C#，数值计算——偏微分方程，Mglin的计算方法与源程序

1 文本格式

using System;
using System.Collections.Generic;

namespace Legalsoft.Truffer
{
public class Mglin
{
private int n { get; set; }
private int ng { get; set; }
private double[,] uj1 { get; set; }
private List<double[,]> rho { get; set; } = new List<double[,]>();

public Mglin(double[,] u, int ncycle)
{
this.n = u.GetLength(0);
this.ng = 0;
int nn = n;
while ((nn >>= 1) != 0)
{
ng++;
}
if ((n - 1) != (1 << ng))
{
throw new Exception("n-1 must be a power of 2 in mglin.");
}
nn = n;
int ngrid = ng - 1;
//rho.resize(ng);
rho = new List<double[,]>(ng);
rho[ngrid] = new double[nn, nn];
rho[ngrid] = u;
while (nn > 3)
{
nn = nn / 2 + 1;
rho[--ngrid] = new double[nn, nn];

//rstrct(ref rho[ngrid], rho[ngrid + 1]);
double[,] tmp = rho[ngrid];
rstrct(tmp, rho[ngrid + 1]);
//rho[ngrid] = new double[,](tmp);
rho[ngrid] = Globals.CopyFrom(tmp);
}
nn = 3;
double[,] uj = new double[nn, nn];
slvsml(uj, rho[0]);
for (int j = 1; j < ng; j++)
{
nn = 2 * nn - 1;
uj1 = uj;
uj = new double[nn, nn];
interp(uj, uj1);
uj1 = null;
for (int jcycle = 0; jcycle < ncycle; jcycle++)
{
mg(j, uj, rho[j]);
}
}
u = uj;
}

public void interp(double[,] uf, double[,] uc)
{
int nf = uf.GetLength(0);
int nc = nf / 2 + 1;
for (int jc = 0; jc < nc; jc++)
{
for (int ic = 0; ic < nc; ic++)
{
uf[2 * ic, 2 * jc] = uc[ic, jc];
}
}
for (int jf = 0; jf < nf; jf += 2)
{
for (int iif = 1; iif < nf - 1; iif += 2)
{
uf[iif, jf] = 0.5 * (uf[iif + 1, jf] + uf[iif - 1, jf]);
}
}
for (int jf = 1; jf < nf - 1; jf += 2)
{
for (int iif = 0; iif < nf; iif++)
{
uf[iif, jf] = 0.5 * (uf[iif, jf + 1] + uf[iif, jf - 1]);
}
}
}

public void addint(double[,] uf, double[,] uc, double[,] res)
{
int nf = uf.GetLength(0);
interp(res, uc);
for (int j = 0; j < nf; j++)
{
for (int i = 0; i < nf; i++)
{
uf[i, j] += res[i, j];
}
}
}

public void slvsml(double[,] u, double[,] rhs)
{
double h = 0.5;
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
u[i, j] = 0.0;
}
}
u[1, 1] = -h * h * rhs[1, 1] / 4.0;
}

public void relax(double[,] u, double[,] rhs)
{
int n = u.GetLength(0);
double h = 1.0 / (n - 1);
double h2 = h * h;
for (int ipass = 0, jsw = 1; ipass < 2; ipass++, jsw = 3 - jsw)
{
for (int j = 1, isw = jsw; j < n - 1; j++, isw = 3 - isw)
{
for (int i = isw; i < n - 1; i += 2)
{
u[i, j] = 0.25 * (u[i + 1, j] + u[i - 1, j] + u[i, j + 1] + u[i, j - 1] - h2 * rhs[i, j]);
}
}
}
}

public void resid(double[,] res, double[,] u, double[,] rhs)
{
int n = u.GetLength(0);
double h = 1.0 / (n - 1);
double h2i = 1.0 / (h * h);
for (int j = 1; j < n - 1; j++)
{
for (int i = 1; i < n - 1; i++)
{
res[i, j] = -h2i * (u[i + 1, j] + u[i - 1, j] + u[i, j + 1] + u[i, j - 1] - 4.0 * u[i, j]) + rhs[i, j];
}
}
for (int i = 0; i < n; i++)
{
res[i, 0] = res[i, n - 1] = res[0, i] = res[n - 1, i] = 0.0;
}
}

public void rstrct(double[,] uc, double[,] uf)
{
int nc = uc.GetLength(0);
int ncc = 2 * nc - 2;
for (int jf = 2, jc = 1; jc < nc - 1; jc++, jf += 2)
{
for (int iif = 2, ic = 1; ic < nc - 1; ic++, iif += 2)
{
uc[ic, jc] = 0.5 * uf[iif, jf] + 0.125 * (uf[iif + 1, jf] + uf[iif - 1, jf] + uf[iif, jf + 1] + uf[iif, jf - 1]);
}
}
for (int jc = 0, ic = 0; ic < nc; ic++, jc += 2)
{
uc[ic, 0] = uf[jc, 0];
uc[ic, nc - 1] = uf[jc, ncc];
}
for (int jc = 0, ic = 0; ic < nc; ic++, jc += 2)
{
uc[0, ic] = uf[0, jc];
uc[nc - 1, ic] = uf[ncc, jc];
}
}

public void mg(int j, double[,] u, double[,] rhs)
{
const int NPRE = 1;
const int NPOST = 1;
int nf = u.GetLength(0);
int nc = (nf + 1) / 2;
if (j == 0)
{
slvsml(u, rhs);
}
else
{
double[,] res = new double[nc, nc];
double[,] v = new double[nc, nc];
double[,] temp = new double[nf, nf];
for (int jpre = 0; jpre < NPRE; jpre++)
{
relax(u, rhs);
}
resid(temp, u, rhs);
rstrct(res, temp);
mg(j - 1, v, res);
addint(u, v, temp);
for (int jpost = 0; jpost < NPOST; jpost++)
{
relax(u, rhs);
}
}
}
}
}

2 代码格式

using System;
using System.Collections.Generic;

namespace Legalsoft.Truffer
{
    public class Mglin
    {
        private int n { get; set; }
        private int ng { get; set; }
        private double[,] uj1 { get; set; }
        private List<double[,]> rho { get; set; } = new List<double[,]>();

        public Mglin(double[,] u, int ncycle)
        {
            this.n = u.GetLength(0);
            this.ng = 0;
            int nn = n;
            while ((nn >>= 1) != 0)
            {
                ng++;
            }
            if ((n - 1) != (1 << ng))
            {
                throw new Exception("n-1 must be a power of 2 in mglin.");
            }
            nn = n;
            int ngrid = ng - 1;
            //rho.resize(ng);
            rho = new List<double[,]>(ng);
            rho[ngrid] = new double[nn, nn];
            rho[ngrid] = u;
            while (nn > 3)
            {
                nn = nn / 2 + 1;
                rho[--ngrid] = new double[nn, nn];

                //rstrct(ref rho[ngrid], rho[ngrid + 1]);
                double[,] tmp = rho[ngrid];
                rstrct(tmp, rho[ngrid + 1]);
                //rho[ngrid] = new double[,](tmp);
                rho[ngrid] = Globals.CopyFrom(tmp);
            }
            nn = 3;
            double[,] uj = new double[nn, nn];
            slvsml(uj, rho[0]);
            for (int j = 1; j < ng; j++)
            {
                nn = 2 * nn - 1;
                uj1 = uj;
                uj = new double[nn, nn];
                interp(uj, uj1);
                uj1 = null;
                for (int jcycle = 0; jcycle < ncycle; jcycle++)
                {
                    mg(j, uj, rho[j]);
                }
            }
            u = uj;
        }

        public void interp(double[,] uf, double[,] uc)
        {
            int nf = uf.GetLength(0);
            int nc = nf / 2 + 1;
            for (int jc = 0; jc < nc; jc++)
            {
                for (int ic = 0; ic < nc; ic++)
                {
                    uf[2 * ic, 2 * jc] = uc[ic, jc];
                }
            }
            for (int jf = 0; jf < nf; jf += 2)
            {
                for (int iif = 1; iif < nf - 1; iif += 2)
                {
                    uf[iif, jf] = 0.5 * (uf[iif + 1, jf] + uf[iif - 1, jf]);
                }
            }
            for (int jf = 1; jf < nf - 1; jf += 2)
            {
                for (int iif = 0; iif < nf; iif++)
                {
                    uf[iif, jf] = 0.5 * (uf[iif, jf + 1] + uf[iif, jf - 1]);
                }
            }
        }

        public void addint(double[,] uf, double[,] uc, double[,] res)
        {
            int nf = uf.GetLength(0);
            interp(res, uc);
            for (int j = 0; j < nf; j++)
            {
                for (int i = 0; i < nf; i++)
                {
                    uf[i, j] += res[i, j];
                }
            }
        }

        public void slvsml(double[,] u, double[,] rhs)
        {
            double h = 0.5;
            for (int i = 0; i < 3; i++)
            {
                for (int j = 0; j < 3; j++)
                {
                    u[i, j] = 0.0;
                }
            }
            u[1, 1] = -h * h * rhs[1, 1] / 4.0;
        }

        public void relax(double[,] u, double[,] rhs)
        {
            int n = u.GetLength(0);
            double h = 1.0 / (n - 1);
            double h2 = h * h;
            for (int ipass = 0, jsw = 1; ipass < 2; ipass++, jsw = 3 - jsw)
            {
                for (int j = 1, isw = jsw; j < n - 1; j++, isw = 3 - isw)
                {
                    for (int i = isw; i < n - 1; i += 2)
                    {
                        u[i, j] = 0.25 * (u[i + 1, j] + u[i - 1, j] + u[i, j + 1] + u[i, j - 1] - h2 * rhs[i, j]);
                    }
                }
            }
        }

        public void resid(double[,] res, double[,] u, double[,] rhs)
        {
            int n = u.GetLength(0);
            double h = 1.0 / (n - 1);
            double h2i = 1.0 / (h * h);
            for (int j = 1; j < n - 1; j++)
            {
                for (int i = 1; i < n - 1; i++)
                {
                    res[i, j] = -h2i * (u[i + 1, j] + u[i - 1, j] + u[i, j + 1] + u[i, j - 1] - 4.0 * u[i, j]) + rhs[i, j];
                }
            }
            for (int i = 0; i < n; i++)
            {
                res[i, 0] = res[i, n - 1] = res[0, i] = res[n - 1, i] = 0.0;
            }
        }

        public void rstrct(double[,] uc, double[,] uf)
        {
            int nc = uc.GetLength(0);
            int ncc = 2 * nc - 2;
            for (int jf = 2, jc = 1; jc < nc - 1; jc++, jf += 2)
            {
                for (int iif = 2, ic = 1; ic < nc - 1; ic++, iif += 2)
                {
                    uc[ic, jc] = 0.5 * uf[iif, jf] + 0.125 * (uf[iif + 1, jf] + uf[iif - 1, jf] + uf[iif, jf + 1] + uf[iif, jf - 1]);
                }
            }
            for (int jc = 0, ic = 0; ic < nc; ic++, jc += 2)
            {
                uc[ic, 0] = uf[jc, 0];
                uc[ic, nc - 1] = uf[jc, ncc];
            }
            for (int jc = 0, ic = 0; ic < nc; ic++, jc += 2)
            {
                uc[0, ic] = uf[0, jc];
                uc[nc - 1, ic] = uf[ncc, jc];
            }
        }

        public void mg(int j, double[,] u, double[,] rhs)
        {
            const int NPRE = 1;
            const int NPOST = 1;
            int nf = u.GetLength(0);
            int nc = (nf + 1) / 2;
            if (j == 0)
            {
                slvsml(u, rhs);
            }
            else
            {
                double[,] res = new double[nc, nc];
                double[,] v = new double[nc, nc];
                double[,] temp = new double[nf, nf];
                for (int jpre = 0; jpre < NPRE; jpre++)
                {
                    relax(u, rhs);
                }
                resid(temp, u, rhs);
                rstrct(res, temp);
                mg(j - 1, v, res);
                addint(u, v, temp);
                for (int jpost = 0; jpost < NPOST; jpost++)
                {
                    relax(u, rhs);
                }
            }
        }
    }
}

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