?? twodimension.h

?? 偏微分方程數值解有限元法面向對象變分問題剖分問題邊值處理誤差分析橢圓方程
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#ifndef Twodimension_h
#define Twodimension_h
#include "FinityElement.h"
#include "mymath.h"
#include "Point.h"
#define filename2 "twoinitial.txt"
double H;
Point T[50][50];
class Twodimension:public FinityElement<Point>{
private:
 	Point leftlow,rightlow,lefthigh,righthigh;
	double steplen,wideth,height;
	int Nrow,Ncol;//剖分點個數
	Point t[50][50];//自變量、
	double sol[50][50],exactsol[50][50],noncoef[50][50];//解、精確解、非齊次系數
	double stiffness[16][16][16][16];//剛度矩陣
    double exactf(Point p);//精確解函數
	void calstiffness();//計算剛度矩陣
	void calnoncoef();//計算非齊次項系數
	void calequation();//計算有限元方程組
	double upedge1(Point p);//第一上邊值條件
	double downedge1(Point p);//第一下邊值條件
	friend double leftedge2(Point p);//第二左邊值條件
	double rightedge2(Point p);//第二右邊值條件
	void egdeprocess();//邊值處理
protected:
public:
	Twodimension();
	~Twodimension(){}
	void Equation();//方程
	void Function();//變分問題
	void Dispart();//剖分
	void Radix();//基函數
	void Finity();//有限元方程
	void Calculate();//計算
    void Exact();//精確解;
	void Error();//誤差

};
Twodimension::Twodimension(){
    ifstream fin(filename2,ios::in|ios::nocreate);
	if(!fin){
		cout<<filename2<<" cannot be openned!"<<endl;exit(1);
	}
	cout<<"Input leftlow:"<<endl;fin>>leftlow;	
	cout<<"Input rightlow:"<<endl;fin>>rightlow;
	cout<<"Input rightehigh:"<<endl;fin>>righthigh;
	cout<<"Input lefthigh:"<<endl;fin>>lefthigh;
	cout<<endl<<"輸入x方向的剖分點數Nrow（如4，5，8,10）:";cin>>Nrow;
	fin.close();
}
void Twodimension::Dispart(){
	int i,j;
	wideth=rightlow.x-leftlow.x;	
	H=steplen=wideth/Nrow;
	height=righthigh.y-rightlow.y;
	Ncol=int(height/steplen);
    for(i=0;i<Nrow+1;i++){
		for(j=0;j<Ncol+1;j++){
		{T[i][j].x=t[i][j].x=leftlow.x+i*steplen;
		 T[i][j].y=t[i][j].y=leftlow.y+j*steplen;
		}
		}
	}
}
void Twodimension::Radix(){//剛度矩陣初始化為0
	int i,j,k,l;
    for(i=0;i<Nrow+1;i++)
	for(j=0;j<Ncol+1;j++)
	for(k=0;k<Nrow+1;k++)
	for(l=0;l<Ncol+1;l++)
	stiffness[i][j][k][l]=0;
}
double commonx1(Point p,int r,int l){//下面函數代表一系列小公共操作
	return (1+(p.x-T[r][l].x)/H)/H;
}
double negcommonx1(Point p,int r,int l){
	return -commonx1(p,r,l);
}
double commonx2(Point p,int r,int l){
	return (1-(p.x-T[r][l].x)/H)/H;
}
double negcommonx2(Point p,int r,int l){
	return -commonx2(p,r,l);
}
double commony1(Point p,int r,int l){
	return (1+(p.y-T[r][l].y)/H)/H;
}
double negcommony1(Point p,int r,int l){
	return -commony1(p,r,l);
}
double commony2(Point p,int r,int l){
	return (1-(p.y-T[r][l].y)/H)/H;
}
double negcommony2(Point p,int r,int l){
	return -commony2(p,r,l);
}
double F11(Point p,int r,int l){//下面函數為計算剛度矩陣調用
	return
		negcommony2(p, r, l)*negcommony2(p, r, l)+negcommonx2(p, r, l)*negcommonx2(p, r, l);		
}
double F12(Point p,int r,int l){
	return 
		commony2(p, r, l)*commony2(p, r, l)+negcommonx1(p, r, l)*negcommonx1(p, r, l);
}
double F13(Point p,int r,int l){
	return 
		commony1(p, r, l)*commony1(p, r, l)+commonx1(p, r, l)*commonx1(p, r, l);
}
double F14(Point p,int r,int l){
	return 
		negcommony1(p, r, l)*negcommony1(p, r, l)+commonx2(p, r, l)*commonx2(p, r, l);
}
double F21(Point p,int r,int l){
	return negcommony2(p, r, l)*commony2(p, r, l)+negcommonx2(p, r, l)*negcommonx1(p, r+1, l);
}
double F22(Point p,int r,int l){
	return negcommony1(p, r, l)*commony1(p, r, l)+commonx2(p, r, l)*commonx1(p, r+1, l);
}
double F3(Point p,int r,int l){
	return negcommony2(p, r, l)*commony1(p, r, l+1)+negcommonx2(p, r, l)*commonx1(p, r+1, l);
}
double F41(Point p,int r,int l){
	return negcommony2(p, r, l)*negcommony1(p, r, l+1)+negcommonx2(p, r, l)*commonx2(p, r, l);
}
double F42(Point p,int r,int l){
	return commony2(p, r, l)*commony1(p, r, l+1)+negcommonx1(p, r, l)*commonx1(p, r, l);
}
double F5(Point p,int r,int l){
	return commony2(p, r, l)*negcommony1(p, r, l+1)+negcommonx1(p, r, l)*commonx2(p, r-1, l);
}
double F61(Point p,int r,int l){
	return commony2(p, r, l)*negcommony2(p, r, l)+negcommonx1(p, r, l)*negcommonx2(p, r-1, l);
}
double F62(Point p,int r,int l){
	return commony1(p, r, l)*negcommony1(p, r, l)+commonx1(p, r, l)*commonx2(p, r-1, l);
}
double F7(Point p,int r,int l){
	return commony1(p, r, l)*negcommony2(p, r, l-1)+commonx1(p, r, l)*negcommonx2(p, r-1, l);
}
double F81(Point p,int r,int l){
	return commony1(p, r, l)*commony2(p, r, l-1)+commonx1(p, r, l)*negcommonx1(p, r, l);
}
double F82(Point p,int r,int l){
	return negcommony1(p, r, l)*negcommony2(p, r, l-1)+commonx2(p, r, l)*negcommonx2(p, r, l);
}
double F9(Point p,int r,int l){
	return negcommony1(p, r, l)*commony2(p, r, l-1)+commonx2(p, r, l)*negcommonx1(p, r+1, l);
}
void Twodimension::calstiffness(){//計算剛度矩陣
	int i,j;
	//處理所有中央點
	for(i=1;i<Nrow;i++)
	{for(j=1;j<Ncol;j++)
	{
	stiffness[i][j][i][j]=Guass4(F11,i,j,T[i][j],T[i+1][j],T[i+1][j+1],T[i][j+1])+
	Guass4(F12,i,j,T[i-1][j],T[i][j],T[i][j+1],T[i-1][j+1])+
	Guass4(F13,i,j,T[i-1][j-1],T[i][j-1],T[i][j],T[i-1][j])+
	Guass4(F14,i,j,T[i][j-1],T[i+1][j-1],T[i+1][j],T[i][j]);
	stiffness[i][j][i+1][j]=Guass4(F21,i,j,T[i][j],T[i+1][j],T[i+1][j+1],T[i][j+1])+
	Guass4(F22,i,j,T[i][j-1],T[i+1][j-1],T[i+1][j],T[i][j]);
	stiffness[i][j][i+1][j+1]=Guass4(F3,i,j,T[i][j],T[i+1][j],T[i+1][j+1],T[i][j+1]);
	stiffness[i][j][i][j+1]=Guass4(F41,i,j,T[i][j],T[i+1][j],T[i+1][j+1],T[i][j+1])+
    Guass4(F42,i,j,T[i-1][j],T[i][j],T[i][j+1],T[i-1][j+1]);
	stiffness[i][j][i-1][j+1]=Guass4(F5,i,j,T[i-1][j],T[i][j],T[i][j+1],T[i-1][j+1]);
 	stiffness[i][j][i-1][j]=Guass4(F61,i,j,T[i-1][j],T[i][j],T[i][j+1],T[i-1][j+1])+
    Guass4(F62,i,j,T[i-1][j-1],T[i][j-1],T[i][j],T[i-1][j]);
	stiffness[i][j][i-1][j-1]=Guass4(F7,i,j,T[i-1][j-1],T[i][j-1],T[i][j],T[i-1][j]);
  	stiffness[i][j][i][j-1]=Guass4(F81,i,j,T[i-1][j-1],T[i][j-1],T[i][j],T[i-1][j])+
    Guass4(F82,i,j,T[i][j-1],T[i+1][j-1],T[i+1][j],T[i][j]);
	stiffness[i][j][i+1][j-1]=Guass4(F9,i,j,T[i][j-1],T[i+1][j-1],T[i+1][j],T[i][j]);
  	}
	}
	//處理第一第二邊值交界點，有四個[0][0],[Nrow][0],[Nrow][Ncol],[0][Ncol];
    stiffness[0][0][0][0]=Guass4(F11,0,0,T[0][0],T[0+1][0],T[0+1][0+1],T[0][0+1]);
    stiffness[0][0][1][1]=Guass4(F3,0,0,T[0][0],T[0+1][0],T[0+1][0+1],T[0][0+1]);
    stiffness[0][0][0][1]=Guass4(F21,0,0,T[0][0],T[1][0],T[1][1],T[0][1]);
    stiffness[0][0][1][0]=Guass4(F41,0,0,T[0][0],T[1][0],T[1][1],T[0][1]);
	//左下點結束
    stiffness[Nrow][0][Nrow][0]=
		Guass4(F12,Nrow,0,T[Nrow-1][0],T[Nrow][0],T[Nrow][0+1],T[Nrow-1][0+1]);
	stiffness[Nrow][0][Nrow-1][1]=
		Guass4(F5,Nrow,0,T[Nrow-1][0],T[Nrow][0],T[Nrow][0+1],T[Nrow-1][0+1]);
    stiffness[Nrow][0][Nrow][1]=
		Guass4(F42,Nrow,0,T[Nrow-1][0],T[Nrow][0],T[Nrow][0+1],T[Nrow-1][0+1]);
    stiffness[Nrow][0][Nrow-1][0]=
		Guass4(F61,Nrow,0,T[Nrow-1][0],T[Nrow][0],T[Nrow][0+1],T[Nrow-1][0+1]);
    //右下點結束
    stiffness[Nrow][Ncol][Nrow][Ncol]=
		Guass4(F13,Nrow,Ncol,T[Nrow-1][Ncol-1],T[Nrow][Ncol-1],T[Nrow][Ncol],T[Nrow-1][Ncol]);
	stiffness[Nrow][Ncol][Nrow-1][Ncol-1]=
		Guass4(F7,Nrow,Ncol,T[Nrow-1][Ncol-1],T[Nrow][Ncol-1],T[Nrow][Ncol],T[Nrow-1][Ncol]);
     stiffness[Nrow][Ncol][Nrow-1][Ncol]=
		Guass4(F62,Nrow,Ncol,T[Nrow-1][Ncol-1],T[Nrow][Ncol-1],T[Nrow][Ncol],T[Nrow-1][Ncol]);
    stiffness[Nrow][Ncol][Nrow][Ncol-1]=
		Guass4(F81,Nrow,Ncol,T[Nrow-1][Ncol-1],T[Nrow][Ncol-1],T[Nrow][Ncol],T[Nrow-1][Ncol]);
    //右上點結束
    stiffness[0][Ncol][0][Ncol]=
	Guass4(F14,0,Ncol,T[0][Ncol-1],T[0+1][Ncol-1],T[0+1][Ncol],T[0][Ncol]);
	stiffness[0][Ncol][1][Ncol-1]=
		Guass4(F9,0,Ncol,T[0][Ncol-1],T[0+1][Ncol-1],T[0+1][Ncol],T[0][Ncol]);
     stiffness[0][Ncol][1][Ncol]=
		Guass4(F22,0,Ncol,T[0][Ncol-1],T[0+1][Ncol-1],T[0+1][Ncol],T[0][Ncol]);
    stiffness[0][Ncol][0][Ncol-1]=
		Guass4(F82,0,Ncol,T[0][Ncol-1],T[0+1][Ncol-1],T[0+1][Ncol],T[0][Ncol]);
    //左上點結束

	//處理下邊界點
	for(i=1;i<Nrow;i++){
    stiffness[i][0][i][0]=Guass4(F11,i,0,T[i][0],T[i+1][0],T[i+1][0+1],T[i][0+1])+
	Guass4(F12,i,0,T[i-1][0],T[i][0],T[i][0+1],T[i-1][0+1]);
	stiffness[i][0][i+1][0]=Guass4(F21,i,0,T[i][0],T[i+1][0],T[i+1][0+1],T[i][0+1]);
	stiffness[i][0][i+1][0+1]=Guass4(F3,i,0,T[i][0],T[i+1][0],T[i+1][0+1],T[i][0+1]);
 	stiffness[i][0][i][0+1]=Guass4(F41,i,0,T[i][0],T[i+1][0],T[i+1][0+1],T[i][0+1])+
    Guass4(F42,i,0,T[i-1][0],T[i][0],T[i][0+1],T[i-1][0+1]);
	stiffness[i][0][i-1][0+1]=Guass4(F5,i,0,T[i-1][0],T[i][0],T[i][0+1],T[i-1][0+1]);
	stiffness[i][0][i-1][0]=Guass4(F61,i,0,T[i-1][0],T[i][0],T[i][0+1],T[i-1][0+1]);
	}
	//處理右邊界點
	for(j=1;j<Ncol;j++){
    stiffness[Nrow][j][Nrow][j]=
	Guass4(F12,Nrow,j,T[Nrow-1][j],T[Nrow][j],T[Nrow][j+1],T[Nrow-1][j+1])+
	Guass4(F13,Nrow,j,T[Nrow-1][j-1],T[Nrow][j-1],T[Nrow][j],T[Nrow-1][j]);
	stiffness[Nrow][j][Nrow][j+1]=
    Guass4(F42,Nrow,j,T[Nrow-1][j],T[Nrow][j],T[Nrow][j+1],T[Nrow-1][j+1]);
	stiffness[Nrow][j][Nrow-1][j+1]=
		Guass4(F5,Nrow,j,T[Nrow-1][j],T[Nrow][j],T[Nrow][j+1],T[Nrow-1][j+1]);
	stiffness[Nrow][j][Nrow-1][j]=
		Guass4(F61,Nrow,j,T[Nrow-1][j],T[Nrow][j],T[Nrow][j+1],T[Nrow-1][j+1])+
    Guass4(F62,Nrow,j,T[Nrow-1][j-1],T[Nrow][j-1],T[Nrow][j],T[Nrow-1][j]);
	stiffness[Nrow][j][Nrow-1][j-1]=
		Guass4(F7,Nrow,j,T[Nrow-1][j-1],T[Nrow][j-1],T[Nrow][j],T[Nrow-1][j]);
 	stiffness[Nrow][j][Nrow][j-1]=
		Guass4(F81,Nrow,j,T[Nrow-1][j-1],T[Nrow][j-1],T[Nrow][j],T[Nrow-1][j]);    
	}
	//處理上邊界點
	for(i=Nrow-1;i>0;i--){
	stiffness[i][Ncol][i][Ncol]=
	Guass4(F13,i,Ncol,T[i-1][Ncol-1],T[i][Ncol-1],T[i][Ncol],T[i-1][Ncol])+
	Guass4(F14,i,Ncol,T[i][Ncol-1],T[i+1][Ncol-1],T[i+1][Ncol],T[i][Ncol]);
	stiffness[i][Ncol][i+1][Ncol]=
	Guass4(F22,i,Ncol,T[i][Ncol-1],T[i+1][Ncol-1],T[i+1][Ncol],T[i][Ncol]);
	stiffness[i][Ncol][i-1][Ncol]=
    Guass4(F62,i,Ncol,T[i-1][Ncol-1],T[i][Ncol-1],T[i][Ncol],T[i-1][Ncol]);
	stiffness[i][Ncol][i-1][Ncol-1]=
		Guass4(F7,i,Ncol,T[i-1][Ncol-1],T[i][Ncol-1],T[i][Ncol],T[i-1][Ncol]);
 	stiffness[i][Ncol][i][Ncol-1]=
		Guass4(F81,i,Ncol,T[i-1][Ncol-1],T[i][Ncol-1],T[i][Ncol],T[i-1][Ncol])+
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?? twodimension.h

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