Revision 5f38ecb5e1f4ef9a6cd70970703557a4ffddf54c authored by Eh Tan on 20 November 2009, 21:58:43 UTC, committed by Eh Tan on 20 November 2009, 21:58:43 UTC
1 parent aca8438
Sphere_harmonics.c
/* Functions relating to the building and use of mesh locations ... */
#include <math.h>
#include <sys/types.h>
#include "element_definitions.h"
#include "global_defs.h"
#include <stdlib.h>
static void compute_sphereh_table(struct All_variables *);
/* ======================================================================
====================================================================== */
void set_sphere_harmonics(E)
struct All_variables *E;
{
int m,node,ll,mm,i,j;
i=0;
for (ll=0;ll<=E->output.llmax;ll++)
for (mm=0;mm<=ll;mm++) {
E->sphere.hindex[ll][mm] = i;
i++;
}
E->sphere.hindice = i;
/* spherical harmonic coeff (0=cos, 1=sin)
for surface topo, cmb topo and geoid */
for (i=0;i<=1;i++) {
E->sphere.harm_geoid[i]=(float*)malloc(E->sphere.hindice*sizeof(float));
E->sphere.harm_geoid_from_bncy[i]=(float*)malloc(E->sphere.hindice*sizeof(float));
E->sphere.harm_geoid_from_bncy_botm[i]=(float*)malloc(E->sphere.hindice*sizeof(float));
E->sphere.harm_geoid_from_tpgt[i]=(float*)malloc(E->sphere.hindice*sizeof(float));
E->sphere.harm_geoid_from_tpgb[i]=(float*)malloc(E->sphere.hindice*sizeof(float));
E->sphere.harm_tpgt[i]=(float*)malloc(E->sphere.hindice*sizeof(float));
E->sphere.harm_tpgb[i]=(float*)malloc(E->sphere.hindice*sizeof(float));
}
compute_sphereh_table(E);
return;
}
/* =====================================
Generalized Legendre polynomials
=====================================*/
double modified_plgndr_a(int l, int m, double t)
{
int i,ll;
double x,fact1,fact2,fact,pll,pmm,pmmp1,somx2,plgndr;
const double three=3.0;
const double two=2.0;
const double one=1.0;
x = cos(t);
pmm=one;
if(m>0) {
somx2=sqrt((one-x)*(one+x));
fact1= three;
fact2= two;
for (i=1;i<=m;i++) {
fact=sqrt(fact1/fact2);
pmm = -pmm*fact*somx2;
fact1+= two;
fact2+= two;
}
}
if (l==m)
plgndr = pmm;
else {
pmmp1 = x*sqrt(two*m+three)*pmm;
if(l==m+1)
plgndr = pmmp1;
else {
for (ll=m+2;ll<=l;ll++) {
fact1= sqrt((4.0*ll*ll-one)*(double)(ll-m)/(double)(ll+m));
fact2= sqrt((2.0*ll+one)*(ll-m)*(ll+m-one)*(ll-m-one)
/(double)((two*ll-three)*(ll+m)));
pll = ( x*fact1*pmmp1-fact2*pmm)/(ll-m);
pmm = pmmp1;
pmmp1 = pll;
}
plgndr = pll;
}
}
plgndr /= sqrt(4.0*M_PI);
if (m!=0) plgndr *= sqrt(two);
return plgndr;
}
/* =========================================================
expand the field TG into spherical harmonics
========================================================= */
void sphere_expansion(E,TG,sphc,sphs)
struct All_variables *E;
float **TG,*sphc,*sphs;
{
int el,nint,d,p,i,m,j,es,mm,ll,rand();
void sum_across_surf_sph1();
for (i=0;i<E->sphere.hindice;i++) {
sphc[i] = 0.0;
sphs[i] = 0.0;
}
for (m=1;m<=E->sphere.caps_per_proc;m++)
for (es=1;es<=E->lmesh.snel;es++) {
for (ll=0;ll<=E->output.llmax;ll++)
for (mm=0; mm<=ll; mm++) {
p = E->sphere.hindex[ll][mm];
for(nint=1;nint<=onedvpoints[E->mesh.nsd];nint++) {
for(d=1;d<=onedvpoints[E->mesh.nsd];d++) {
j = E->sien[m][es].node[d];
sphc[p] += TG[m][E->sien[m][es].node[d]]
* E->sphere.tablesplm[m][j][p]
* E->sphere.tablescosf[m][j][mm]
* E->M.vpt[GMVINDEX(d,nint)]
* E->surf_det[m][nint][es];
sphs[p] += TG[m][E->sien[m][es].node[d]]
* E->sphere.tablesplm[m][j][p]
* E->sphere.tablessinf[m][j][mm]
* E->M.vpt[GMVINDEX(d,nint)]
* E->surf_det[m][nint][es];
}
}
} /* end for ll and mm */
}
sum_across_surf_sph1(E,sphc,sphs);
return;
}
void debug_sphere_expansion(struct All_variables *E)
{
/* expand temperature field (which should be a sph. harm. load)
* and output the expansion coeff. to stderr
*/
int m, i, j, k, p, node;
int ll, mm;
float *TT[NCS], *sph_harm[2];
for(m=1;m<=E->sphere.caps_per_proc;m++)
TT[m] = (float *) malloc ((E->lmesh.nsf+1)*sizeof(float));
/* sin coeff */
sph_harm[0] = (float*)malloc(E->sphere.hindice*sizeof(float));
/* cos coeff */
sph_harm[1] = (float*)malloc(E->sphere.hindice*sizeof(float));
for(k=1;k<=E->lmesh.noz;k++) {
for(m=1;m<=E->sphere.caps_per_proc;m++)
for(i=1;i<=E->lmesh.noy;i++)
for(j=1;j<=E->lmesh.nox;j++) {
node= k + (j-1)*E->lmesh.noz + (i-1)*E->lmesh.nox*E->lmesh.noz;
p = j + (i-1)*E->lmesh.nox;
TT[m][p] = E->T[m][node];
}
/* expand TT into spherical harmonics */
sphere_expansion(E, TT, sph_harm[0], sph_harm[1]);
/* only the first nprocz CPU needs output */
if(E->parallel.me < E->parallel.nprocz) {
for (ll=0;ll<=E->output.llmax;ll++)
for (mm=0; mm<=ll; mm++) {
p = E->sphere.hindex[ll][mm];
fprintf(stderr, "T expanded layer=%d ll=%d mm=%d -- %12g %12g\n",
k+E->lmesh.nzs-1, ll, mm,
sph_harm[0][p], sph_harm[1][p]);
}
}
}
return;
}
/* ==================================================*/
/* ==================================================*/
static void compute_sphereh_table(E)
struct All_variables *E;
{
double modified_plgndr_a();
int m,node,ll,mm,i,j,p;
double t,f,mmf;
for(m=1;m<=E->sphere.caps_per_proc;m++) {
E->sphere.tablesplm[m] = (double **) malloc((E->lmesh.nsf+1)*sizeof(double*));
E->sphere.tablescosf[m] = (double **) malloc((E->lmesh.nsf+1)*sizeof(double*));
E->sphere.tablessinf[m] = (double **) malloc((E->lmesh.nsf+1)*sizeof(double*));
for (i=1;i<=E->lmesh.nsf;i++) {
E->sphere.tablesplm[m][i]= (double *)malloc((E->sphere.hindice)*sizeof(double));
E->sphere.tablescosf[m][i]= (double *)malloc((E->output.llmax+1)*sizeof(double));
E->sphere.tablessinf[m][i]= (double *)malloc((E->output.llmax+1)*sizeof(double));
}
}
for(m=1;m<=E->sphere.caps_per_proc;m++) {
for (j=1;j<=E->lmesh.nsf;j++) {
node = j*E->lmesh.noz;
f=E->sx[m][2][node];
t=E->sx[m][1][node];
for (mm=0;mm<=E->output.llmax;mm++) {
mmf = (double)(mm)*f;
E->sphere.tablescosf[m][j][mm] = cos( mmf );
E->sphere.tablessinf[m][j][mm] = sin( mmf );
}
for (ll=0;ll<=E->output.llmax;ll++)
for (mm=0;mm<=ll;mm++) {
p = E->sphere.hindex[ll][mm];
E->sphere.tablesplm[m][j][p] = modified_plgndr_a(ll,mm,t) ;
}
}
}
return;
}
![swh spinner](/static/img/swh-spinner.gif)
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