spars.cpp

一个2D电磁场FEM计算的VC++源程序

#include <stdafx.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include "spars.h"

CEntry::CEntry()
{
	next=NULL;
	x=0;
	c=0;
}

CBigLinProb::CBigLinProb()
{
	n=0;
	Precision=1.e-8;	// default solver precision
	bar=NULL;
}

CBigLinProb::~CBigLinProb()
{
	if (n==0) return;

	int i;
	CEntry *uo,*ui;

	free(b); free(P); free(R); 
	free(V); free(U); free(Z);

	for(i=0;i<n;i++)
	{
		ui=M[i];
		do{
			uo=ui;
			ui=uo->next;
			delete uo;
		} while(ui!=NULL);
	}

	free(M);
}

int CBigLinProb::Create(int d, int bw)
{
	int i;

	bdw=bw;
	b=(double *)calloc(d,sizeof(double));
	V=(double *)calloc(d,sizeof(double));
	P=(double *)calloc(d,sizeof(double));
	R=(double *)calloc(d,sizeof(double));
	U=(double *)calloc(d,sizeof(double));
	Z=(double *)calloc(d,sizeof(double));
	M=(CEntry **)calloc(d,sizeof(CEntry *));
	n=d;

	for(i=0;i<d;i++){
		M[i] = new CEntry;
		M[i]->c = i;
	}

	return 1;
}

void CBigLinProb::Put(double v, int p, int q)
{
	CEntry *e,*l;
	int i;

	if(q<p){ i=p; p=q; q=i; }

	e=M[p];

	while((e->c < q) && (e->next != NULL))
	{
		l=e; 
		e=e->next;
	}

	if(e->c == q){
		e->x=v;
		return;
	}

	CEntry *m = new CEntry;
	
	if((e->next == NULL) && (q > e->c)){
		e->next = m;
		m->c = q;
		m->x = v;
	}
	else{
		l->next=m;
		m->next=e;
		m->c=q;
		m->x=v;
	}
	return;
}

double CBigLinProb::Get(int p, int q)
{
	CEntry *e;

	if(q<p){ int i; i=p; p=q; q=i; }

	e=M[p];

	while((e->c < q) && (e->next != NULL)) e=e->next;

	if(e->c == q) return e->x;
	
	return 0;
}

void CBigLinProb::MultA(double *X, double *Y)
{
	int i;
	CEntry *e;

	for(i=0;i<n;i++) Y[i]=0;

	for(i=0;i<n;i++){
		Y[i]+=M[i]->x*X[i];
		e=M[i]->next;
		while(e!=NULL)
		{
			Y[i]+=e->x*X[e->c];
			Y[e->c]+=e->x*X[i];
			e=e->next;
		}
	}
}

double CBigLinProb::Dot(double *X, double *Y)
{
	int i;
	double z;

	for(i=0,z=0;i<n;i++) z+=X[i]*Y[i];

	return z;
}

void CBigLinProb::MultPC(double *X, double *Y)
{
	// Jacobi preconditioner:
	//	int i;
	// for(i=0;i<n;i++) Y[i]=X[i]/M[i]->x;

	// SSOR preconditioner:
	int i;
	double c;
	CEntry *e;

	c= Lambda*(2-Lambda);
	for(i=0;i<n;i++) Y[i]=X[i]*c;
	
	// invert Lower Triangle;
	for(i=0;i<n;i++){
		Y[i]/= M[i]->x;
		e=M[i]->next;
		while(e!=NULL)
		{
			Y[e->c] -= e->x * Y[i] * Lambda;
			e=e->next;
		}	
	}

	for(i=0;i<n;i++) Y[i]*=M[i]->x;

	// invert Upper Triangle
	for(i=n-1;i>=0;i--){
		e=M[i]->next;
		while(e!=NULL)
		{
			Y[i] -= e->x * Y[e->c] * Lambda;
			e=e->next;
		}
		Y[i]/= M[i]->x;
	}
}

int CBigLinProb::PCGSolve(int flag)
{
	int i;
	double res,res_o,res_new;
	double er,del,rho,pAp;

	// quick check for most obvious sign of singularity;
	for(i=0;i<n;i++) if(M[i]->x==0){
		fprintf(stderr,"singular flag tripped.");
		return 0;
	}

	// initialize progress bar;
	if(bar!=NULL){
		bar->SetPos(0);
		Pump();
	}
	int prg1=0;
	int prg2;

	// Best guess for relaxation parameter
	Lambda=1.5;

	// residual with V=0
	MultPC(b,Z);
	res_o=Dot(Z,b);
	if(res_o==0) return 1;

	// if flag is false, initialize V with zeros;
	if (flag==0) for(i=0;i<n;i++) V[i]=0;

	// form residual;
	MultA(V,R);
	for(i=0;i<n;i++) R[i]=b[i]-R[i];
	
	// form initial search direction;
	MultPC(R,Z);
	for(i=0;i<n;i++) P[i]=Z[i];
	res=Dot(Z,R);

	// do iteration;
	do{
		// step i)
		MultA(P,U);
		pAp=Dot(P,U);
		del=res/pAp;

		// step ii)
		for(i=0;i<n;i++) V[i]+=(del*P[i]);
					
		// step iii)
		for(i=0;i<n;i++) R[i]-=(del*U[i]);
			
		// step iv)
		MultPC(R,Z);
		res_new=Dot(Z,R);
		rho=res_new/res;
		res=res_new;

		// step v)
		for(i=0;i<n;i++) P[i]=Z[i]+(rho*P[i]);

		// have we converged yet?
		er=sqrt(res/res_o);
		prg2=(int) (100.*log10(er)/(log10(Precision)));
		if(prg2>prg1){
			prg1=prg2;
			if (bar!=NULL) bar->SetPos(prg2);
			Pump();
		}

	} while(er>Precision); 

	return 1;
}		

void CBigLinProb::SetValue(int i, double x)
{
    int k,fst,lst;
    double z;

	if(bdw==0){
		fst=0;
		lst=n;
	}
	else{
		fst=i-bdw; if (fst<0) fst=0;
		lst=i+bdw; if (lst>n) lst=n;
	}

    for(k=fst;k<lst;k++)
    {
        z=Get(k,i);
        if(z!=0){
            b[k]=b[k]-(z*x);
            if(i!=k) Put(0.,k,i);
        }
    }
    b[i]=Get(i,i)*x;
}

void CBigLinProb::Wipe()
{
	int i;
	CEntry *e;

	for(i=0;i<n;i++){
		b[i]=0.;
		e=M[i];
		do{
			e->x=0;
			e=e->next;
		} while(e!=NULL);
	}
}

void CBigLinProb::Periodicity(int i, int j)
{
	int k;
	double v1,v2,c;

	for(k=0;k<n;k++)
		if((k!=i) && (k!=j))
		{
			v1=Get(k,i);
			v2=Get(k,j);
			if ((v1!=0) || (v2!=0)) {
				c=(v1+v2)/2.;
				Put(c,k,i);
				Put(c,k,j);
			}	
		}
	
	c=(Get(i,i)+Get(j,j))/2.;
	Put(c,i,i);
	Put(c,j,j);

	c=0.5*(b[i]+b[j]);
	b[i]=c;
	b[j]=c;
}

void CBigLinProb::AntiPeriodicity(int i, int j)
{
	int k;
	double v1,v2,c;

	for(k=0;k<n;k++)
		if((k!=i) && (k!=j))
		{
			v1=Get(k,i);
			v2=Get(k,j);
			if ((v1!=0) || (v2!=0)){
				c=(v1-v2)/2.;
				Put(c,k,i);
				Put(-c,k,j);
			}
		}
	
	c=0.5*(Get(i,i)+Get(j,j));
	Put(c,i,i);
	Put(c,j,j);

	// is this the right forcing for the RHS?
	c=0.5*(b[i]-b[j]);
	b[i]=c;
	b[j]=-c;
}

BOOL CBigLinProb::Pump()
{

	BOOL bIllegal=FALSE;
    MSG msg;

	while ( ::PeekMessage( &msg, NULL, 0, 0, PM_REMOVE ) ) 
	{ 
		if ((msg.message == WM_KEYDOWN) && (msg.wParam == VK_PAUSE))
		{
			MessageBeep(MB_ICONEXCLAMATION);
			return TRUE;
		}
		if(msg.message==WM_KEYDOWN) bIllegal=TRUE;
		if(msg.message==WM_LBUTTONDBLCLK) bIllegal=TRUE;
		if(msg.message==WM_RBUTTONDBLCLK) bIllegal=TRUE;
		if(msg.message==WM_COMMAND) bIllegal=TRUE;
		
		if (bIllegal==FALSE) DispatchMessage(&msg);
	}

	return FALSE;
}