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30 results

fluid_solver_base.cpp

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  • Cristian C Lalescu's avatar
    Cristian Lalescu authored
    at the moment it's broken because I needed to change the prototype of
    rspace_stats.
    05c681b4
    History
    fluid_solver_base.cpp 21.40 KiB
    /**********************************************************************
    *                                                                     *
    *  Copyright 2015 Max Planck Institute                                *
    *                 for Dynamics and Self-Organization                  *
    *                                                                     *
    *  This file is part of bfps.                                         *
    *                                                                     *
    *  bfps is free software: you can redistribute it and/or modify       *
    *  it under the terms of the GNU General Public License as published  *
    *  by the Free Software Foundation, either version 3 of the License,  *
    *  or (at your option) any later version.                             *
    *                                                                     *
    *  bfps 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.                       *
    *                                                                     *
    *  You should have received a copy of the GNU General Public License  *
    *  along with bfps.  If not, see <http://www.gnu.org/licenses/>       *
    *                                                                     *
    * Contact: Cristian.Lalescu@ds.mpg.de                                 *
    *                                                                     *
    **********************************************************************/
    
    // code is generally compiled via setuptools, therefore NDEBUG is present
    //#ifdef NDEBUG
    //#undef NDEBUG
    //#endif//NDEBUG
    
    #include <cassert>
    #include <cmath>
    #include <cstring>
    #include "base.hpp"
    #include "fluid_solver_base.hpp"
    #include "fftw_tools.hpp"
    
    
    template <class rnumber>
    void fluid_solver_base<rnumber>::fill_up_filename(const char *base_name, char *destination)
    {
        sprintf(destination, "%s_%s_i%.5x", this->name, base_name, this->iteration);
    }
    
    template <class rnumber>
    void fluid_solver_base<rnumber>::clean_up_real_space(rnumber *a, int howmany)
    {
        for (ptrdiff_t rindex = 0; rindex < this->cd->local_size*2; rindex += howmany*(this->rd->subsizes[2]+2))
            std::fill_n(a+rindex+this->rd->subsizes[2]*howmany, 2*howmany, 0.0);
    }
    
    template <class rnumber>
    double fluid_solver_base<rnumber>::autocorrel(cnumber *a)
    {
        double *spec = fftw_alloc_real(this->nshells*9);
        double sum_local;
        this->cospectrum(a, a, spec);
        sum_local = 0.0;
        for (int n = 0; n < this->nshells; n++)
        {
            sum_local += spec[n*9] + spec[n*9 + 4] + spec[n*9 + 8];
        }
        fftw_free(spec);
        return sum_local;
    }
    
    template <class rnumber>
    void fluid_solver_base<rnumber>::cospectrum(cnumber *a, cnumber *b, double *spec)
    {
        double *cospec_local = fftw_alloc_real(this->nshells*9);
        std::fill_n(cospec_local, this->nshells*9, 0);
        int tmp_int;
        CLOOP_K2_NXMODES(
                if (k2 <= this->kM2)
                {
                    tmp_int = int(sqrt(k2)/this->dk)*9;
                    for (int i=0; i<3; i++)
                        for (int j=0; j<3; j++)
                        {
                            cospec_local[tmp_int+i*3+j] += nxmodes * (
                            (*(a + 3*cindex+i))[0] * (*(b + 3*cindex+j))[0] +
                            (*(a + 3*cindex+i))[1] * (*(b + 3*cindex+j))[1]);
                        }
                }
                );
        MPI_Allreduce(
                (void*)cospec_local,
                (void*)spec,
                this->nshells*9,
                MPI_DOUBLE, MPI_SUM, this->cd->comm);
        fftw_free(cospec_local);
    }
    
    template <class rnumber>
    void fluid_solver_base<rnumber>::cospectrum(cnumber *a, cnumber *b, double *spec, const double k2exponent)
    {
        double *cospec_local = fftw_alloc_real(this->nshells*9);
        std::fill_n(cospec_local, this->nshells*9, 0);
        double factor = 1;
        int tmp_int;
        CLOOP_K2_NXMODES(
                if (k2 <= this->kM2)
                {
                    factor = nxmodes*pow(k2, k2exponent);
                    tmp_int = int(sqrt(k2)/this->dk)*9;
                    for (int i=0; i<3; i++)
                        for (int j=0; j<3; j++)
                        {
                            cospec_local[tmp_int+i*3+j] += factor * (
                            (*(a + 3*cindex+i))[0] * (*(b + 3*cindex+j))[0] +
                            (*(a + 3*cindex+i))[1] * (*(b + 3*cindex+j))[1]);
                        }
                }
                );
        MPI_Allreduce(
                (void*)cospec_local,
                (void*)spec,
                this->nshells*9,
                MPI_DOUBLE, MPI_SUM, this->cd->comm);
        //for (int n=0; n<this->nshells; n++)
        //{
        //    spec[n] *= 12.5663706144*pow(this->kshell[n], 2) / this->nshell[n];
        //    /*is normalization needed?
        //     * spec[n] /= this->normalization_factor*/
        //}
        fftw_free(cospec_local);
    }
    
    template <class rnumber>
    void fluid_solver_base<rnumber>::compute_rspace_stats(
            rnumber *a,
            double *moments,
            ptrdiff_t *hist,
            double max_estimate[],
            int nbins)
    {
        double *local_moments = fftw_alloc_real(10*4);
        double val_tmp[4], binsize[4], pow_tmp[4];
        ptrdiff_t *local_hist = new ptrdiff_t[nbins*4];
        int bin;
        for (int i=0; i<4; i++)
            binsize[i] = 2*max_estimate[i] / nbins;
        std::fill_n(local_hist, nbins*4, 0);
        std::fill_n(local_moments, 10*4, 0);
        local_moments[3] = max_estimate[3];
        RLOOP(
            this,
            std::fill_n(pow_tmp, 4, 1.0);
            val_tmp[3] = 0.0;
            for (int i=0; i<3; i++)
            {
                val_tmp[i] = a[rindex*3+i];
                val_tmp[3] += val_tmp[i]*val_tmp[i];
            }
            val_tmp[3] = sqrt(val_tmp[3]);
            if (val_tmp[3] < local_moments[0*4+3])
                local_moments[0*4+3] = val_tmp[3];
            if (val_tmp[3] > local_moments[9*4+3])
                local_moments[9*4+3] = val_tmp[3];
            bin = int(val_tmp[3]*2/binsize[3]);
            if (bin >= 0 && bin < nbins)
                local_hist[bin*4+3]++;
            for (int i=0; i<3; i++)
            {
                if (val_tmp[i] < local_moments[0*4+i])
                    local_moments[0*4+i] = val_tmp[i];
                if (val_tmp[i] > local_moments[9*4+i])
                    local_moments[9*4+i] = val_tmp[i];
                bin = int((val_tmp[i] + max_estimate[i]) / binsize[i]);
                if (bin >= 0 && bin < nbins)
                    local_hist[bin*4+i]++;
            }
            for (int n=1; n<9; n++)
                for (int i=0; i<4; i++)
                    local_moments[n*4 + i] += (pow_tmp[i] = val_tmp[i]*pow_tmp[i]);
            );
        MPI_Allreduce(
                (void*)local_moments,
                (void*)moments,
                4,
                MPI_DOUBLE, MPI_MIN, this->cd->comm);
        MPI_Allreduce(
                (void*)(local_moments + 4),
                (void*)(moments+4),
                8*4,
                MPI_DOUBLE, MPI_SUM, this->cd->comm);
        MPI_Allreduce(
                (void*)(local_moments + 9*4),
                (void*)(moments+9*4),
                4,
                MPI_DOUBLE, MPI_MAX, this->cd->comm);
        MPI_Allreduce(
                (void*)local_hist,
                (void*)hist,
                nbins*4,
                MPI_INT64_T, MPI_SUM, this->cd->comm);
        for (int n=1; n<9; n++)
            for (int i=0; i<4; i++)
                moments[n*4 + i] /= this->normalization_factor;
        fftw_free(local_moments);
        delete[] local_hist;
    }
    
    template <class rnumber>
    void fluid_solver_base<rnumber>::write_spectrum(const char *fname, cnumber *a, const double k2exponent)
    {
        double *spec = fftw_alloc_real(this->nshells);
        this->cospectrum(a, a, spec, k2exponent);
        if (this->cd->myrank == 0)
        {
            FILE *spec_file;
            char full_name[512];
            sprintf(full_name, "%s_%s_spec", this->name, fname);
            spec_file = fopen(full_name, "ab");
            fwrite((void*)&this->iteration, sizeof(int), 1, spec_file);
            fwrite((void*)spec, sizeof(double), this->nshells, spec_file);
            fclose(spec_file);
        }
        fftw_free(spec);
    }
    
    /*****************************************************************************/
    /* macro for specializations to numeric types compatible with FFTW           */
    
    #define FLUID_SOLVER_BASE_DEFINITIONS(FFTW, R, MPI_RNUM, MPI_CNUM) \
     \
    template<> \
    fluid_solver_base<R>::fluid_solver_base( \
            const char *NAME, \
            int nx, \
            int ny, \
            int nz, \
            double DKX, \
            double DKY, \
            double DKZ, \
            int DEALIAS_TYPE, \
            unsigned FFTW_PLAN_RIGOR) \
    { \
        strncpy(this->name, NAME, 256); \
        this->name[255] = '\0'; \
        this->iteration = 0; \
        this->fftw_plan_rigor = FFTW_PLAN_RIGOR; \
     \
        int ntmp[4]; \
        ntmp[0] = nz; \
        ntmp[1] = ny; \
        ntmp[2] = nx; \
        ntmp[3] = 3; \
        this->rd = new field_descriptor<R>( \
                4, ntmp, MPI_RNUM, MPI_COMM_WORLD);\
        this->normalization_factor = (this->rd->full_size/3); \
        ntmp[0] = ny; \
        ntmp[1] = nz; \
        ntmp[2] = nx/2 + 1; \
        ntmp[3] = 3; \
        this->cd = new field_descriptor<R>( \
                4, ntmp, MPI_CNUM, this->rd->comm);\
     \
        this->dkx = DKX; \
        this->dky = DKY; \
        this->dkz = DKZ; \
        this->kx = new double[this->cd->sizes[2]]; \
        this->ky = new double[this->cd->subsizes[0]]; \
        this->kz = new double[this->cd->sizes[1]]; \
        this->dealias_type = DEALIAS_TYPE; \
        switch(this->dealias_type) \
        { \
            /* HL07 smooth filter */ \
            case 1: \
                this->kMx = this->dkx*(int(this->rd->sizes[2] / 2)); \
                this->kMy = this->dky*(int(this->rd->sizes[1] / 2)); \
                this->kMz = this->dkz*(int(this->rd->sizes[0] / 2)); \
                break; \
            default: \
                this->kMx = this->dkx*(int(this->rd->sizes[2] / 3)-1); \
                this->kMy = this->dky*(int(this->rd->sizes[1] / 3)-1); \
                this->kMz = this->dkz*(int(this->rd->sizes[0] / 3)-1); \
        } \
        int i, ii; \
        for (i = 0; i<this->cd->sizes[2]; i++) \
            this->kx[i] = i*this->dkx; \
        for (i = 0; i<this->cd->subsizes[0]; i++) \
        { \
            ii = i + this->cd->starts[0]; \
            if (ii <= this->rd->sizes[1]/2) \
                this->ky[i] = this->dky*ii; \
            else \
                this->ky[i] = this->dky*(ii - this->rd->sizes[1]); \
        } \
        for (i = 0; i<this->cd->sizes[1]; i++) \
        { \
            if (i <= this->rd->sizes[0]/2) \
                this->kz[i] = this->dkz*i; \
            else \
                this->kz[i] = this->dkz*(i - this->rd->sizes[0]); \
        } \
        this->kM = this->kMx; \
        if (this->kM < this->kMy) this->kM = this->kMy; \
        if (this->kM < this->kMz) this->kM = this->kMz; \
        this->kM2 = this->kM * this->kM; \
        this->dk = this->dkx; \
        if (this->dk > this->dky) this->dk = this->dky; \
        if (this->dk > this->dkz) this->dk = this->dkz; \
        this->dk2 = this->dk*this->dk; \
        DEBUG_MSG( \
                "kM = %g, kM2 = %g, dk = %g, dk2 = %g\n", \
                this->kM, this->kM2, this->dk, this->dk2); \
        /* spectra stuff */ \
        this->nshells = int(this->kM / this->dk) + 2; \
        this->kshell = new double[this->nshells]; \
        std::fill_n(this->kshell, this->nshells, 0.0); \
        this->nshell = new int64_t[this->nshells]; \
        std::fill_n(this->nshell, this->nshells, 0); \
        double *kshell_local = new double[this->nshells]; \
        std::fill_n(kshell_local, this->nshells, 0.0); \
        int64_t *nshell_local = new int64_t[this->nshells]; \
        std::fill_n(nshell_local, this->nshells, 0.0); \
        double knorm; \
        CLOOP_K2_NXMODES( \
                if (k2 < this->kM2) \
                { \
                    knorm = sqrt(k2); \
                    nshell_local[int(knorm/this->dk)] += nxmodes; \
                    kshell_local[int(knorm/this->dk)] += nxmodes*knorm; \
                } \
                this->Fourier_filter[int(round(k2 / this->dk2))] = exp(-36.0 * pow(k2/this->kM2, 18.)); \
                ); \
        \
        MPI_Allreduce( \
                (void*)(nshell_local), \
                (void*)(this->nshell), \
                this->nshells, \
                MPI_INT64_T, MPI_SUM, this->cd->comm); \
        MPI_Allreduce( \
                (void*)(kshell_local), \
                (void*)(this->kshell), \
                this->nshells, \
                MPI_DOUBLE, MPI_SUM, this->cd->comm); \
        for (int n=0; n<this->nshells; n++) \
        { \
            this->kshell[n] /= this->nshell[n]; \
        } \
        delete[] nshell_local; \
        delete[] kshell_local; \
    } \
     \
    template<> \
    fluid_solver_base<R>::~fluid_solver_base() \
    { \
        DEBUG_MSG("entered ~fluid_solver_base\n"); \
        delete[] this->kshell; \
        delete[] this->nshell; \
     \
        delete[] this->kx; \
        delete[] this->ky; \
        delete[] this->kz; \
     \
        delete this->cd; \
        delete this->rd; \
        DEBUG_MSG("exiting ~fluid_solver_base\n"); \
    } \
     \
    template<> \
    void fluid_solver_base<R>::low_pass_Fourier(FFTW(complex) *a, const int howmany, const double kmax) \
    { \
        const double km2 = kmax*kmax; \
        const int howmany2 = 2*howmany; \
        /*DEBUG_MSG("entered low_pass_Fourier, kmax=%lg km2=%lg howmany2=%d\n", kmax, km2, howmany2);*/ \
        CLOOP_K2( \
                /*DEBUG_MSG("kx=%lg ky=%lg kz=%lg k2=%lg\n", \
                          this->kx[xindex], \
                          this->ky[yindex], \
                          this->kz[zindex], \
                          k2);*/ \
                if (k2 >= km2) \
                    std::fill_n((R*)(a + howmany*cindex), howmany2, 0.0); \
                );\
    } \
     \
    template<> \
    void fluid_solver_base<R>::dealias(FFTW(complex) *a, const int howmany) \
    { \
        if (this->dealias_type == 0) \
            { \
                this->low_pass_Fourier(a, howmany, this->kM); \
                return; \
            } \
        double tval; \
        CLOOP_K2( \
                tval = this->Fourier_filter[int(round(k2/this->dk2))]; \
                for (int tcounter = 0; tcounter < howmany; tcounter++) \
                for (int i=0; i<2; i++) \
                    a[howmany*cindex+tcounter][i] *= tval; \
             ); \
    } \
     \
    template<> \
    void fluid_solver_base<R>::force_divfree(FFTW(complex) *a) \
    { \
        FFTW(complex) tval; \
        CLOOP_K2( \
                if (k2 > 0) \
                { \
                    tval[0] = (this->kx[xindex]*((*(a + cindex*3  ))[0]) + \
                               this->ky[yindex]*((*(a + cindex*3+1))[0]) + \
                               this->kz[zindex]*((*(a + cindex*3+2))[0]) ) / k2; \
                    tval[1] = (this->kx[xindex]*((*(a + cindex*3  ))[1]) + \
                               this->ky[yindex]*((*(a + cindex*3+1))[1]) + \
                               this->kz[zindex]*((*(a + cindex*3+2))[1]) ) / k2; \
                    for (int imag_part=0; imag_part<2; imag_part++) \
                    { \
                        a[cindex*3  ][imag_part] -= tval[imag_part]*this->kx[xindex]; \
                        a[cindex*3+1][imag_part] -= tval[imag_part]*this->ky[yindex]; \
                        a[cindex*3+2][imag_part] -= tval[imag_part]*this->kz[zindex]; \
                    } \
                } \
                );\
        if (this->cd->myrank == this->cd->rank[0]) \
            std::fill_n((R*)(a), 6, 0.0); \
    } \
     \
    template<> \
    void fluid_solver_base<R>::compute_vector_gradient(FFTW(complex) *A, FFTW(complex) *cvec) \
    { \
        ptrdiff_t tindex; \
        std::fill_n((R*)A, 3*2*this->cd->local_size, 0.0); \
        FFTW(complex) *dx_u, *dy_u, *dz_u; \
        dx_u = A; \
        dy_u = A + this->cd->local_size; \
        dz_u = A + 2*this->cd->local_size; \
        CLOOP_K2( \
                if (k2 <= this->kM2) \
                { \
                    tindex = 3*cindex; \
                    for (int cc=0; cc<3; cc++) \
                    { \
                        dx_u[tindex + cc][0] = -this->kx[xindex]*cvec[tindex+cc][1]; \
                        dx_u[tindex + cc][1] =  this->kx[xindex]*cvec[tindex+cc][0]; \
                        dy_u[tindex + cc][0] = -this->ky[yindex]*cvec[tindex+cc][1]; \
                        dy_u[tindex + cc][1] =  this->ky[yindex]*cvec[tindex+cc][0]; \
                        dz_u[tindex + cc][0] = -this->kz[zindex]*cvec[tindex+cc][1]; \
                        dz_u[tindex + cc][1] =  this->kz[zindex]*cvec[tindex+cc][0]; \
                    } \
                } \
                ); \
    } \
     \
    template<> \
    void fluid_solver_base<R>::symmetrize(FFTW(complex) *data, const int howmany) \
    { \
        ptrdiff_t ii, cc; \
        MPI_Status *mpistatus = new MPI_Status; \
        if (this->cd->myrank == this->cd->rank[0]) \
        { \
            for (cc = 0; cc < howmany; cc++) \
                data[cc][1] = 0.0; \
            for (ii = 1; ii < this->cd->sizes[1]/2; ii++) \
                for (cc = 0; cc < howmany; cc++) { \
                    ( *(data + cc + howmany*(this->cd->sizes[1] - ii)*this->cd->sizes[2]))[0] = \
                     (*(data + cc + howmany*(                     ii)*this->cd->sizes[2]))[0]; \
                    ( *(data + cc + howmany*(this->cd->sizes[1] - ii)*this->cd->sizes[2]))[1] = \
                    -(*(data + cc + howmany*(                     ii)*this->cd->sizes[2]))[1]; \
                    } \
        } \
        FFTW(complex) *buffer; \
        buffer = FFTW(alloc_complex)(howmany*this->cd->sizes[1]); \
        ptrdiff_t yy; \
        /*ptrdiff_t tindex;*/ \
        int ranksrc, rankdst; \
        for (yy = 1; yy < this->cd->sizes[0]/2; yy++) { \
            ranksrc = this->cd->rank[yy]; \
            rankdst = this->cd->rank[this->cd->sizes[0] - yy]; \
            if (this->cd->myrank == ranksrc) \
                for (ii = 0; ii < this->cd->sizes[1]; ii++) \
                    for (cc = 0; cc < howmany; cc++) \
                        for (int imag_comp=0; imag_comp<2; imag_comp++) \
                        (*(buffer + howmany*ii+cc))[imag_comp] = \
                            (*(data + howmany*((yy - this->cd->starts[0])*this->cd->sizes[1] + ii)*this->cd->sizes[2] + cc))[imag_comp]; \
            if (ranksrc != rankdst) \
            { \
                DEBUG_MSG("inside fluid_solver_base::symmetrize, about to send/recv data\n"); \
                if (this->cd->myrank == ranksrc) \
                    MPI_Send((void*)buffer, \
                             howmany*this->cd->sizes[1], MPI_CNUM, rankdst, yy, \
                             this->cd->comm); \
                if (this->cd->myrank == rankdst) \
                    MPI_Recv((void*)buffer, \
                             howmany*this->cd->sizes[1], MPI_CNUM, ranksrc, yy, \
                             this->cd->comm, mpistatus); \
                DEBUG_MSG("inside fluid_solver_base::symmetrize, after send/recv data\n"); \
            } \
            if (this->cd->myrank == rankdst) \
            { \
                for (ii = 1; ii < this->cd->sizes[1]; ii++) \
                    for (cc = 0; cc < howmany; cc++) \
                    { \
                        (*(data + howmany*((this->cd->sizes[0] - yy - this->cd->starts[0])*this->cd->sizes[1] + ii)*this->cd->sizes[2] + cc))[0] = \
                            (*(buffer + howmany*(this->cd->sizes[1]-ii)+cc))[0]; \
                        (*(data + howmany*((this->cd->sizes[0] - yy - this->cd->starts[0])*this->cd->sizes[1] + ii)*this->cd->sizes[2] + cc))[1] = \
                           -(*(buffer + howmany*(this->cd->sizes[1]-ii)+cc))[1]; \
                    } \
                for (cc = 0; cc < howmany; cc++) \
                { \
                    (*((data + cc + howmany*(this->cd->sizes[0] - yy - this->cd->starts[0])*this->cd->sizes[1]*this->cd->sizes[2])))[0] =  (*(buffer + cc))[0]; \
                    (*((data + cc + howmany*(this->cd->sizes[0] - yy - this->cd->starts[0])*this->cd->sizes[1]*this->cd->sizes[2])))[1] = -(*(buffer + cc))[1]; \
                } \
            } \
        } \
        FFTW(free)(buffer); \
        delete mpistatus; \
        /* put asymmetric data to 0 */\
        /*if (this->cd->myrank == this->cd->rank[this->cd->sizes[0]/2]) \
        { \
            tindex = howmany*(this->cd->sizes[0]/2 - this->cd->starts[0])*this->cd->sizes[1]*this->cd->sizes[2]; \
            for (ii = 0; ii < this->cd->sizes[1]; ii++) \
            { \
                std::fill_n((R*)(data + tindex), howmany*2*this->cd->sizes[2], 0.0); \
                tindex += howmany*this->cd->sizes[2]; \
            } \
        } \
        tindex = howmany*(); \
        std::fill_n((R*)(data + tindex), howmany*2, 0.0);*/ \
    } \
     \
    template<> \
    int fluid_solver_base<R>::read_base(const char *fname, R *data) \
    { \
        char full_name[512]; \
        sprintf(full_name, "%s_%s_i%.5x", this->name, fname, this->iteration); \
        return this->rd->read(full_name, (void*)data); \
    } \
     \
    template<> \
    int fluid_solver_base<R>::read_base(const char *fname, FFTW(complex) *data) \
    { \
        char full_name[512]; \
        sprintf(full_name, "%s_%s_i%.5x", this->name, fname, this->iteration); \
        return this->cd->read(full_name, (void*)data); \
    } \
     \
    template<> \
    int fluid_solver_base<R>::write_base(const char *fname, R *data) \
    { \
        char full_name[512]; \
        sprintf(full_name, "%s_%s_i%.5x", this->name, fname, this->iteration); \
        return this->rd->write(full_name, (void*)data); \
    } \
     \
    template<> \
    int fluid_solver_base<R>::write_base(const char *fname, FFTW(complex) *data) \
    { \
        char full_name[512]; \
        sprintf(full_name, "%s_%s_i%.5x", this->name, fname, this->iteration); \
        return this->cd->write(full_name, (void*)data); \
    }
    
    /*****************************************************************************/
    
    
    
    /*****************************************************************************/
    /* now actually use the macro defined above                                  */
    FLUID_SOLVER_BASE_DEFINITIONS(
            FFTW_MANGLE_FLOAT,
            float,
            MPI_FLOAT,
            MPI_COMPLEX)
    FLUID_SOLVER_BASE_DEFINITIONS(
            FFTW_MANGLE_DOUBLE,
            double,
            MPI_DOUBLE,
            BFPS_MPICXX_DOUBLE_COMPLEX)
    /*****************************************************************************/
    
    
    
    /*****************************************************************************/
    /* finally, force generation of code for single precision                    */
    template class fluid_solver_base<float>;
    template class fluid_solver_base<double>;
    /*****************************************************************************/