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dif2d_orth.m
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dif2d_orth.m
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clc
clear all
close all
%SOL=@(x,y) sin(pi*x)*sin(pi*y)+1;
%MSOL=@(x,y) -2*pi^2*sin(pi*x)*sin(pi*y);
SOL=@(x,y) sin(pi/2*x)*sin(pi/2*y);
MSOL=@(x,y) -1*pi^2/2*sin(pi/2*x)*sin(pi/2*y);
DIF=1.0;
XMIN=0.0;
XMAX=1.0;
YMIN=0.0;
YMAX=1.0;
ALPHAX=0.95;
ALPHAY=0.95;
N=20; % KV's in einer Koordinatenrichtung, macht N^2 KV gesamt
NN=N*N;
X = zeros(1,N+1);
for I=1:N+1
X(I) = XMIN + (ALPHAX^(I-1)-1)/(ALPHAX^N-1)*(XMAX-XMIN);
end
Y = zeros(1,N+1);
for I=1:N+1
Y(I) = YMIN + (ALPHAY^(I-1)-1)/(ALPHAY^N-1)*(YMAX-YMIN);
end
%NDIVS = 1;
%% N halbieren
%for j=1:NDIVS
%idx =1;
%X2=0;
%for i=1:length(X)+1
%if mod(i, 2)==1
%X2(idx)=X(i);
%idx=idx+1;
%end
%end
%X=X2;
%N=length(X)-1;
%end
%for j=1:NDIVS
%idx =1;
%Y2=0;
%for i=1:length(Y)+1
%if mod(i, 2)==1
%Y2(idx)=Y(i);
%idx=idx+1;
%end
%end
%Y=Y2;
%N=length(Y)-1;
%end
%NN=N*N;
XC = (X(1:N)+X(2:N+1))/2;
YC = (Y(1:N)+Y(2:N+1))/2;
XCR = [XMIN, XC, XMAX];
YCR = [YMIN, YC, YMAX];
%%% ANALYTISCHE LÖSUNG
TA = zeros(N, N);
for I=1:N
for J=1:N
TA(I, J)=SOL(XC(I), YC(J));
end
end
figure(1)
surf(XC, YC, TA');
title('Analytische Loesung')
xlabel('X')
ylabel('Y')
%%% FVM Lösung
% Randbedingungen
for I=1:N RBS(I)=SOL(XC(I), 0); end
for I=1:N RBN(I)=SOL(XC(I), 1); end
for I=1:N RBE(I)=SOL(1, YC(I)); end
for I=1:N RBW(I)=SOL(0, YC(I)); end
% Koeffizienten speichern
AP = zeros(N);
AE = zeros(N);
AN = zeros(N);
AW = zeros(N);
AS = zeros(N);
for I=1:N
for J=1:N
DX = X(I+1)-X(I);
DY = Y(J+1)-Y(J);
DXE = XCR(I+2)-XCR(I+1);
DXW = XCR(I+1)-XCR(I);
DYN = YCR(J+2)-YCR(J+1);
DYS = YCR(J+1)-YCR(J);
AE(I,J) = DIF*DY/DXE;
AW(I,J) = DIF*DY/DXW;
AN(I,J) = DIF*DX/DYN;
AS(I,J) = DIF*DX/DYS;
AP(I,J) = -AE(I,J)-AN(I,J)-AW(I,J)-AS(I,J);
end
end
% Gesamtgleichungssystem aufstellen
A = zeros(NN);
b = zeros(NN, 1);
for J=1:N
for I=1:N
IDX = (J-1)*N + I;
DX = X(I+1)-X(I);
DY = Y(J+1)-Y(J);
b(IDX) = MSOL(XC(I),YC(J))*DX*DY;
% Hauptdiagonale
A(IDX, IDX) = AP(I,J);
% Westliche Nebendiagonale
if mod(IDX,N)==1
b(IDX) = b(IDX)-AW(I,J)*RBW(J);
else
A(IDX, IDX-1) = AW(I,J);
end
% Östliche Nebendiagonale
if mod(IDX,N)==0
b(IDX) = b(IDX)-AE(I,J)*RBE(J);
else
A(IDX, IDX+1) = AE(I,J);
end
% Nördliche Nebendiagonale
if IDX > NN-N
b(IDX) = b(IDX)-AN(I,J)*RBN(I);
else
A(IDX, IDX+N) = AN(I,J);
end
% Südliche Nebendiagonale
if IDX <= N
b(IDX) = b(IDX)-AS(I,J)*RBS(I);
else
A(IDX, IDX-N) = AS(I,J);
end
end
end
t=A\b;
T=reshape(t,N,N);
% mit Randwerten
T2 = zeros(N+2);
T2(2:N+1,2:N+1) = T;
figure(2)
surf(XC, YC, T');
title('Numerische Loesung')
xlabel('X')
ylabel('Y')
%%% Lösungsfehler berechnen
SERR=0.0;
ERR=zeros(N);
for I=1:N
for J=1:N
ERR(I,J)=T(I, J)-TA(I, J);
SERR=SERR+ERR(I,J)^2;
end
end
SERR=sqrt(SERR/NN);
figure(3)
surf(XC, YC, ERR');
title('Loesungsfehler')
fprintf('Summierter Fehler %16.10e NN=%g\n', SERR, NN);
%%% ORDNUNG BESTIMMEN
% testfall 3
ERR5=2.5533815252e-02;
ERR10=5.2848291306e-03;
ERR20=1.2692480449e-03;
ERR40=3.1459455034e-04;
op=log((ERR5)/(ERR10))/log(2);
fprintf('Ordnung des Verfahrens %16.10e \n',op );
op=log((ERR10)/(ERR20))/log(2);
fprintf('Ordnung des Verfahrens %16.10e \n',op );
op=log((ERR20)/(ERR40))/log(2);
fprintf('Ordnung des Verfahrens %16.10e \n',op );
%%% RESIDUUM BERECHNEN
s=zeros(N);
for I=1:N
for J=1:N
s(I, J)=SOL(XC(I), YC(J));
end
end
s=reshape(s, NN, 1);
RES=A*s-b;
RES2 = reshape(RES, N, N);
figure(4)
%surf(XC(2:N-1), YC(2:N-1), [RES2(2:N-1,2:N-1)]');
surf(XC, YC, RES2');
xlabel('XC')
ylabel('YC')
zlabel('RES')
title('Residuum')
%%% Truncation Error berechnen
% b ohne Randwerte
TERR=zeros(N);
b=zeros(N);
for I=1:N
for J=1:N
DX = X(I+1)-X(I);
DY = Y(J+1)-Y(J);
b(I,J) = MSOL(XC(I),YC(J))*DX*DY;
end
end
% source term
TERRS=zeros(N);
for I=1:N
for J=1:N
% benötigte Werte zwischenspeichern
XP=XCR(I+1);
YP=YCR(J+1);
Xe=X(I+1);
Xw=X(I);
Yn=Y(J+1);
Ys=Y(J);
DX = Xe-Xw;
DY = Yn-Ys;
fP = b(I,J);
% west
if I==1
fE=b(I+1);
XE=XCR(I+2);
TERRS1 = 1/(6*DX)*((fE-fP)/(XE-XP)-(fP-RBW(J))/(XP-Xw))*((Xe-XP)^3-(Xw-XP)^3)*DY;
% east
elseif I==N
fW=b(I-1);
XW=XCR(I);
TERRS1 = 1/(6*DX)*((RBE(J)-fP)/(Xe-XP)-(fP-fW)/(XP-XW))*((Xe-XP)^3-(Xw-XP)^3)*DY;
% central
else
fE=b(I+1,J);
XE=XCR(I+2);
fW=b(I-1,J);
XW=XCR(I);
TERRS1 = 1/(6*DX)*((fE-fP)/(XE-XP) - (fP-fW)/(XP-XW))* ((Xe-XP)^3-(Xw-XP)^3)*DY;
end
% south
if J==1
fN=b(I,J+1);
YN=YCR(J+2);
TERRS2 = 1/(6*DY)*((fN-fP)/(YN-YP) - (fP-RBS(I))/(YP-Ys))* ((Yn-YP)^3 - (Ys-YP)^3)*DX;
% west
elseif J==N
fS=b(I,J-1);
YS=YCR(J);
TERRS2 = 1/(6*DY)*((RBN(I)-fP)/(Yn-YP) - (fP-fS)/(YP-YS))* ((Yn-YP)^3 - (Ys-YP)^3)*DX;
% central
else
fN=b(I,J+1);
YN=YCR(J+2);
fS=b(I,J-1);
YS=YCR(J);
TERRS2 = 1/(6*DY)*((fN-fP)/(YN-YP) - (fP-fS)/(YP-YS))* ((Yn-YP)^3 - (Ys-YP)^3)*DX;
end
TERRS(I,J) = TERRS1 + TERRS2;
end
end
TERRDE=zeros(N);
TERRDW=zeros(N);
TERRDN=zeros(N);
TERRDS=zeros(N);
for I=1:N
for J=1:N
% benötigte Werte zwischenspeichern
XP=XCR(I+1);
YP=YCR(J+1);
Xe=X(I+1);
Xw=X(I);
Yn=Y(J+1);
Ys=Y(J);
DX = Xe-Xw;
DY = Yn-Ys;
TP=T(I,J);
% west
if I==1
XE=XCR(I+2);
TE=T(I+1,J);
Xee=X(I+2);
XEE=XCR(I+3);
TEE=T(I+2,J);
De = (Xe-XP)/(XE-XP);
Te = De * TE + (1-De) * TP;
TERRDE(I,J) = 1/(2*(XE-XP))*((TEE-TP)/(XEE-XP)-(TE-RBW(J))/(XE-Xw))...
* (((XP-Xe)^2-(XE-Xe)^2)/(XE-XP))...
+ (1/(Xee-Xe)*((TEE-TE)/(XEE-XE)-(TE-TP)/(XE-XP)) - 1/(Xe-Xw)*((TE-TP)/(XE-XP)-(TP-RBW(J))/(XP-Xw)))...
* 1/(6*(XE-XP))*(((XP-Xe)^3-(XE-Xe)^3)/(XE-XP))...
+ (1/(Xee-Xe)*((TEE-TE)/(XEE-XE)-(TE-TP)/(XE-XP)) - 1/(Xe-Xw)*((TE-TP)/(XE-XP)-(TP-RBW(J))/(XP-Xw)))...
* 1/(6*(XE-XP)) * ((Yn-YP)^3 - (Ys-YP)^3);
TERRDW(I,J) = -1/2*((Te-RBW(J))/(Xe-Xw) - (TP-RBW(J))/(XP-Xw));
% west +1
elseif I==2
XE=XCR(I+2);
TE=T(I+1,J);
Xee=X(I+2);
XEE=XCR(I+3);
TEE=T(I+2,J);
XW=XCR(I);
TW=T(I-1,J);
Xww=X(I-1);
TERRDE(I,J) = 1/(2*(XE-XP))*((TEE-TP)/(XEE-XP)-(TE-TW)/(XE-XW))...
* (((XP-Xe)^2-(XE-Xe)^2)/(XE-XP))...
+ (1/(Xee-Xe)*((TEE-TE)/(XEE-XE)-(TE-TP)/(XE-XP)) - 1/(Xe-Xw)*((TE-TP)/(XE-XP)-(TP-TW)/(XP-XW)))...
* 1/(6*(XE-XP))*(((XP-Xe)^3-(XE-Xe)^3)/(XE-XP))...
+ (1/(Xee-Xe)*((TEE-TE)/(XEE-XE)-(TE-TP)/(XE-XP)) - 1/(Xe-Xw)*((TE-TP)/(XE-XP)-(TP-TW)/(XP-XW)))...
* 1/(6*(XE-XP)) * ((Yn-YP)^3 - (Ys-YP)^3);
TERRDW(I,J) = 1/(2*(XP-XW))*((TE-TW)/(XE-XW)-(TP-RBW(J))/(XP-Xww))...
* (((XW-Xw)^2-(XP-Xw)^2)/(XP-XW))...
+ (1/(Xe-Xw)*((TE-TP)/(XE-XP)-(TP-TW)/(XP-XW)) - 1/(Xw-Xww)*((TP-TW)/(XP-XW)-(TW-RBW(J))/(XW-Xww)))...
* 1/(6*(XP-XW))*(((XW-Xw)^3-(XP-Xw)^3)/(XP-XW))...
+ (1/(Xe-Xw)*((TE-TP)/(XE-XP)-(TP-TW)/(XP-XW)) - 1/(Xw-Xww)*((TP-TW)/(XP-XW)-(TW-RBW(J))/(XW-Xww)))...
* 1/(6*(XP-XW)) * ((Yn-YP)^3 - (Ys-YP)^3);
% east -1
elseif I==N-1
XE=XCR(I+2);
TE=T(I+1,J);
Xee=X(I+2);
XW=XCR(I);
TW=T(I-1,J);
Xww=X(I-1);
XWW=XCR(I-1);
TWW=T(I-2,J);
TERRDE(I,J) = 1/(2*(XE-XP))*((RBE(J)-TP)/(Xee-XP)-(TE-TW)/(XE-XW))...
* (((XP-Xe)^2-(XE-Xe)^2)/(XE-XP))...
+ (1/(Xee-Xe)*((RBE(J)-TE)/(Xee-XE)-(TE-TP)/(XE-XP)) - 1/(Xe-Xw)*((TE-TP)/(XE-XP)-(TP-TW)/(XP-XW)))...
* 1/(6*(XE-XP))*(((XP-Xe)^3-(XE-Xe)^3)/(XE-XP))...
+ (1/(Xee-Xe)*((RBE(J)-TE)/(Xee-XE)-(TE-TP)/(XE-XP)) - 1/(Xe-Xw)*((TE-TP)/(XE-XP)-(TP-TW)/(XP-XW)))...
* 1/(6*(XE-XP)) * ((Yn-YP)^3 - (Ys-YP)^3);
TERRDW(I,J) = 1/(2*(XP-XW))*((TE-TW)/(XE-XW)-(TP-TWW)/(XP-XWW))...
* (((XW-Xw)^2-(XP-Xw)^2)/(XP-XW))...
+ (1/(Xe-Xw)*((TE-TP)/(XE-XP)-(TP-TW)/(XP-XW)) - 1/(Xw-Xww)*((TP-TW)/(XP-XW)-(TW-TWW)/(XW-XWW)))...
* 1/(6*(XP-XW))*(((XW-Xw)^3-(XP-Xw)^3)/(XP-XW))...
+ (1/(Xe-Xw)*((TE-TP)/(XE-XP)-(TP-TW)/(XP-XW)) - 1/(Xw-Xww)*((TP-TW)/(XP-XW)-(TW-TWW)/(XW-XWW)))...
* 1/(6*(XP-XW)) * ((Yn-YP)^3 - (Ys-YP)^3);
% east
elseif I==N
XW=XCR(I);
TW=T(I-1,J);
Xww=X(I-1);
XWW=XCR(I-1);
TWW=T(I-2,J);
Dw = (XP-Xw)/(XP-XW);
Tw = Dw * TW + (1-Dw)*TP;
TERRDE(I,J) = 1/2*((RBE(J)-TP)/(Xe-XP) - (RBE(J)-Tw)/(Xe-Xw));
TERRDW(I,J) = 1/(2*(XP-XW))*((RBE(J)-TW)/(Xe-XW)-(TP-TWW)/(XP-XWW))...
* (((XW-Xw)^2-(XP-Xw)^2)/(XP-XW))...
+ (1/(Xe-Xw)*((RBE(J)-TP)/(Xe-XP)-(TP-TW)/(XP-XW)) - 1/(Xw-Xww)*((TP-TW)/(XP-XW)-(TW-TWW)/(XW-XWW)))...
* 1/(6*(XP-XW))*(((XW-Xw)^3-(XP-Xw)^3)/(XP-XW))...
+ (1/(Xe-Xw)*((RBE(J)-TP)/(Xe-XP)-(TP-TW)/(XP-XW)) - 1/(Xw-Xww)*((TP-TW)/(XP-XW)-(TW-TWW)/(XW-XWW)))...
* 1/(6*(XP-XW)) * ((Yn-YP)^3 - (Ys-YP)^3);
else
XW=XCR(I);
TW=T(I-1,J);
Xww=X(I-1);
XE=XCR(I+2);
TE=T(I+1,J);
Xee=X(I+2);
XWW=XCR(I-1);
TWW=T(I-2,J);
XEE=XCR(I+3);
TEE=T(I+2,J);
TERRDE(I,J) = 1/(2*(XE-XP))*((TEE-TP)/(XEE-XP)-(TE-TW)/(XE-XW))...
* (((XP-Xe)^2-(XE-Xe)^2)/(XE-XP))...
+ (1/(Xee-Xe)*((TEE-TE)/(XEE-XE)-(TE-TP)/(XE-XP)) - 1/(Xe-Xw)*((TE-TP)/(XE-XP)-(TP-TW)/(XP-XW)))...
* 1/(6*(XE-XP))*(((XP-Xe)^3-(XE-Xe)^3)/(XE-XP))...
+ (1/(Xee-Xe)*((TEE-TE)/(XEE-XE)-(TE-TP)/(XE-XP)) - 1/(Xe-Xw)*((TE-TP)/(XE-XP)-(TP-TW)/(XP-XW)))...
* 1/(6*(XE-XP)) * ((Yn-YP)^3 - (Ys-YP)^3);
TERRDW(I,J) = 1/(2*(XP-XW))*((TE-TW)/(XE-XW)-(TP-TWW)/(XP-XWW))...
* (((XW-Xw)^2-(XP-Xw)^2)/(XP-XW))...
+ (1/(Xe-Xw)*((TE-TP)/(XE-XP)-(TP-TW)/(XP-XW)) - 1/(Xw-Xww)*((TP-TW)/(XP-XW)-(TW-TWW)/(XW-XWW)))...
* 1/(6*(XP-XW))*(((XW-Xw)^3-(XP-Xw)^3)/(XP-XW))...
+ (1/(Xe-Xw)*((TE-TP)/(XE-XP)-(TP-TW)/(XP-XW)) - 1/(Xw-Xww)*((TP-TW)/(XP-XW)-(TW-TWW)/(XW-XWW)))...
* 1/(6*(XP-XW)) * ((Yn-YP)^3 - (Ys-YP)^3);
end
% south
if J==1
YN=YCR(J+2);
Ynn=Y(J+2);
TN=T(I,J+1);
YNN=YCR(J+3);
TNN=T(I,J+2);
Dn = (Yn-YP)/(YN-YP);
Tn = Dn * TN + (1-Dn) * TP;
TERRDN(I,J) = 1/(2*(YN-YP))*((TNN-TP)/(YNN-YP)-(TN-RBS(I))/(YN-Ys))...
* (((YP-Yn)^2-(YN-Yn)^2)/(YN-YP))...
+ (1/(Ynn-Yn)*((TNN-TN)/(YNN-YN)-(TN-TP)/(YN-YP)) - 1/(Yn-Ys)*((TN-TP)/(YN-YP)-(TP-RBS(I))/(YP-Ys)))...
* 1/(6*(YN-YP))*(((YP-Yn)^3-(YN-Yn)^3)/(YN-YP))...
+ (1/(Ynn-Yn)*((TNN-TN)/(YNN-YN)-(TN-TP)/(YN-YP)) - 1/(Yn-Ys)*((TN-TP)/(YN-YP)-(TP-RBS(I))/(YP-Ys)))...
* 1/(6*(YN-YP)) * ((Xe-XP)^3 - (Xw-XP)^3);
TERRDW(I,J) = -1/2*((Tn-RBS(I))/(Yn-Ys) - (TP-RBS(I))/(YP-Ys));
% south +1
elseif J==2
YN=YCR(J+2);
Ynn=Y(J+2);
TN=T(I,J+1);
YS=YCR(J);
Yss=Y(J-1);
TS=T(I,J-1);
YNN=YCR(J+3);
TNN=T(I,J+2);
TERRDN(I,J) = 1/(2*(YN-YP))*((TNN-TP)/(YNN-YP)-(TN-TS)/(YN-YS))...
* (((YP-Yn)^2-(YN-Yn)^2)/(YN-YP))...
+ (1/(Ynn-Yn)*((TNN-TN)/(YNN-YN)-(TN-TP)/(YN-YP)) - 1/(Yn-Ys)*((TN-TP)/(YN-YP)-(TP-TS)/(YP-YS)))...
* 1/(6*(YN-YP))*(((YP-Yn)^3-(YN-Yn)^3)/(YN-YP))...
+ (1/(Ynn-Yn)*((TNN-TN)/(YNN-YN)-(TN-TP)/(YN-YP)) - 1/(Yn-Ys)*((TN-TP)/(YN-YP)-(TP-TS)/(YP-YS)))...
* 1/(6*(YN-YP)) * ((Xe-XP)^3 - (Xw-XP)^3);
TERRDS(I,J) = 1/(2*(YP-YS))*((TN-TS)/(YN-YS)-(TP-RBS(I))/(YP-Yss))...
* (((YS-Ys)^2-(YP-Ys)^2)/(YP-YS))...
+ (1/(Yn-Ys)*((TN-TP)/(YN-YP)-(TP-TS)/(YP-YS)) - 1/(Ys-Yss)*((TP-TS)/(YP-YS)-(TS-RBS(I))/(YS-Yss)))...
* 1/(6*(YP-YS))*(((YS-Ys)^3-(YP-Ys)^3)/(YP-YS))...
+ (1/(Yn-Ys)*((TN-TP)/(YN-YP)-(TP-TS)/(YP-YS)) - 1/(Ys-Yss)*((TP-TS)/(YP-YS)-(TS-RBS(I))/(YS-Yss)))...
* 1/(6*(YP-YS)) * ((Xe-XP)^3 - (Xw-XP)^3);
% north -1
elseif J==N-1
YN=YCR(J+2);
Ynn=Y(J+2);
TN=T(I,J+1);
YS=YCR(J);
Yss=Y(J-1);
TS=T(I,J-1);
YSS=YCR(J-1);
TSS=T(I,J-2);
TERRDN(I,J) = 1/(2*(YN-YP))*((RBN(I)-TP)/(Ynn-YP)-(TN-TS)/(YN-YS))...
* (((YP-Yn)^2-(YN-Yn)^2)/(YN-YP))...
+ (1/(Ynn-Yn)*((RBN(I)-TN)/(Ynn-YN)-(TN-TP)/(YN-YP)) - 1/(Yn-Ys)*((TN-TP)/(YN-YP)-(TP-TS)/(YP-YS)))...
* 1/(6*(YN-YP))*(((YP-Yn)^3-(YN-Yn)^3)/(YN-YP))...
+ (1/(Ynn-Yn)*((RBN(I)-TN)/(Ynn-YN)-(TN-TP)/(YN-YP)) - 1/(Yn-Ys)*((TN-TP)/(YN-YP)-(TP-TS)/(YP-YS)))...
* 1/(6*(YN-YP)) * ((Xe-XP)^3 - (Xw-XP)^3);
TERRDS(I,J) = 1/(2*(YP-YS))*((TN-TS)/(YN-YS)-(TP-TSS)/(YP-YSS))...
* (((YS-Ys)^2-(YP-Ys)^2)/(YP-YS))...
+ (1/(Yn-Ys)*((TN-TP)/(YN-YP)-(TP-TS)/(YP-YS)) - 1/(Ys-Yss)*((TP-TS)/(YP-YS)-(TS-TSS)/(YS-YSS)))...
* 1/(6*(YP-YS))*(((YS-Ys)^3-(YP-Ys)^3)/(YP-YS))...
+ (1/(Yn-Ys)*((TN-TP)/(YN-YP)-(TP-TS)/(YP-YS)) - 1/(Ys-Yss)*((TP-TS)/(YP-YS)-(TS-TSS)/(YS-YSS)))...
* 1/(6*(YP-YS)) * ((Xe-XP)^3 - (Xw-XP)^3);
% north
elseif J==N
YS=YCR(J);
Yss=Y(J-1);
TS=T(I,J-1);
YSS=YCR(J-1);
TSS=T(I,J-2);
Ds = (YP-Ys)/(YP-YS);
Ts = Ds * TS + (1-Ds)*TP;
TERRDN(I,J) = 1/2*((RBN(I)-TP)/(Yn-YP) - (RBN(I)-Ts)/(Yn-Ys));
TERRDS(I,J) = 1/(2*(YP-YS))*((RBN(I)-TS)/(Yn-YS)-(TP-TSS)/(YP-YSS))...
* (((YS-Ys)^2-(YP-Ys)^2)/(YP-YS))...
+ (1/(Yn-Ys)*((RBN(I)-TP)/(Yn-YP)-(TP-TS)/(YP-YS)) - 1/(Ys-Yss)*((TP-TS)/(YP-YS)-(TS-TSS)/(YS-YSS)))...
* 1/(6*(YP-YS))*(((YS-Ys)^3-(YP-Ys)^3)/(YP-YS))...
+ (1/(Yn-Ys)*((RBN(I)-TP)/(Yn-YP)-(TP-TS)/(YP-YS)) - 1/(Ys-Yss)*((TP-TS)/(YP-YS)-(TS-TSS)/(YS-YSS)))...
* 1/(6*(YP-YS)) * ((Xe-XP)^3 - (Xw-XP)^3);
% else
else
YN=YCR(J+2);
Ynn=Y(J+2);
TN=T(I,J+1);
YS=YCR(J);
Yss=Y(J-1);
TS=T(I,J-1);
YSS=YCR(J-1);
TSS=T(I,J-2);
YNN=YCR(J+3);
TNN=T(I,J+2);
TERRDN(I,J) = 1/(2*(YN-YP))*((TNN-TP)/(YNN-YP)-(TN-TS)/(YN-YS))...
* (((YP-Yn)^2-(YN-Yn)^2)/(YN-YP))...
+ (1/(Ynn-Yn)*((TNN-TN)/(YNN-YN)-(TN-TP)/(YN-YP)) - 1/(Yn-Ys)*((TN-TP)/(YN-YP)-(TP-TS)/(YP-YS)))...
* 1/(6*(YN-YP))*(((YP-Yn)^3-(YN-Yn)^3)/(YN-YP))...
+ (1/(Ynn-Yn)*((TNN-TN)/(YNN-YN)-(TN-TP)/(YN-YP)) - 1/(Yn-Ys)*((TN-TP)/(YN-YP)-(TP-TS)/(YP-YS)))...
* 1/(6*(YN-YP)) * ((Xe-XP)^3 - (Xw-XP)^3);
TERRDS(I,J) = 1/(2*(YP-YS))*((TN-TS)/(YN-YS)-(TP-TSS)/(YP-YSS))...
* (((YS-Ys)^2-(YP-Ys)^2)/(YP-YS))...
+ (1/(Yn-Ys)*((TN-TP)/(YN-YP)-(TP-TS)/(YP-YS)) - 1/(Ys-Yss)*((TP-TS)/(YP-YS)-(TS-TSS)/(YS-YSS)))...
* 1/(6*(YP-YS))*(((YS-Ys)^3-(YP-Ys)^3)/(YP-YS))...
+ (1/(Yn-Ys)*((TN-TP)/(YN-YP)-(TP-TS)/(YP-YS)) - 1/(Ys-Yss)*((TP-TS)/(YP-YS)-(TS-TSS)/(YS-YSS)))...
* 1/(6*(YP-YS)) * ((Xe-XP)^3 - (Xw-XP)^3);
end
TERR(I,J) = TERRS(I,J) - TERRDE(I,J)*DY + TERRDW(I,J)*DY - TERRDN(I,J)*DX + TERRDS(I,J)*DX;
end
end
figure(5)
surf(XC(2:N-1), YC(2:N-1), TERR(2:N-1,2:N-1)');
%surf(XC, YC, TERR');
title('TE');
xlabel('x');
ylabel('y');
RESTE = RES2-TERR;
figure(6)
surf(XC(3:N-2), YC(3:N-2), RESTE(3:N-2, 3:N-2)');
%surf(XC, YC, RESTE');
title('RES-TE')