOY[lv];k++) {
node = 1 + (k-1) * E->mesh.NOZ[lv]*E->mesh.NOX[lv];
E->curvilinear.cost[lv][k] = cos(E->SX[lv][3][node]);
E->curvilinear.sint[lv][k] = sin(E->SX[lv][3][node]);
}
for(i=1;i<=E->mesh.NOX[lv];i++)
for(k=1;k<=E->mesh.NOY[lv];k++)
for(j=1;j<=E->mesh.NOZ[lv];j++) {
node = j + (i-1) * E->mesh.NOZ[lv] + (k-1) * E->mesh.NOZ[lv] * E->mesh.NOX[lv] ;
E->X[lv][1][node] = E->SX[lv][2][node] * E->curvilinear.cost[lv][k] * E->curvilinear.sinph[lv][i]; /* X */
E->X[lv][2][node] = E->SX[lv][2][node] * E->curvilinear.cost[lv][k] * E->curvilinear.cosph[lv][i]; /* Z */
E->X[lv][3][node] = E->SX[lv][2][node] * E->curvilinear.sint[lv][k]; /* Y */
}
}
}
if(E->control.CYLINDER) {
for(lv=E->mesh.levmin;lv<=E->mesh.levmax;lv++) {
for(i=1;i<=E->mesh.NOX[lv];i++) {
node = 1 + (i-1) * E->mesh.NOZ[lv];
E->curvilinear.cosph[lv][i] = cos(E->SX[lv][1][node]);
E->curvilinear.sinph[lv][i] = sin(E->SX[lv][1][node]);
}
for(i=1;i<=E->mesh.NOX[lv];i++)
for(j=1;j<=E->mesh.NOZ[lv];j++) {
node = j + (i-1) * E->mesh.NOZ[lv];
E->X[lv][1][node] = E->SX[lv][2][node] * E->curvilinear.sinph[lv][i]; /* X */
E->X[lv][2][node] = E->SX[lv][2][node] * E->curvilinear.cosph[lv][i]; /* Z */
/* fprintf(stderr,"%d, Coords: %d/%d (%g,%g) -> (%g,%g)\n",lv,node,
E->mesh.NNO[lv],E->SX[lv][2][node],E->SX[lv][2][node],
E->X[lv][2][node],E->X[lv][2][node]); */
}
}
}
}
if(E->control.verbose)
fprintf(stderr,"Computing all node locations\n");
for(d=1;d<=dims;d++)
free((void *)XX[d]);
return; }
void set_spacing_functions(
struct All_variables *E
)
{
standard_precision regular_spacing();
standard_precision bound_lyr_spacing();
standard_precision region_spacing();
standard_precision file_spacing();
int i;
char parsing_string[100];
char direction[3][2];
const int dims = E->mesh.nsd ;
strcpy(direction[0],"x");
strcpy(direction[1],"z");
strcpy(direction[2],"y");
for(i=0;i<dims;i++){
switch(E->control.GRID_TYPE[i]) {
case 1:
E->node_space_function[i]=region_spacing;
sprintf(parsing_string,"regions_%s",direction[i]);
input_int(parsing_string,&(E->mesh.spacing[i].numb),"0,0,39");
fprintf(E->fp,"Regional (%d) spacing of nodes in %s direction\n",E->mesh.spacing[i].numb,direction[i]);
fflush(E->fp);
sprintf(parsing_string,"region_offset_%s",direction[i]);
input_std_precision_vector(parsing_string,E->mesh.spacing[i].numb,E->mesh.spacing[i].offset);
sprintf(parsing_string,"region_compression_%s",direction[i]);
input_std_precision_vector(parsing_string,E->mesh.spacing[i].numb,E->mesh.spacing[i].compression);
sprintf(parsing_string,"region_width_%s",direction[i]);
input_std_precision_vector(parsing_string,E->mesh.spacing[i].numb,E->mesh.spacing[i].width);
sprintf(parsing_string,"region_edge_width_%s",direction[i]);
input_std_precision_vector(parsing_string,E->mesh.spacing[i].numb,E->mesh.spacing[i].edge_width);
break;
case 2:
E->node_space_function[i]=file_spacing;
fprintf(E->fp,"Spacing of nodes from files for %s direction\n",direction[i]);fflush(E->fp);
sprintf(parsing_string,"node_locations_file_%s",direction[i]);
input_string(parsing_string,E->mesh.gridfile[i],"");
break;
}
}
return;
}
/* location is a coordinate in direction d (1,2,3) at edge node i */
standard_precision region_spacing(
struct All_variables *E,
standard_precision locn,
int d,
int i
)
{
standard_precision location,delta,scale,radius,spacing[40],output,recip_width,width_scale;
int ii;
/* The commented expression causes the code to misinterpret grid element compression instructions. */
width_scale = E->mesh.layer1[d] ; /* /E->mesh.layer1[2]; */
recip_width = 1.0/width_scale;
locn *= width_scale;
scale = 1.0/(E->mesh.nnx[d]-1.0);
for(ii=0;ii<E->mesh.spacing[d-1].numb;ii++) {
radius = (locn-E->mesh.spacing[d-1].offset[ii])*(locn-E->mesh.spacing[d-1].offset[ii]);
if(radius < E->mesh.spacing[d-1].width[ii]*E->mesh.spacing[d-1].width[ii]) {
spacing[ii]=scale*E->mesh.spacing[d-1].compression[ii];
}
else {
radius -= E->mesh.spacing[d-1].width[ii]*E->mesh.spacing[d-1].width[ii];
spacing[ii]= scale*(1.0 - (1.0-E->mesh.spacing[d-1].compression[ii]) *
exp(-radius/(E->mesh.spacing[d-1].edge_width[ii]*E->mesh.spacing[d-1].edge_width[ii])) );
}
}
output=scale;
for(ii=0;ii<E->mesh.spacing[d-1].numb;ii++) {
output=min(output,spacing[ii]);
}
return(output);
}
standard_precision file_spacing(
struct All_variables *E,
standard_precision locn,
int d,
int i
)
{ /* note, the format here is a little bit odd because the function should return the current spacing not
the absolute position, hmmm. Also, the layer dimensions ought to be reset to reflect the values in the
files and not any previously set values */
static int been_here[4];
const int dims=E->mesh.nsd;
const int dofs=E->mesh.dof;
standard_precision *location[4];
float temporary;
int dd,ii,err;
FILE *fp;
if(0==been_here[d]) {
location[d]=(standard_precision *)Malloc0((E->mesh.nox+1)*sizeof(standard_precision));
/* open files */
err=0.0;
if((fp=fopen(E->mesh.gridfile[d-1],"r")) == NULL) {
fprintf(E->fp,"Error reading the grid information file: %s\n",E->mesh.gridfile[d-1]);
fflush(E->fp);
exit(1);
}
else {
for(ii=1;ii<=E->mesh.nnx[d];ii++) {
fscanf(fp,"%f",&(temporary));
location[d][ii] = (standard_precision) temporary;
}
fclose(fp);
}
E->mesh.layer1[d] = location[d][E->mesh.nnx[d]];
been_here[d]++;
}
return(location[d][i]-location[d][i-1]);
}
void dlogical_mesh_to_real(
struct All_variables *E,
higher_precision *data,
int level
)
{ int i,j,n1,n2;
if(E->mesh.periodic_x)
for(i=1;i<=E->mesh.NOZ[level];i++)
for(j=1;j<=E->mesh.NOY[level];j++)
{ n1 = i + (j-1)* E->mesh.NOX[level]*E->mesh.NOZ[level];
n2 = n1 + (E->mesh.NOX[level]-1)*E->mesh.NOZ[level];
data[n2] = data[n1];
}
if(E->mesh.periodic_y)
for(i=1;i<=E->mesh.NOZ[level];i++)
for(j=1;j<=E->mesh.NOX[level];j++)
{ n1 = i + (j-1)* E->mesh.NOZ[level];
n2 = n1 + (E->mesh.NOY[level]-1)*E->mesh.NOZ[level]*E->mesh.NOX[level];
data[n2] = data[n1];
}
if(E->mesh.periodic_y && E->mesh.periodic_x) /* then need to do the 1st one again */
for(i=1;i<=E->mesh.NOZ[level];i++)
for(j=1;j<=E->mesh.NOY[level];j++)
{ n1 = i + (j-1)* E->mesh.NOX[level]*E->mesh.NOZ[level];
n2 = n1 + (E->mesh.NOX[level]-1)*E->mesh.NOZ[level];
data[n2] = data[n1];
}
return;
}
void flogical_mesh_to_real(
struct All_variables *E,
standard_precision *data,
int level
)
{
int i,j,n1,n2;
if(E->mesh.periodic_x)
for(i=1;i<=E->mesh.NOZ[level];i++)
for(j=1;j<=E->mesh.NOY[level];j++) {
n1 = i + (j-1)* E->mesh.NOX[level]*E->mesh.NOZ[level];
n2 = n1 + (E->mesh.NOX[level]-1)*E->mesh.NOZ[level];
data[n2] = data[n1];
}
if(E->mesh.periodic_y)
for(i=1;i<=E->mesh.NOZ[level];i++)
for(j=1;j<=E->mesh.NOX[level];j++)
{ n1 = i + (j-1)* E->mesh.NOZ[level];
n2 = n1 + (E->mesh.NOY[level]-1)*E->mesh.NOZ[level]*E->mesh.NOX[level];
data[n2] = data[n1];
}
if(E->mesh.periodic_y && E->mesh.periodic_x) /* then need to do the 1st one again */
for(i=1;i<=E->mesh.NOZ[level];i++)
for(j=1;j<=E->mesh.NOY[level];j++)
{ n1 = i + (j-1)* E->mesh.NOX[level]*E->mesh.NOZ[level];
n2 = n1 + (E->mesh.NOX[level]-1)*E->mesh.NOZ[level];
data[n2] = data[n1];
}
return;
}
standard_precision nodal_interpolated_value(
struct All_variables *E,
standard_precision *field,
standard_precision x,
standard_precision z,
standard_precision y
)
{
int found,element,count,level,i,j;
standard_precision eta1,eta2,eta3;
standard_precision lN[ELNMAX+1];
standard_precision dOmega;
standard_precision interpolant;
const int dims = E->mesh.nsd;
level=E->mesh.levmax;
element=1;
count=0;
do {
count++;
found=1;
general_element_coords(E,element,x,z,y,&eta1,&eta2,&eta3,level);
if((eta1-1.0) > 1.0e-12) { /* find in X direction */
element += E->mesh.ELZ[level];
found = 0;
}
else if((eta1+1.0) < -1.0e-12) {
element -= E->mesh.ELZ[level];
found = 0;
}
if((eta2-1.0) > 1.0e-12) { /* find in Z direction */
element += 1;
found = 0;
}
else if((eta2+1.0) < -1.0e-12) {
element -= 1;
found = 0;
}
if(3==dims && (eta3-1.0) > 1.0e-12) { /* find in Y direction */
element += E->mesh.ELX[level] * E->mesh.ELZ[level];
found = 0;
}
else if(3==dims && (eta3+1.0) < -1.0e-12) { /*RAA: 23/01/03, was missing '-' here*/
element -= E->mesh.ELX[level] * E->mesh.ELZ[level];
found = 0;
}
if(element < 1)
element = 1;
else if(element > E->mesh.NEL[level])
element = E->mesh.NEL[level];
} while (found == 0 && count <= E->mesh.NEL[level]);
if(!found) {
fprintf(stderr,"%g,%g,%g is not in the domain !\n",x,z,y);
exit(-1);
}
v_shape_fn(E,element,lN,eta1,eta2,eta3,level);
interpolant=0.0;
for(j=1;j<=enodes[dims];j++) {
interpolant += field[E->IEN[level][element].node[j]] * lN[j];
}
/*
fprintf(stderr,"%g %g %g -> %g\n",x,z,y,interpolant);
*/
return(interpolant);
}
/* ===========================================================================
Function to create the element locations from the node positions.
=========================================================================== */
void element_locations_from_nodes(
struct All_variables *E
)
{
int i,j,k,d,element,node;
int elx,elz,ely,lev;
int xhighnum,xlownum;
int n1,n2,n3,n4,n5,n6,n7,n8;
standard_precision xlowmean,xhighmean,xmean;
standard_precision zlowmean,zhighmean;
standard_precision ylowmean,yhighmean;
standard_precision area;
void inject_node_values();
const int dims = E->mesh.nsd;
for(i=1;i<=E->mesh.elx;i++)
for(j=1;j<=E->mesh.elz;j++)
for(k=1;k<=E->mesh.ely;k++) {
element = j + (i-1)*E->mesh.elz + (k-1)*E->mesh.elz*E->mesh.elx;
area = 1.0;
for(d=1;d<=dims;d++) {
/* Get the mean of the coordinates in direction d, and
the mean of the differences from the centroid which give us
a measure of the size of the element */
xmean = 0.0;
for(node=1;node<=enodes[dims];node++) {
n1=E->ien[element].node[node];
/*RAA: 23/10/01, added !per_y part to line directly below*/
if(E->mesh.periodic_x && !E->mesh.periodic_y && i == E->mesh.elx && loc[node].plus[0]==0)
n1 += (E->mesh.nox-1)*E->mesh.noz;
/*RAA: 9/10/01, 24/10/01, added rest of statements below */
else if(E->mesh.periodic_y && !E->mesh.periodic_x && k == E->mesh.ely && (node==5 || node==6 || node==7 || node==8))
n1 += (E->mesh.noy-1)*E->mesh.nox*E->mesh.noz;
else if(3==dims && E->mesh.periodic_x && E->mesh.periodic_y) {
if(i == E->mesh.elx && k != E->mesh.ely && loc[node].plus[0]==0)
n1 += (E->mesh.nox-1)*E->mesh.noz;
else if(k == E->mesh.ely && i != E->mesh.elx && (node==5 || node==6 || node==7 || node==8))
n1 += (E->mesh.noy-1)*E->mesh.nox*E->mesh.noz;
else if(k == E->mesh.ely && i == E->mesh.elx) {
if(d==1 || d==2) {
if(node==3 || node==4 || node == 7 || node == 8)
n1 += (E->mesh.nox-1)*E->mesh.noz;
else if(node==5 || node==6)
n1 += (E->mesh.noy-1)*E->mesh.nox*E->mesh.noz;
}
else if(d==3) {
if(node==3 || node==4)
n1 += (E->mesh.nox-1)*E->mesh.noz;
else if(node==5 || node==6 || node == 7 || node == 8)
n1 += (E->mesh.noy-1)*E->mesh.nox*E->mesh.noz;
}
}
} /*end else if per_x and per_y*/
xmean += E->x[d][n1];
}
xmean /= (standard_precision) enodes[dims];
xlowmean = xhighmean = 0.0;
xlownum = xhighnum = 0;
for(node=1;node<=enodes[dims];node++) {
n1=E->ien[element].node[node];
/*RAA: 23/10/01, added !per_y part to line directly below*/
if(E->mesh.periodic_x && !E->mesh.periodic_y && i == E->mesh.elx && loc[node].plus[0]==0)
n1 += (E->mesh.nox-1)*E->mesh.noz;
/*RAA: 9/10/01, 24/10/01, added rest of statements below */
else if(E->mesh.periodic_y && !E->mesh.periodic_x && k == E->mesh.ely && (node==5 || node==6 || node==7 || node==8))
n1 += (E->mesh.noy-1)*E->mesh.nox*E->mesh.noz;
else if(3==dims && E->mesh.periodic_x && E->mesh.periodic_y) {
if(i == E->mesh.elx && k != E->mesh.ely && loc[node].plus[0]==0)
n1 += (E->mesh.nox-1)*E->mesh.noz;
else if(k == E->mesh.ely && i != E->mesh.elx && (node==5 || node==6 || node==7 || node==8))
n1 += (E->mesh.noy-1)*E->mesh.nox*E->mesh.noz;
else if(k == E->mesh.ely && i == E->mesh.elx) {
if(d==1 || d==2) {
if(node==3 || node==4 || node == 7 || node == 8)
n1 += (E->mesh.nox-1)*E->mesh.noz;
else if(node==5 || node==6)
n1 += (E->mesh.noy-1)*E->mesh.nox*E->mesh.noz;
}
else if(d==3) {
if(node==3 || node==4)
n1 += (E->mesh.nox-1)*E->mesh.noz;
else if(node==5 || node==6 || node == 7 || node == 8)
n1 += (E->mesh.noy-1)*E->mesh.nox*E->mesh.noz;
}
}
} /*end else if per_x and per_y*/
if (E->x[d][n1] <= xmean) {
xlownum++;
xlowmean += E->x[d][n1];
}
else {
xhighnum++;
xhighmean += E->x[d][n1];
}
}
if( xlownum > 0)
xlowmean /= (standard_precision) xlownum;
else
xlowmean = xmean;
if( xhighnum > 0)
xhighmean /= (standard_precision) xhighnum;
else
xhighmean = xmean;
E->eco[element].size[d] = 0.5 * (xhighmean-xlowmean);
E->eco[element].recip_size[d] = 1.0/E->eco[element].size[d];
E->eco[element].centre[d] = xmean;
area *= E->eco[element].size[d];
}
E->eco[element].area = area;
/* if(area < 0.0) */
/* fprintf(stderr,"element %d - area = %g (%g x %g) (%g , %g)\n",element,area,
E->eco[element].size[1],E->eco[element].size[2],
E->eco[element].centre[1],E->eco[element].centre[2] ); */
}/*end of the big loop*/
/* now project them to lower levels where appropriate */
for(lev=E->mesh.levmax-1;lev>=E->mesh.levmin;lev--) {
elx = E->mesh.ELX[lev];
elz = E->mesh.ELZ[lev];
ely = E->mesh.ELY[lev];
for(i=1;i<=elx;i++)
for(j=1;j<=elz;j++)
for(k=1;k<=ely;k++) {
element = (k-1)*elx*elz + (i-1)*elz + j;
area = 1.0;
for(d=1;d<=dims;d++) {
/* Get The Mean Of The Coordinates In Direction D, And
The Mean Of The Differences From The Centroid Which Give Us
A Measure Of The Size Of The Element */
xmean = 0.0;
for(node=1;node<=enodes[dims];node++) {
n1=E->IEN[lev][element].node[node];
/*RAA: 23/10/01, added !per_y part to line directly below*/
if(E->mesh.periodic_x && !E->mesh.periodic_y && i == E->mesh.ELX[lev] && loc[node].plus[0]==0)
n1 += (E->mesh.NOX[lev]-1)*E->mesh.NOZ[lev];
/*RAA: 9/10/01, 24/10/01, added the rest of the statements below*/
else if(E->mesh.periodic_y && !E->mesh.periodic_x && k == E->mesh.ELY[lev] && (node==5 || node==6 || node==7 || node==8))
n1 += (E->mesh.NOY[lev]-1)*E->mesh.NOX[lev]*E->mesh.NOZ[lev];
else if(3==dims && E->mesh.periodic_x && E->mesh.periodic_y) {
if(i == E->mesh.ELX[lev] && k != E->mesh.ELY[lev] && loc[node].plus[0]==0)
n1 += (E->mesh.NOX[lev]-1)*E->mesh.NOZ[lev];
else if(k == E->mesh.ELY[lev] && i != E->mesh.ELX[lev] && (node==5 || node==6 || node==7 || node==8))
n1 += (E->mesh.NOY[lev]-1)*E->mesh.NOX[lev]*E->mesh.NOZ[lev];
else if(k == E->mesh.ELY[lev] && i == E->mesh.ELX[lev]) {
if(d==1 || d==2) {
if(node==3 || node==4 || node==7 || node==8)
n1 += (E->mesh.NOX[lev]-1)*E->mesh.NOZ[lev];
else if(node==5 || node==6)
n1 += (E->mesh.NOY[lev]-1)*E->mesh.NOX[lev]*E->mesh.NOZ[lev];
}
else if(d==3) {
if(node==3 || node==4)
n1 += (E->mesh.NOX[lev]-1)*E->mesh.NOZ[lev];
else if(node==5 || node==6 || node==7 || node==8)
n1 += (E->mesh.NOY[lev]-1)*E->mesh.NOX[lev]*E->mesh.NOZ[lev];
}
}
} /*end else if per_x and per_y*/
xmean += E->X[lev][d][n1];
}
xmean /= (standard_precision) enodes[dims] ;
xlowmean = xhighmean = 0.0;
xlownum = xhighnum = 0;
for(node=1;node<=enodes[dims];node++) {
n1=E->IEN[lev][element].node[node];
/*RAA: 23/10/01, added !per_y part to line directly below*/
if(E->mesh.periodic_x && !E->mesh.periodic_y && i == E->mesh.ELX[lev] && loc[node].plus[0]==0)
n1 += (E->mesh.NOX[lev]-1)*E->mesh.NOZ[lev];
/*RAA: 9/10/01, 24/10/01, added the rest of the statements below*/
else if(E->mesh.periodic_y && !E->mesh.periodic_x && k == E->mesh.ELY[lev] && (node==5 || node==6 || node==7 || node==8))
n1 += (E->mesh.NOY[lev]-1)*E->mesh.NOX[lev]*E->mesh.NOZ[lev];
else if(3==dims && E->mesh.periodic_x && E->mesh.periodic_y) {
if(i == E->mesh.ELX[lev] && k != E->mesh.ELY[lev] && loc[node].plus[0]==0)
n1 += (E->mesh.NOX[lev]-1)*E->mesh.NOZ[lev];
else if(k == E->mesh.ELY[lev] && i != E->mesh.ELX[lev] && (node==5 || node==6 || node==7 || node==8))
n1 += (E->mesh.NOY[lev]-1)*E->mesh.NOX[lev]*E->mesh.NOZ[lev];
else if(k == E->mesh.ELY[lev] && i == E->mesh.ELX[lev]) {
if(d==1 || d==2) {
if(node==3 || node==4 || node==7 || node==8)
n1 += (E->mesh.NOX[lev]-1)*E->mesh.NOZ[lev];
else if(node==5 || node==6)
n1 += (E->mesh.NOY[lev]-1)*E->mesh.NOX[lev]*E->mesh.NOZ[lev];
}
else if(d==3) {
if(node==3 || node==4)
n1 += (E->mesh.NOX[lev]-1)*E->mesh.NOZ[lev];
else if(node==5 || node==6 || node==7 || node==8)
n1 += (E->mesh.NOY[lev]-1)*E->mesh.NOX[lev]*E->mesh.NOZ[lev];
}
}
} /*end else if per_x and per_y*/
if (E->X[lev][d][n1] <= xmean) {
xlownum++;
xlowmean += E->X[lev][d][n1];
}
else {
xhighnum++;
xhighmean += E->X[lev][d][n1];
}
}
if( xlownum > 0)
xlowmean /= (standard_precision) xlownum;
else
xlowmean = xmean;
if( xhighnum > 0)
xhighmean /= (standard_precision) xhighnum;
else
xhighmean = xmean;
E->ECO[lev][element].size[d] = 0.5 * (xhighmean-xlowmean);
E->ECO[lev][element].recip_size[d] = 1.0/E->ECO[lev][element].size[d];
E->ECO[lev][element].centre[d] = xmean;
area *= E->ECO[lev][element].size[d];
}
E->ECO[lev][element].area = area;
}
/* onto next level */
}
/* Generate data for the advection scheme: element characteristic sizes and directions ... */
for(lev=E->mesh.levmin;lev<=E->mesh.levmax;lev++) {
elx = E->mesh.ELX[lev];
elz = E->mesh.ELZ[lev];
ely = E->mesh.ELY[lev];
for(i=1;i<=elx;i++)
for(j=1;j<=elz;j++)
for(k=1;k<=ely;k++) {
element = (k-1)*elx*elz + (i-1)*elz + j;
n1=E->IEN[lev][element].node[1];
n2=E->IEN[lev][element].node[2];
n3=E->IEN[lev][element].node[3];
n4=E->IEN[lev][element].node[4];
if(3==dims){
n5=E->IEN[lev][element].node[5];
n6=E->IEN[lev][element].node[6];
n7=E->IEN[lev][element].node[7];
n8=E->IEN[lev][element].node[8];
}
/*RAA: 24/10/01, added !per_y to statement directly below */
if(i==elx && E->mesh.periodic_x && !E->mesh.periodic_y) {
/* fprintf(stderr,"%d: el %d, node 3 %d ->%d [%d]\n",lev,element,
n3,n3+(E->mesh.NOX[lev]-1) * E->mesh.NOZ[lev],E->mesh.NNO[lev]); */
n3 += (E->mesh.NOX[lev]-1) * E->mesh.NOZ[lev];
n4 += (E->mesh.NOX[lev]-1) * E->mesh.NOZ[lev];
if(3==dims) {
n7 += (E->mesh.NOX[lev]-1) * E->mesh.NOZ[lev];
n8 += (E->mesh.NOX[lev]-1) * E->mesh.NOZ[lev];
}
}
/*RAA: 9/10/01, 24/10/01, added statements below */
else if(3==dims && E->mesh.periodic_y && !E->mesh.periodic_x && k==ely) {
n5 += (E->mesh.NOY[lev]-1) * E->mesh.NOX[lev] * E->mesh.NOZ[lev];
n6 += (E->mesh.NOY[lev]-1) * E->mesh.NOX[lev] * E->mesh.NOZ[lev];
n7 += (E->mesh.NOY[lev]-1) * E->mesh.NOX[lev] * E->mesh.NOZ[lev];
n8 += (E->mesh.NOY[lev]-1) * E->mesh.NOX[lev] * E->mesh.NOZ[lev];
}
/*RAA: 24/10/01, separate out this section for clarity */
else if(3==dims && E->mesh.periodic_y && E->mesh.periodic_x) {
if(k!=ely && i==elx) {
n3 += (E->mesh.NOX[lev]-1) * E->mesh.NOZ[lev];
n4 += (E->mesh.NOX[lev]-1) * E->mesh.NOZ[lev];
n7 += (E->mesh.NOX[lev]-1) * E->mesh.NOZ[lev];
n8 += (E->mesh.NOX[lev]-1) * E->mesh.NOZ[lev];
}
else if(k==ely && i!=elx) {
n5 += (E->mesh.NOY[lev]-1) * E->mesh.NOX[lev] * E->mesh.NOZ[lev];
n6 += (E->mesh.NOY[lev]-1) * E->mesh.NOX[lev] * E->mesh.NOZ[lev];
n7 += (E->mesh.NOY[lev]-1) * E->mesh.NOX[lev] * E->mesh.NOZ[lev];
n8 += (E->mesh.NOY[lev]-1) * E->mesh.NOX[lev] * E->mesh.NOZ[lev];
}
else if(k==ely && i==elx) {
n3 += (E->mesh.NOX[lev]-1) * E->mesh.NOZ[lev];
n4 += (E->mesh.NOX[lev]-1) * E->mesh.NOZ[lev];
n5 += (E->mesh.NOY[lev]-1) * E->mesh.NOX[lev] * E->mesh.NOZ[lev];
n6 += (E->mesh.NOY[lev]-1) * E->mesh.NOX[lev] * E->mesh.NOZ[lev];
/* n7 += (E->mesh.NOX[lev]-1) * E->mesh.NOZ[lev];
n8 += (E->mesh.NOX[lev]-1) * E->mesh.NOZ[lev];
*/
}
} /*RAA: end of per_x and per_y addition*/
/* 1: x direction */
if(2==dims) {
xlowmean = (E->X[lev][1][n1] +
E->X[lev][1][n2] ) * 0.5;
xhighmean = (E->X[lev][1][n3] +
E->X[lev][1][n4] ) * 0.5;
zlowmean = (E->X[lev][2][n1] +
E->X[lev][2][n2] ) * 0.5;
zhighmean = (E->X[lev][2][n3] +
E->X[lev][2][n4] ) * 0.5;
E->ECO[lev][element].ntl_dirns[1][1] = xhighmean - xlowmean;
E->ECO[lev][element].ntl_dirns[1][2] = zhighmean - zlowmean;
E->ECO[lev][element].ntl_size[1] = sqrt(E->ECO[lev][element].ntl_dirns[1][1] *
E->ECO[lev][element].ntl_dirns[1][1] +
E->ECO[lev][element].ntl_dirns[1][2] *
E->ECO[lev][element].ntl_dirns[1][2] );
E->ECO[lev][element].ntl_recip_size[1] = 1.0 / E->ECO[lev][element].ntl_size[1] ;
E->ECO[lev][element].ntl_dirns[1][1] *= E->ECO[lev][element].ntl_recip_size[1];
E->ECO[lev][element].ntl_dirns[1][2] *= E->ECO[lev][element].ntl_recip_size[1];
E->ECO[lev][element].ntl_size[1] *= 0.5; /* consistent with other element definitions */
E->ECO[lev][element].ntl_recip_size[1] *= 2.0;
}
else {
xlowmean = (E->X[lev][1][n1] +
E->X[lev][1][n2] +
E->X[lev][1][n5] +
E->X[lev][1][n6] ) * 0.25;
xhighmean = (E->X[lev][1][n3] +
E->X[lev][1][n4] +
E->X[lev][1][n7] +
E->X[lev][1][n8] ) * 0.25;
zlowmean = (E->X[lev][2][n1] +
E->X[lev][2][n2] +
E->X[lev][2][n5] +
E->X[lev][2][n6] ) * 0.25;
zhighmean = (E->X[lev][2][n3] +
E->X[lev][2][n4] +
E->X[lev][2][n7] +
E->X[lev][2][n8] ) * 0.25;
ylowmean = (E->X[lev][3][n1] +
E->X[lev][3][n2] +
E->X[lev][3][n5] +
E->X[lev][3][n6] ) * 0.25;
yhighmean = (E->X[lev][3][n3] +
E->X[lev][3][n4] +
E->X[lev][3][n7] +
E->X[lev][3][n8] ) * 0.25;
E->ECO[lev][element].ntl_dirns[1][1] = xhighmean - xlowmean;
E->ECO[lev][element].ntl_dirns[1][2] = zhighmean - zlowmean;
E->ECO[lev][element].ntl_dirns[1][3] = yhighmean - ylowmean;
E->ECO[lev][element].ntl_size[1] = sqrt(E->ECO[lev][element].ntl_dirns[1][1] *
E->ECO[lev][element].ntl_dirns[1][1] +
E->ECO[lev][element].ntl_dirns[1][2] *
E->ECO[lev][element].ntl_dirns[1][2] +
E->ECO[lev][element].ntl_dirns[1][3] *
E->ECO[lev][element].ntl_dirns[1][3] );
E->ECO[lev][element].ntl_recip_size[1] = 1.0 / E->ECO[lev][element].ntl_size[1] ;
E->ECO[lev][element].ntl_dirns[1][1] *= E->ECO[lev][element].ntl_recip_size[1];
E->ECO[lev][element].ntl_dirns[1][2] *= E->ECO[lev][element].ntl_recip_size[1];
E->ECO[lev][element].ntl_dirns[1][3] *= E->ECO[lev][element].ntl_recip_size[1];
E->ECO[lev][element].ntl_size[1] *= 0.5;
E->ECO[lev][element].ntl_recip_size[1] *= 2.0;
}
/* 2: z direction */
if(2==dims) {
xlowmean = (E->X[lev][1][n1] +
E->X[lev][1][n4] ) * 0.5;
xhighmean = (E->X[lev][1][n2] +
E->X[lev][1][n3] ) * 0.5;
zlowmean = (E->X[lev][2][n1] +
E->X[lev][2][n4] ) * 0.5;
zhighmean = (E->X[lev][2][n2] +
E->X[lev][2][n3] ) * 0.5;
E->ECO[lev][element].ntl_dirns[2][1] = xhighmean - xlowmean;
E->ECO[lev][element].ntl_dirns[2][2] = zhighmean - zlowmean;
E->ECO[lev][element].ntl_size[2] = sqrt(E->ECO[lev][element].ntl_dirns[2][1] *
E->ECO[lev][element].ntl_dirns[2][1] +