https://github.com/geodynamics/citcoms
Revision bcf06ab870d4cfd4a7c8594146ed51e41b23d5f9 authored by Eh Tan on 09 August 2007, 22:57:28 UTC, committed by Eh Tan on 09 August 2007, 22:57:28 UTC
Two non-dimensional parameters are added: "dissipation_number" and "gruneisen"
under the Solver component. One can use the original incompressible solver by
setting "gruneisen=0". The code will treat this as "gruneisen=infinity". 
Setting non-zero value to "gruneisen" will switch to compressible solver.

One can use the TALA solver for incompressible case by setting "gruneisen" to
a non-zero value while setting "dissipation_number=0". This is useful when
debugging the compressible solver.

Two implementations are available: one by Wei Leng (U. Colorado) and one by
Eh Tan (CIG). Leng's version uses the original conjugate gradient method for
the Uzawa iteration and moves the contribution of compressibility to the RHS,
similar to the method of Ita and King, JGR, 1994. Tan's version uses the
bi-conjugate gradient stablized method for the Uzawa iteration, similar to the
method of Tan and Gurnis, JGR, 2007. Both versions agree very well. In the
benchmark case, 33x33x33 nodes per cap, Di/gamma=1.0, Ra=1.0, delta function
of load at the mid mantle, the peak velocity differs by only 0.007%. Leng's
version is enabled by default. Edit function solve_Ahat_p_fhat() in
lib/Stokes_flow_Incomp.c to switch to Tan's version.

1 parent 91bcb85
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Tip revision: bcf06ab870d4cfd4a7c8594146ed51e41b23d5f9 authored by Eh Tan on 09 August 2007, 22:57:28 UTC
Finished the compressible Stokes solver for TALA.
Tip revision: bcf06ab
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+2)*sizeof(float));
        E->sphere.harm_geoid_from_bncy[i]=(float*)malloc((E->sphere.hindice+2)*sizeof(float));
        E->sphere.harm_geoid_from_tpgt[i]=(float*)malloc((E->sphere.hindice+2)*sizeof(float));
        E->sphere.harm_geoid_from_tpgb[i]=(float*)malloc((E->sphere.hindice+2)*sizeof(float));
    }

    compute_sphereh_table(E);

    return;
}

/* =========================================================
   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();
    //double t,f,sphere_h();
    void sum_across_surf_sph1();
    void get_global_1d_shape_fn();
    struct Shape_function1 M;
    struct Shape_function1_dA dGamma;

    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++)   {
            el = es*E->lmesh.elz;

            get_global_1d_shape_fn(E,el,&M,&dGamma,1,m);

            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)]
                                * dGamma.vpt[GMVGAMMA(1,nint)];
                            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)]
                                * dGamma.vpt[GMVGAMMA(1,nint)];
                        }
                    }

                }       /* end for ll and mm  */

        }

    sum_across_surf_sph1(E,sphc,sphs);

    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;


    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+3)*sizeof(double));
            E->sphere.tablescosf[m][i]= (double *)malloc((E->output.llmax+3)*sizeof(double));
            E->sphere.tablessinf[m][i]= (double *)malloc((E->output.llmax+3)*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++)   {
                E->sphere.tablescosf[m][j][mm] = cos( (double)(mm)*f );
                E->sphere.tablessinf[m][j][mm] = sin( (double)(mm)*f );
            }

            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;
}

/* ================================================
   compute angle and area
   ================================================*/

void compute_angle_surf_area (E)
     struct All_variables *E;
{

    int es,el,m,i,j,ii,ia[5],lev;
    double aa,y1[4],y2[4],angle[6],xx[4][5],area_sphere_cap();
    void get_angle_sphere_cap();
    void parallel_process_termination();

    for (m=1;m<=E->sphere.caps_per_proc;m++)   {
        ia[1] = 1;
        ia[2] = E->lmesh.noz*E->lmesh.nox-E->lmesh.noz+1;
        ia[3] = E->lmesh.nno-E->lmesh.noz+1;
        ia[4] = ia[3]-E->lmesh.noz*(E->lmesh.nox-1);

        for (i=1;i<=4;i++)  {
            xx[1][i] = E->x[m][1][ia[i]]/E->sx[m][3][ia[1]];
            xx[2][i] = E->x[m][2][ia[i]]/E->sx[m][3][ia[1]];
            xx[3][i] = E->x[m][3][ia[i]]/E->sx[m][3][ia[1]];
        }

        get_angle_sphere_cap(xx,angle);

        for (i=1;i<=4;i++)         /* angle1: bet 1 & 2; angle2: bet 2 & 3 ..*/
            E->sphere.angle[m][i] = angle[i];

        E->sphere.area[m] = area_sphere_cap(angle);

        for (lev=E->mesh.levmax;lev>=E->mesh.levmin;lev--)
            for (es=1;es<=E->lmesh.SNEL[lev];es++)              {
                el = (es-1)*E->lmesh.ELZ[lev]+1;
                for (i=1;i<=4;i++)
                    ia[i] = E->IEN[lev][m][el].node[i];

                for (i=1;i<=4;i++)  {
                    xx[1][i] = E->X[lev][m][1][ia[i]]/E->SX[lev][m][3][ia[1]];
                    xx[2][i] = E->X[lev][m][2][ia[i]]/E->SX[lev][m][3][ia[1]];
                    xx[3][i] = E->X[lev][m][3][ia[i]]/E->SX[lev][m][3][ia[1]];
                }

                get_angle_sphere_cap(xx,angle);

                for (i=1;i<=4;i++)         /* angle1: bet 1 & 2; angle2: bet 2 & 3 ..*/
                    E->sphere.angle1[lev][m][i][es] = angle[i];

                E->sphere.area1[lev][m][es] = area_sphere_cap(angle);

/*              fprintf(E->fp_out,"lev%d %d %.6e %.6e %.6e %.6e %.6e\n",lev,es,angle[1],angle[2],angle[3],angle[4],E->sphere.area1[lev][m][es]); */

            }  /* end for lev and es */

    }  /* end for m */

    return;
}

/* ================================================
   area of spherical rectangle
   ================================================ */
double area_sphere_cap(angle)
     double angle[6];
{

    double area,a,b,c;
    double area_of_sphere_triag();

    a = angle[1];
    b = angle[2];
    c = angle[5];
    area = area_of_sphere_triag(a,b,c);

    a = angle[3];
    b = angle[4];
    c = angle[5];
    area += area_of_sphere_triag(a,b,c);

    return (area);
}

/* ================================================
   area of spherical triangle
   ================================================ */
double area_of_sphere_triag(a,b,c)
     double a,b,c;
{

    double ss,ak,aa,bb,cc,area;
    const double e_16 = 1.0e-16;
    const double two = 2.0;
    const double pt5 = 0.5;

    ss = (a+b+c)*pt5;
    area=0.0;
    a = sin(ss-a);
    b = sin(ss-b);
    c = sin(ss-c);
    ak = a*b*c/sin(ss);   /* sin(ss-a)*sin(ss-b)*sin(ss-c)/sin(ss)  */
    if(ak<e_16) return (area);
    ak = sqrt(ak);
    aa = two*atan(ak/a);
    bb = two*atan(ak/b);
    cc = two*atan(ak/c);
    area = aa+bb+cc-M_PI;

    return (area);
}

/*  =====================================================================
    get the area for given five points (4 nodes for a rectangle and one test node)
    angle [i]: angle bet test node and node i of the rectangle
    angle1[i]: angle bet nodes i and i+1 of the rectangle
    ====================================================================== */
double area_of_5points(E,lev,m,el,x,ne)
     struct All_variables *E;
     int lev,m,el,ne;
     double x[4];
{
    int i,es,ia[5];
    double area1,get_angle(),area_of_sphere_triag();
    double xx[4],angle[5],angle1[5];

    for (i=1;i<=4;i++)
        ia[i] = E->IEN[lev][m][el].node[i];

    es = (el-1)/E->lmesh.ELZ[lev]+1;

    for (i=1;i<=4;i++)                 {
        xx[1] = E->X[lev][m][1][ia[i]]/E->SX[lev][m][3][ia[1]];
        xx[2] = E->X[lev][m][2][ia[i]]/E->SX[lev][m][3][ia[1]];
        xx[3] = E->X[lev][m][3][ia[i]]/E->SX[lev][m][3][ia[1]];
        angle[i] = get_angle(x,xx);  /* get angle bet (i,j) and other four*/
        angle1[i]= E->sphere.angle1[lev][m][i][es];
    }

    area1 = area_of_sphere_triag(angle[1],angle[2],angle1[1])
        + area_of_sphere_triag(angle[2],angle[3],angle1[2])
        + area_of_sphere_triag(angle[3],angle[4],angle1[3])
        + area_of_sphere_triag(angle[4],angle[1],angle1[4]);

    return (area1);
}

/*  ================================
    get the angle for given four points spherical rectangle
    ================================= */

void  get_angle_sphere_cap(xx,angle)
     double xx[4][5],angle[6];
{

    int i,j,ii;
    double y1[4],y2[4],get_angle();;

    for (i=1;i<=4;i++)     {     /* angle1: bet 1 & 2; angle2: bet 2 & 3 ..*/
        for (j=1;j<=3;j++)     {
            ii=(i==4)?1:(i+1);
            y1[j] = xx[j][i];
            y2[j] = xx[j][ii];
        }
        angle[i] = get_angle(y1,y2);
    }

    for (j=1;j<=3;j++) {
        y1[j] = xx[j][1];
        y2[j] = xx[j][3];
    }

    angle[5] = get_angle(y1,y2);     /* angle5 for betw 1 and 3: diagonal */
    return;
}

/*  ================================
    get the angle for given two points
    ================================= */
double get_angle(x,xx)
     double x[4],xx[4];
{
    double dist,angle;
    const double pt5 = 0.5;
    const double two = 2.0;

    dist=sqrt( (x[1]-xx[1])*(x[1]-xx[1])
               + (x[2]-xx[2])*(x[2]-xx[2])
               + (x[3]-xx[3])*(x[3]-xx[3]) )*pt5;
    angle = asin(dist)*two;

    return (angle);
}
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