Interp1PrimFifthOrderCompactUpwind.c

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#include <stdio.h>
#include <basic.h>
#include <arrayfunctions.h>
#include <mathfunctions.h>
#include <interpolation.h>
#include <tridiagLU.h>
#include <mpivars.h>
#include <hypar.h>

#ifdef with_omp
#include <omp.h>
#endif

#undef  _MINIMUM_GHOSTS_

#define _MINIMUM_GHOSTS_ 3 

int Interp1PrimFifthOrderCompactUpwind(
                                        double *fI,  
                                        double *fC,  
                                        double *u,   
                                        double *x,   
                                        int    upw,  
                                        int    dir,  
                                        void   *s,   
                                        void   *m,   
                                        int    uflag 
                                      )
{
  HyPar           *solver = (HyPar*)          s;
  MPIVariables    *mpi    = (MPIVariables*)   m;
  CompactScheme   *compact= (CompactScheme*)  solver->compact;
  TridiagLU       *lu     = (TridiagLU*)      solver->lusolver;
  int             sys,Nsys,d,v;
  _DECLARE_IERR_;

  int ghosts = solver->ghosts;
  int ndims  = solver->ndims;
  int nvars  = solver->nvars;
  int *dim   = solver->dim_local;
  int *stride= solver->stride_with_ghosts;

  /* define some constants */
  static const double one_third            = 1.0/3.0,
                      thirteen_by_sixty    = 13.0/60.0,
                      fortyseven_by_sixty  = 47.0/60.0,
                      twentyseven_by_sixty = 27.0/60.0,
                      one_by_twenty        = 1.0/20.0,
                      one_by_thirty        = 1.0/30.0,
                      nineteen_by_thirty   = 19.0/30.0,
                      three_by_ten         = 3.0/10.0,
                      six_by_ten           = 6.0/10.0,
                      one_by_ten           = 1.0/10.0;

  /* create index and bounds for the outer loop, i.e., to loop over all 1D lines along
     dimension "dir"                                                                    */
  int indexC[ndims], indexI[ndims], index_outer[ndims], bounds_outer[ndims], bounds_inter[ndims];
  _ArrayCopy1D_(dim,bounds_outer,ndims); bounds_outer[dir] =  1;
  _ArrayCopy1D_(dim,bounds_inter,ndims); bounds_inter[dir] += 1;
  int N_outer; _ArrayProduct1D_(bounds_outer,ndims,N_outer);

  /* calculate total number of tridiagonal systems to solve */
  _ArrayProduct1D_(bounds_outer,ndims,Nsys); Nsys *= nvars;

  /* Allocate arrays for tridiagonal system */
  double *A = compact->A;
  double *B = compact->B;
  double *C = compact->C;
  double *R = compact->R;

#pragma omp parallel for schedule(auto) default(shared) private(sys,d,index_outer,indexC,indexI)
  for (sys=0; sys < N_outer; sys++) {
    _ArrayIndexnD_(ndims,sys,bounds_outer,index_outer,0);
    _ArrayCopy1D_(index_outer,indexC,ndims);
    _ArrayCopy1D_(index_outer,indexI,ndims);
    for (indexI[dir] = 0; indexI[dir] < dim[dir]+1; indexI[dir]++) {
      int qm1,qm2,qm3,qp1,qp2,p;
      _ArrayIndex1D_(ndims,bounds_inter,indexI,0,p);
      if (upw > 0) {
        indexC[dir] = indexI[dir]-1; _ArrayIndex1D_(ndims,dim,indexC,ghosts,qm1);
        qm3 = qm1 - 2*stride[dir];
        qm2 = qm1 -   stride[dir];
        qp1 = qm1 +   stride[dir];
        qp2 = qm1 + 2*stride[dir];
      } else {
        indexC[dir] = indexI[dir]  ; _ArrayIndex1D_(ndims,dim,indexC,ghosts,qm1);
        qm3 = qm1 + 2*stride[dir];
        qm2 = qm1 +   stride[dir];
        qp1 = qm1 -   stride[dir];
        qp2 = qm1 - 2*stride[dir];
      }

      /* Defining stencil points */
      double *fm3, *fm2, *fm1, *fp1, *fp2;
      fm3 = fC+qm3*nvars;
      fm2 = fC+qm2*nvars;
      fm1 = fC+qm1*nvars;
      fp1 = fC+qp1*nvars;
      fp2 = fC+qp2*nvars;

      if (   ((mpi->ip[dir] == 0                ) && (indexI[dir] == 0       ))
          || ((mpi->ip[dir] == mpi->iproc[dir]-1) && (indexI[dir] == dim[dir])) ) {

        /* Use 5th order upwind at the physical boundaries */
        _ArraySetValue_((A+Nsys*indexI[dir]+sys*nvars),nvars,0.0)
        _ArraySetValue_((B+Nsys*indexI[dir]+sys*nvars),nvars,1.0)
        _ArraySetValue_((C+Nsys*indexI[dir]+sys*nvars),nvars,0.0)
        for (v=0; v<nvars; v++) {
          (R+Nsys*indexI[dir]+sys*nvars)[v] =   one_by_thirty         * fm3[v]
                                              - thirteen_by_sixty     * fm2[v]
                                              + fortyseven_by_sixty   * fm1[v]
                                              + twentyseven_by_sixty  * fp1[v]
                                              - one_by_twenty         * fp2[v];
        }

      } else {

        /* Use 5th order upwind at the physical boundaries */
        if (upw > 0) {
          _ArraySetValue_((A+Nsys*indexI[dir]+sys*nvars),nvars,three_by_ten);
          _ArraySetValue_((B+Nsys*indexI[dir]+sys*nvars),nvars,six_by_ten  );
          _ArraySetValue_((C+Nsys*indexI[dir]+sys*nvars),nvars,one_by_ten  );
        } else {
          _ArraySetValue_((C+Nsys*indexI[dir]+sys*nvars),nvars,three_by_ten);
          _ArraySetValue_((B+Nsys*indexI[dir]+sys*nvars),nvars,six_by_ten  );
          _ArraySetValue_((A+Nsys*indexI[dir]+sys*nvars),nvars,one_by_ten  );
        }
        for (v=0; v<nvars; v++) {
          (R+Nsys*indexI[dir]+sys*nvars)[v] =   one_by_thirty      * fm2[v]
                                              + nineteen_by_thirty * fm1[v]
                                              + one_third          * fp1[v];
        }
      }
    }
  }

#ifdef serial

  /* Solve the tridiagonal system */
  IERR tridiagLU(A,B,C,R,dim[dir]+1,Nsys,lu,NULL); CHECKERR(ierr);

#else

  /* Solve the tridiagonal system */
  /* all processes except the last will solve without the last interface to avoid overlap */
  if (mpi->ip[dir] != mpi->iproc[dir]-1)  { IERR tridiagLU(A,B,C,R,dim[dir]  ,Nsys,lu,&mpi->comm[dir]); CHECKERR(ierr); }
  else                                    { IERR tridiagLU(A,B,C,R,dim[dir]+1,Nsys,lu,&mpi->comm[dir]); CHECKERR(ierr); }

  /* Now get the solution to the last interface from the next proc */
  double *sendbuf = compact->sendbuf;
  double *recvbuf = compact->recvbuf;
  MPI_Request req[2] = {MPI_REQUEST_NULL,MPI_REQUEST_NULL};
  if (mpi->ip[dir]) for (d=0; d<Nsys; d++) sendbuf[d] = R[d];
  if (mpi->ip[dir] != mpi->iproc[dir]-1) MPI_Irecv(recvbuf,Nsys,MPI_DOUBLE,mpi->ip[dir]+1,214,mpi->comm[dir],&req[0]);
  if (mpi->ip[dir])                      MPI_Isend(sendbuf,Nsys,MPI_DOUBLE,mpi->ip[dir]-1,214,mpi->comm[dir],&req[1]);
  MPI_Status status_arr[2];
  MPI_Waitall(2,&req[0],status_arr);
  if (mpi->ip[dir] != mpi->iproc[dir]-1) for (d=0; d<Nsys; d++) R[d+Nsys*dim[dir]] = recvbuf[d];

#endif

  /* save the solution to fI */
#pragma omp parallel for schedule(auto) default(shared) private(sys,d,index_outer,indexC,indexI)
  for (sys=0; sys < N_outer; sys++) {
    _ArrayIndexnD_(ndims,sys,bounds_outer,index_outer,0);
    _ArrayCopy1D_(index_outer,indexI,ndims);
    for (indexI[dir] = 0; indexI[dir] < dim[dir]+1; indexI[dir]++) {
      int p; _ArrayIndex1D_(ndims,bounds_inter,indexI,0,p);
      _ArrayCopy1D_((R+sys*nvars+Nsys*indexI[dir]),(fI+nvars*p),nvars);
    }
  }

  return(0);
}