\mu_h &= \norm{\varrho^{1/2}(\phi_{h/2} - \phi_h)}_{L^2(\Gamma)}\\
\tilde\mu_h &= \norm{\varrho^{1/2}(\phi_{h/2} - \Pi_h\phi_{h/2})}_{L^2(\Gamma)}
\end{align}
-Dann gilt:
+Dann gilt auf isotropen Netzen:
\begin{itemize}
- \item Schätzer sind equivalent\\ $\eta_h \sim \tilde \eta_h \sim \mu_h \sim \tilde \mu_h$
+ \item Schätzer sind equivalent\\ $\tilde \mu_h \leq \mu_h \leq \sqrt{2}C_3 \eta_h$
\item sie sind effizient
\item sie sind unter Saturationsannahme auch zuverlässig
\end{itemize}
-
\end{sat}
\begin{bew}
Siehe S.F. Paper $\mapsto$ THM 3.2 \& 3.4
+++ /dev/null
-function A_plot()
-
-type2str = ['Analytisch ' ; 'Quad Element' ; 'Quad Achse '; 'Quad Seite '];
-
-%%G_D
-global G_D;
-
-[m n] = size(G_D);
-
-step = round(n/3);
-
-
-if step<1
- disp ('Error: No Data to show.')
-else
-
-figure(4)
-loglog(G_D(:,1),[G_D(:,[3+(0:step-1)*3]),20*G_D(:,1).^(-1/2),6*G_D(:,1).^(-1/4),5*G_D(:,1).^(-3/4)],...
- G_D(1:end-1,1), sqrt(G_D(2:end,[4+(0:step-1)*3])-G_D(1:end-1,[4+(0:step-1)*3])),'--')
-
-title('Fehler')
-xlabel('Elemente');
-ylabel('Schaetzer');
-legend([['m';'m';'m'] type2str(G_D(1,[2+(0:step-1)*3])',:); 'N^{-1/2} '; 'N^{-1/4} '; 'N^{-3/4} ';['g';'g';'g'] type2str(G_D(1,[2+(0:step-1)*3])',:)] ,'location','best');
-
-
-figure(5)
-loglog(G_D(:,1),G_D(:,[4+(0:step-1)*3]))
-title('Energie Norm')
-xlabel('Elemente');
-ylabel('eNorm');
-legend(type2str(G_D(1,[2+(0:step-1)*3])',:));
-end
-
-end
\ No newline at end of file
leg2 = {leg2{:}...
['min hmin/max hmax ' l0 l1{i}]...
['min hmax/max hmax ' l0 l1{i}]...
- ['hmin/hmax ' l0 l1{i}]...
+ ['min hmin/hmax ' l0 l1{i}]...
}';
sym = {sym{:} type2sym{data(1,[2+(i-1)*rows])}}'
end
% sol = interp1(1./X((round(1)):(end),4)',G_D((round(1)):(end),4)',0,'spline')
% sol = 8.28466; % LShape
- sol = 4.60957; % Quad
+ sol = 4.609193; % Quad
% G_D
-function A_run(file,times,mu,type,eta,eps,out)
+function A_run(file,times,zeta,type,eta,eps,out)
% A_AnIso(file,times,mu,type,eta,eps,out)
% file - starting mesh
% times - how often
-% mu - Zulaessigkeitsbed
+% zeta - Zulaessigkeitsbed
% type - art des Tests
% eta - alle verfeinern oder nur wichtige?
% eps - wie verfeinern iso or aniso
% P. Schaefer
%Parameter testen
-assert(length(mu)==max(type)-1||length(mu)==1,...
+assert(length(zeta)==max(type)-1||length(zeta)==1,...
'Pleas set right type and mu parameters');
%Netz laden
end
% Ein kompletter Verfeinerungschritt
- A_step(mu,type,eta,eps,out);
+ A_step(zeta,type,eta,eps,out);
%Zeit Speichern
usedTime = G_T(end,:);
%Flaecheninhalte Berechnen (rhs)
% b = sqrt(sum(quadNorm(coo_fine,ele_fine,'w').^2,2));
- b_fine = area(coo_fine,ele_fine);
+ b_fine = areaQuad(coo_fine,ele_fine);
tic
%data -> ErgebnisMatrix
%Alle MatrixBrechenungsArten mit dem selben Netz berechnen
for i = 1:length(type)
%Matrix aufbauen -> MEX
- A_fine = mex_build_AU(coo_fine,ele_fine,zeta,type(i));
+ A_fine = mex_build_V(coo_fine,ele_fine,zeta,type(i));
%Testet auf Fehlerhafte Einträge (NaN +/-Inf)
[r c] = find(isnan(A_fine)~=isinf(A_fine));
%Lösung Berechnen
x_fine = A_fine\b_fine;
-
-
- [b,tnormal,s] = area(G_C,G_E);
+ [b,tnormal,s] = areaQuad(G_C,G_E);
hmin = min(s,[],2);
hmax = max(s,[],2);
%Fehlerschätzer 2 aufbauen
- A = mex_build_AU(G_C,G_E,zeta,type(i));
+ A = mex_build_V(G_C,G_E,zeta,type(i));
x = A\b;
xo_fine(f2s) = repmat(x,1,4);
xd_fine = xo_fine'-x_fine;
% |||h/2 -h|||
- tmu2 = xd_fine'*A_fine*xd_fine;
+ eta = xd_fine'*A_fine*xd_fine;
% \tilde \mu ( h/2 -h + L_2 )
- tmu3 = hmin.*b.*sum((x_fine(f2s)'-repmat(x',4,1)).^2)'/4;
+ mu = hmin.*b.*sum((x_fine(f2s)'-repmat(x',4,1)).^2)'/4;
%Energienorm^2 Berechnen |||h||| & |||h/2|||
- data = [data type(i) sqrt(sum(tmu)) sqrt(tmu2) xe_fine sqrt(sum(tmu3))...
+ data = [data type(i) sqrt(sum(tmu)) sqrt(eta) xe_fine sqrt(sum(mu))...
min(hmin)/max(hmax) min(hmax)/max(hmax) sqrt(sum((hmin./hmax).^2))];
end
time(2) = toc;
+++ /dev/null
-function A = Aelements(coordinates, elements)
-% This function calculates the Sum of all Surfaces
-%
-% A=Aelements(coordinates,elements)
-%
-% P.Schaefer
-
-elles = size(elements,1);
-A=0;
-for i = 1:elles
- tri = elements(i,:);
- a = (coordinates(tri(1),:)-coordinates(tri(2),:));
- b = (coordinates(tri(1),:)-coordinates(tri(4),:));
- A1 = norm(cross(a',b'));
- A = A+ A1;
-end
-
-end
-
+++ /dev/null
-function [area, vector, sites] = area(coordinates, elements,varargin)
-%
-% [area, vector, sites] = area(coordinates, elements)
-%
-% Diese Funktion Berechnet den Flächeninhalt zu jedem Element (area) und
-% zu jedem Element die Orthogonalen mit Laenge 1, des Weiteren werden auch
-% die Seitenlaengen zu jedem Element gespeichert
-%
-% P.Schaefer
-
- vector = zeros(size(elements,1),3);
- area = zeros(size(elements,1),1);
- sites = zeros(size(elements,1),2);
-
-%% Flaecheninhalt und Normalen berechnen
-
- for i = 1:size(elements,1)
- % normalized Vector on every triangle
- tri = elements(i,:);
- a = (coordinates(tri(2),:)-coordinates(tri(1),:));
- b = (coordinates(tri(4),:)-coordinates(tri(1),:));
- N = cross(a',b');
-
-% area(i) = norm(N);
-
- N = N/norm(N);
- vector(i,:) = N;
- area(i) = norm(a) * norm(b);
- sites(i,:) = [norm(a) norm(b)];
-
- end
-
-end
-
-
-
--- /dev/null
+function [area, vector, sites] = areaQuad(coordinates, elements,varargin)
+%
+% [area, vector, sites] = area(coordinates, elements)
+%
+% Diese Funktion Berechnet den Flächeninhalt zu jedem Element (area) und
+% zu jedem Element die Orthogonalen mit Laenge 1, des Weiteren werden auch
+% die Seitenlaengen zu jedem Element gespeichert
+%
+% P.Schaefer
+
+ vector = zeros(size(elements,1),3);
+ area = zeros(size(elements,1),1);
+ sites = zeros(size(elements,1),2);
+
+%% Flaecheninhalt und Normalen berechnen
+
+ for i = 1:size(elements,1)
+ % normalized Vector on every triangle
+ tri = elements(i,:);
+ a = (coordinates(tri(2),:)-coordinates(tri(1),:));
+ b = (coordinates(tri(4),:)-coordinates(tri(1),:));
+ N = cross(a',b');
+
+% area(i) = norm(N);
+
+ N = N/norm(N);
+ vector(i,:) = N;
+ area(i) = norm(a) * norm(b);
+ sites(i,:) = [norm(a) norm(b)];
+
+ end
+
+end
+
+
+
+++ /dev/null
-function ind=computeEstSlpMuTilde(x_fine,coo,ele,f2s)
-% ind=computeEstSlpMuTilde(x_fine,coo,ele,f2s)
-% Berechnet den Fehlerschätzer über die Elemente
-%
-% x_fine - Phi
-% coo - coordinaten
-% ele - elemente
-% f2s - Vater Sohn beziehungen
-%
-% P. Schaefer
-
-xF2S = x_fine(f2s)';
-
-if(size(xF2S,1)==1)
- xF2S = xF2S';
-end
-
-tmp = abs([sum(coo(ele(:,2),:)-coo(ele(:,1),:),2)...
- sum(coo(ele(:,4),:)-coo(ele(:,1),:),2)]);
-hmin = min(tmp,[],2);
-% hmax = max(tmp,[],2);
-
-% len = min(abs([sum(coo(ele(:,2),:)-coo(ele(:,1),:),2)...
-% sum(coo(ele(:,4),:)-coo(ele(:,1),:),2)]),[],2);
-
-sizes = sqrt(sum(quadNorm(coo,ele,'w').^2,2));
-
-% max(sizes ~= hmin.*hmax)
-
-x_var = sum((xF2S-repmat(sum(xF2S,1)/4,4,1)).^2)';
-
-ind = hmin.* sizes .* x_var/4;
-
-end
\ No newline at end of file
+++ /dev/null
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- cols rows 8 compute_transform
- rbmap gbmap bbmap true 3 colorimage gr}bdef
-/il {newpath moveto lineto stroke}bdef
-currentdict end def
-%%EndProlog
-
-%%BeginSetup
-MathWorks begin
-
-0 cap
-
-end
-%%EndSetup
-
-%%Page: 1 1
-%%BeginPageSetup
-%%PageBoundingBox: 44 195 550 602
-MathWorks begin
-bpage
-%%EndPageSetup
-
-%%BeginObject: obj1
-bplot
-
-/dpi2point 8.33333 def
-portraitMode 0150 5100 csm
-
- 223 79 4218 3390 MR c np
-76 dict begin %Colortable dictionary
-/c0 { 0.000000 0.000000 0.000000 sr} bdef
-/c1 { 1.000000 1.000000 1.000000 sr} bdef
-/c2 { 0.900000 0.000000 0.000000 sr} bdef
-/c3 { 0.000000 0.820000 0.000000 sr} bdef
-/c4 { 0.000000 0.000000 0.800000 sr} bdef
-/c5 { 0.910000 0.820000 0.320000 sr} bdef
-/c6 { 1.000000 0.260000 0.820000 sr} bdef
-/c7 { 0.000000 0.820000 0.820000 sr} bdef
-c0
-1 j
-1 sg
- 0 0 4803 3605 PR
-4.16667 w
-0 2938 3722 0 0 -2938 624 3208 4 MP
-PP
--3722 0 0 2938 3722 0 0 -2938 624 3208 5 MP stroke
-2.77778 w
-DO
-SO
-4.16667 w
-0 sg
- 624 3208 mt 4346 3208 L
- 624 270 mt 4346 270 L
- 624 3208 mt 624 270 L
-4346 3208 mt 4346 270 L
- 624 3208 mt 4346 3208 L
- 624 3208 mt 624 270 L
- 624 3208 mt 624 3189 L
- 624 270 mt 624 288 L
- 624 3208 mt 624 3170 L
- 624 270 mt 624 307 L
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 83.3333 FMSR
-
- 563 3334 mt
-(10) s
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 55.5556 FMSR
-
- 655 3283 mt
-(0) s
- 904 3208 mt 904 3189 L
- 904 270 mt 904 288 L
-1067 3208 mt 1067 3189 L
-1067 270 mt 1067 288 L
-1184 3208 mt 1184 3189 L
-1184 270 mt 1184 288 L
-1274 3208 mt 1274 3189 L
-1274 270 mt 1274 288 L
-1348 3208 mt 1348 3189 L
-1348 270 mt 1348 288 L
-1410 3208 mt 1410 3189 L
-1410 270 mt 1410 288 L
-1464 3208 mt 1464 3189 L
-1464 270 mt 1464 288 L
-1511 3208 mt 1511 3189 L
-1511 270 mt 1511 288 L
-1554 3208 mt 1554 3189 L
-1554 270 mt 1554 288 L
-1554 3208 mt 1554 3170 L
-1554 270 mt 1554 307 L
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 83.3333 FMSR
-
-1493 3334 mt
-(10) s
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 55.5556 FMSR
-
-1585 3283 mt
-(1) s
-1834 3208 mt 1834 3189 L
-1834 270 mt 1834 288 L
-1998 3208 mt 1998 3189 L
-1998 270 mt 1998 288 L
-2114 3208 mt 2114 3189 L
-2114 270 mt 2114 288 L
-2204 3208 mt 2204 3189 L
-2204 270 mt 2204 288 L
-2278 3208 mt 2278 3189 L
-2278 270 mt 2278 288 L
-2340 3208 mt 2340 3189 L
-2340 270 mt 2340 288 L
-2394 3208 mt 2394 3189 L
-2394 270 mt 2394 288 L
-2442 3208 mt 2442 3189 L
-2442 270 mt 2442 288 L
-2485 3208 mt 2485 3189 L
-2485 270 mt 2485 288 L
-2485 3208 mt 2485 3170 L
-2485 270 mt 2485 307 L
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 83.3333 FMSR
-
-2424 3334 mt
-(10) s
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 55.5556 FMSR
-
-2516 3283 mt
-(2) s
-2765 3208 mt 2765 3189 L
-2765 270 mt 2765 288 L
-2928 3208 mt 2928 3189 L
-2928 270 mt 2928 288 L
-3045 3208 mt 3045 3189 L
-3045 270 mt 3045 288 L
-3135 3208 mt 3135 3189 L
-3135 270 mt 3135 288 L
-3209 3208 mt 3209 3189 L
-3209 270 mt 3209 288 L
-3271 3208 mt 3271 3189 L
-3271 270 mt 3271 288 L
-3325 3208 mt 3325 3189 L
-3325 270 mt 3325 288 L
-3372 3208 mt 3372 3189 L
-3372 270 mt 3372 288 L
-3415 3208 mt 3415 3189 L
-3415 270 mt 3415 288 L
-3415 3208 mt 3415 3170 L
-3415 270 mt 3415 307 L
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 83.3333 FMSR
-
-3354 3334 mt
-(10) s
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 55.5556 FMSR
-
-3446 3283 mt
-(3) s
-3695 3208 mt 3695 3189 L
-3695 270 mt 3695 288 L
-3859 3208 mt 3859 3189 L
-3859 270 mt 3859 288 L
-3975 3208 mt 3975 3189 L
-3975 270 mt 3975 288 L
-4065 3208 mt 4065 3189 L
-4065 270 mt 4065 288 L
-4139 3208 mt 4139 3189 L
-4139 270 mt 4139 288 L
-4201 3208 mt 4201 3189 L
-4201 270 mt 4201 288 L
-4255 3208 mt 4255 3189 L
-4255 270 mt 4255 288 L
-4303 3208 mt 4303 3189 L
-4303 270 mt 4303 288 L
-4346 3208 mt 4346 3189 L
-4346 270 mt 4346 288 L
-4346 3208 mt 4346 3170 L
-4346 270 mt 4346 307 L
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 83.3333 FMSR
-
-4285 3334 mt
-(10) s
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 55.5556 FMSR
-
-4377 3283 mt
-(4) s
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 2328 mt 661 2328 L
-4346 2328 mt 4308 2328 L
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 83.3333 FMSR
-
- 400 2358 mt
-(10) s
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 55.5556 FMSR
-
- 492 2307 mt
-(0.65) s
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 1024 mt 661 1024 L
-4346 1024 mt 4308 1024 L
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 83.3333 FMSR
-
- 400 1054 mt
-(10) s
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 55.5556 FMSR
-
- 492 1003 mt
-(0.66) s
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 624 3208 L
- 624 3208 mt 4346 3208 L
- 624 270 mt 4346 270 L
- 624 3208 mt 624 270 L
-4346 3208 mt 4346 270 L
-gs 624 270 3723 2939 MR c np
-/c8 { 0.000000 0.000000 1.000000 sr} bdef
-c8
-68 0 100 0 65 0 95 0 107 0 100 0 97 0 93 0
-87 0 72 -1 55 0 84 -1 55 -1 64 -1 60 -3 60 -3
-62 -5 45 -7 62 -10 48 -14 51 -19 71 -28 51 -38 90 -53
-71 -82 104 -164 122 -184 190 -333 254 -480 560 -1229 1184 3208 31 MP stroke
-gr
-
-c8
-gs 1133 501 3146 2759 MR c np
- 25 25 1184 3208 FO
- 25 25 1744 1979 FO
- 25 25 1998 1499 FO
- 25 25 2188 1166 FO
- 25 25 2310 982 FO
- 25 25 2414 818 FO
- 25 25 2485 736 FO
- 25 25 2575 683 FO
- 25 25 2626 645 FO
- 25 25 2697 617 FO
- 25 25 2748 598 FO
- 25 25 2796 584 FO
- 25 25 2858 574 FO
- 25 25 2903 567 FO
- 25 25 2965 562 FO
- 25 25 3025 559 FO
- 25 25 3085 556 FO
- 25 25 3149 555 FO
- 25 25 3204 554 FO
- 25 25 3288 553 FO
- 25 25 3343 553 FO
- 25 25 3415 552 FO
- 25 25 3502 552 FO
- 25 25 3595 552 FO
- 25 25 3692 552 FO
- 25 25 3792 552 FO
- 25 25 3899 552 FO
- 25 25 3994 552 FO
- 25 25 4059 552 FO
- 25 25 4159 552 FO
- 25 25 4227 552 FO
-gr
-
-gs 624 270 3723 2939 MR c np
-DD
-/c9 { 1.000000 0.000000 0.000000 sr} bdef
-c9
-68 0 100 0 65 0 95 0 107 0 100 0 97 0 93 0
-87 0 72 0 55 0 84 0 55 0 64 0 60 0 60 0
-62 0 45 0 62 0 48 0 51 0 71 0 51 0 90 0
-71 0 104 0 122 0 190 0 254 0 560 0 1184 547 31 MP stroke
-gr
-
-c9
-DD
-0 sg
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 83.3333 FMSR
-
-2226 206 mt
-(Energie Norm) s
-2308 3434 mt
-(Elemente) s
- 343 1883 mt -90 rotate
-(eNorm) s
-90 rotate
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 66.6667 FMSR
-
- 302 1631 mt -90 rotate
-(2) s
-90 rotate
-%%IncludeResource: font Helvetica
-/Helvetica /ISOLatin1Encoding 83.3333 FMSR
-
- 612 3239 mt
-( ) s
-4335 300 mt
-( ) s
-SO
-1 sg
-0 232 1000 0 0 -232 3305 3168 4 MP
-PP
--1000 0 0 232 1000 0 0 -232 3305 3168 5 MP stroke
-2.77778 w
-DO
-SO
-4.16667 w
-0 sg
-3305 3168 mt 4305 3168 L
-3305 2936 mt 4305 2936 L
-3305 3168 mt 3305 2936 L
-4305 3168 mt 4305 2936 L
-3305 3168 mt 4305 3168 L
-3305 3168 mt 3305 2936 L
-3305 3168 mt 4305 3168 L
-3305 2936 mt 4305 2936 L
-3305 3168 mt 3305 2936 L
-4305 3168 mt 4305 2936 L
-3628 3031 mt
-(testAA Analytisch) s
-gs 3305 2936 1001 233 MR c np
-c8
-248 0 3354 3000 2 MP stroke
-gs 3427 2949 103 103 MR c np
- 25 25 3478 3000 FO
-gr
-
-gr
-
-c8
-0 sg
-3628 3134 mt
-(extrapoliert) s
-gs 3305 2936 1001 233 MR c np
-DD
-c9
-248 0 3354 3103 2 MP stroke
-SO
-gr
-
-c9
-
-end %%Color Dict
-
-eplot
-%%EndObject
-
-epage
-end
-
-showpage
-
-%%Trailer
-%%EOF
+++ /dev/null
-/*\r
- * Art der Berechnung durch Parameter bestimmt...\r
- * Analytisch/Semianalytisch/...\r
- *\r
- *\r
- */\r
-//#include <iostream>\r
-#include <cmath>\r
-//#include <cassert>\r
-#include "mex.h"\r
-/*/#include <stdlib.h>\r
-\r
-//#include "gauss.hpp"\r
-*/\r
-#define M_EPS 10e-8\r
-/*\r
-//#include "tbb/parallel_for.h"\r
-*/\r
-#include "slpRectangle.hpp"\r
-/*\r
-//using namespace std;\r
-//using namespace slpR;\r
-*/\r
-int dimOfVec(double* vec) {\r
- if (vec[2] != 0)\r
- return 2;\r
- else if (vec[1] != 0)\r
- return 1;\r
- else if (vec[0] != 0)\r
- return 0;\r
- else {/*\r
-// cerr << "dimOfVec : (" << vec[0] << " " << vec[1] << " " << vec[2]\r
-// << ") alle Werte 0 \n";*/\r
- return -1;\r
- }\r
-\r
-}\r
-\r
-inline int dimOfThird(int a, int b) {\r
- return ((-(a + b) % 3) + 3) % 3;\r
-}\r
-\r
-void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {\r
-/*\r
-// initeQuad();\r
-// cout << Quad[1].nod[0];\r
-*/\r
- int i, j, k; //Schleifenindizes\r
- double tmp; //Zwischenspeicherung der Einzelnen Werte\r
- int count;\r
-\r
- //Sicherheitsabfragen zu Datengroessen\r
- if ((nrhs != 4))\r
- mexErrMsgTxt(\r
- "expected (coordinates(Nx3),elements(Mx4),mu(double),type(int))");\r
- if (nlhs > 1)\r
- mexErrMsgTxt("has only one output argument");\r
-\r
- int cm = mxGetM(prhs[0]);\r
- int cn = mxGetN(prhs[0]);\r
- if (cn != 3)\r
- mexErrMsgTxt("expected coordinates (Nx3)");\r
-// cout << " Koordinaten:" << cm << endl;\r
-\r
- int em = mxGetM(prhs[1]);\r
- int en = mxGetN(prhs[1]);\r
- if (en != 4)\r
- mexErrMsgTxt("expected elements (Mx4)");\r
-// cout << " Elemente:" << em << endl;\r
-\r
- //Auslesen der Parameter\r
-\r
- plhs[0] = mxCreateDoubleMatrix(em, em, mxREAL);\r
- double * A = mxGetPr(plhs[0]);\r
- double * C = mxGetPr(prhs[0]);\r
- double * E = mxGetPr(prhs[1]);\r
-\r
- int type = (int) *(mxGetPr(prhs[3]));\r
- double * mu = mxGetPr(prhs[2]);\r
-\r
- //Initialisieren der Hilfsvektoren\r
-\r
- double * x0 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
- double * x1 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
- double * x2 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
- double * x3 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
- double * xa = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
- double * xb = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
-\r
- double * y0 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
- double * y1 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
- double * y2 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
- double * y3 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
- double * ya = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
- double * yb = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
-\r
- double * d = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
- double * dt = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
-\r
- // Welche Funktion soll verwendet werden\r
- double(*ctypeP)(double, double, double, double, double, double, double,\r
- double*);\r
- double(*ctypeO)(double, double, double, double, double, double, double,\r
- double*);\r
-\r
- //Art der Berechnung bestimmen\r
-// cout << " Typ:" << type << endl;\r
- switch (type) {\r
- default:\r
- ctypeP = cParO1;\r
- ctypeO = NULL;\r
- break;\r
- case 0:\r
- ctypeP = cParO0;\r
- ctypeO = NULL;\r
- break;\r
- case 2:\r
- ctypeP = cParO2;\r
- ctypeO = NULL;\r
- break;\r
- case 3:\r
- ctypeP = cParO3;\r
- ctypeO = NULL;\r
- break;\r
- }\r
-\r
- //LageInformationen\r
- int rx, rxa, rxb, ry, rya, ryb;\r
-\r
-// cout << " Progress: #";\r
- count = 0;\r
- //Ausrechnen\r
- for (j = 0; j < em; ++j) {\r
- x0[0] = C[(int) E[j] - 1];\r
- x0[1] = C[cm + (int) E[j] - 1];\r
- x0[2] = C[2 * cm + (int) E[j] - 1];\r
-\r
- x1[0] = C[(int) E[em + j] - 1];\r
- x1[1] = C[cm + (int) E[em + j] - 1];\r
- x1[2] = C[2 * cm + (int) E[em + j] - 1];\r
-\r
- x2[0] = C[(int) E[2 * em + j] - 1];\r
- x2[1] = C[cm + (int) E[2 * em + j] - 1];\r
- x2[2] = C[2 * cm + (int) E[2 * em + j] - 1];\r
-\r
- x3[0] = C[(int) E[3 * em + j] - 1];\r
- x3[1] = C[cm + (int) E[3 * em + j] - 1];\r
- x3[2] = C[2 * cm + (int) E[3 * em + j] - 1];\r
-\r
- for (i = 0; i < 3; ++i)\r
- xa[i] = x1[i] - x0[i];\r
-\r
- for (i = 0; i < 3; ++i)\r
- xb[i] = x3[i] - x0[i];\r
-\r
- // Lageeigenschaften des Flaechenstuecks\r
-\r
- rxa = dimOfVec(xa);\r
- rxb = dimOfVec(xb);\r
- rx = dimOfThird(rxa, rxb);\r
-\r
- //kleinste Ecke finden und fuer \delta verwenden\r
-\r
- if (xa[rxa] > 0) {\r
- if (xb[rxb] > 0) {\r
- for (i = 0; i < 3; ++i)\r
- dt[i] = -x0[i];\r
- } else {\r
- for (i = 0; i < 3; ++i)\r
- dt[i] = -x3[i];\r
- }\r
- } else {\r
- if (xb[rxb] > 0) {\r
- for (i = 0; i < 3; ++i)\r
- dt[i] = -x1[i];\r
- } else {\r
- for (i = 0; i < 3; ++i)\r
- dt[i] = -x2[i];\r
- }\r
- }\r
-\r
- for (k = 0; k <= j; ++k) {\r
- y0[0] = C[(int) E[k] - 1];\r
- y0[1] = C[cm + (int) E[k] - 1];\r
- y0[2] = C[2 * cm + (int) E[k] - 1];\r
-\r
- y1[0] = C[(int) E[em + k] - 1];\r
- y1[1] = C[cm + (int) E[em + k] - 1];\r
- y1[2] = C[2 * cm + (int) E[em + k] - 1];\r
-\r
- y2[0] = C[(int) E[2 * em + k] - 1];\r
- y2[1] = C[cm + (int) E[2 * em + k] - 1];\r
- y2[2] = C[2 * cm + (int) E[2 * em + k] - 1];\r
-\r
- y3[0] = C[(int) E[3 * em + k] - 1];\r
- y3[1] = C[cm + (int) E[3 * em + k] - 1];\r
- y3[2] = C[2 * cm + (int) E[3 * em + k] - 1];\r
-\r
- for (i = 0; i < 3; ++i)\r
- ya[i] = y1[i] - y0[i];\r
-\r
- for (i = 0; i < 3; ++i)\r
- yb[i] = y3[i] - y0[i];\r
-\r
- // Lageeigenschaften des Flaechenstuecks\r
-\r
- rya = dimOfVec(ya);\r
- ryb = dimOfVec(yb);\r
- ry = dimOfThird(rya, ryb);\r
-\r
- //kleinste Ecke finden und fuer \delta verwenden\r
-\r
- if (ya[rya] > 0) {\r
- if (yb[ryb] > 0) {\r
- for (i = 0; i < 3; ++i)\r
- d[i] = dt[i] + y0[i];\r
- } else {\r
- for (i = 0; i < 3; ++i)\r
- d[i] = dt[i] + y3[i];\r
- }\r
- } else {\r
- if (yb[ryb] > 0) {\r
- for (i = 0; i < 3; ++i)\r
- d[i] = dt[i] + y1[i];\r
- } else {\r
- for (i = 0; i < 3; ++i)\r
- d[i] = dt[i] + y2[i];\r
- }\r
- }\r
-\r
- if (rx == ry) {\r
- if (rxa == rya) {\r
- tmp = ctypeP(fabs(xa[rxa]), fabs(xb[rxb]), fabs(ya[rxa]),\r
- fabs(yb[rxb]), d[rxa], d[rxb], d[rx], mu);\r
-\r
- } else {\r
- tmp = ctypeP(fabs(xa[rxa]), fabs(xb[rxb]), fabs(yb[rxa]),\r
- fabs(ya[rxb]), d[rxa], d[rxb], d[rx], mu);\r
- }\r
-\r
- } else {\r
-\r
- if (rxa == rya) {\r
- tmp = ctypeO(fabs(xb[rxb]), fabs(xa[rxa]), fabs(ya[rya]),\r
- fabs(yb[ryb]), d[rxb], d[rxa], d[rx], mu);\r
- } else if (rxa == ryb) {\r
- tmp = ctypeO(fabs(xb[rxb]), fabs(xa[rxa]), fabs(yb[ryb]),\r
- fabs(ya[rya]), d[rxb], d[rxa], d[rx], mu);\r
- } else if (rxb == rya) {\r
- tmp = ctypeO(fabs(xa[rxa]), fabs(xb[rxb]), fabs(ya[rya]),\r
- fabs(yb[ryb]), d[rxa], d[rxb], d[rx], mu);\r
- } else {\r
- tmp = ctypeO(fabs(xa[rxa]), fabs(xb[rxb]), fabs(yb[ryb]),\r
- fabs(ya[rya]), d[rxa], d[rxb], d[rx], mu);\r
- }\r
-\r
- }\r
- A[(k * em) + j] = 1. / (4 * M_PI) * tmp;\r
- if (k != j)\r
- A[(j * em) + k] = 1. / (4 * M_PI) * tmp;\r
-/* if (count++ > ((em * (em + 1)) / 2) / 10) {\r
- count = 0;\r
-// mexPrintf("#");\r
-// cout << "#";\r
-// cout.flush();\r
- }*/\r
-\r
- }\r
-\r
- }\r
-// cout << endl;\r
- //Rueckgabe (eventuell zurueck schreiben)\r
-/* mxFree(x0);\r
- mxFree(x1);\r
- mxFree(x3);\r
- mxFree(xa);\r
- mxFree(xb);\r
- mxFree(y0);\r
- mxFree(y1);\r
- mxFree(y3);\r
- mxFree(ya);\r
- mxFree(yb);\r
- mxFree(d);\r
- mxFree(dt);\r
-*/\r
- return;\r
-}\r
--- /dev/null
+/*\r
+ * Art der Berechnung durch Parameter bestimmt...\r
+ * Analytisch/Semianalytisch/...\r
+ *\r
+ *\r
+ */\r
+//#include <iostream>\r
+#include <cmath>\r
+//#include <cassert>\r
+#include "mex.h"\r
+/*/#include <stdlib.h>\r
+\r
+//#include "gauss.hpp"\r
+*/\r
+//#define M_EPS 10e-8\r
+/*\r
+//#include "tbb/parallel_for.h"\r
+*/\r
+#include "slpRectangle.hpp"\r
+/*\r
+//using namespace std;\r
+//using namespace slpR;\r
+*/\r
+int dimOfVec(double* vec) {\r
+ if (vec[2] != 0)\r
+ return 2;\r
+ else if (vec[1] != 0)\r
+ return 1;\r
+ else if (vec[0] != 0)\r
+ return 0;\r
+ else {\r
+ mexErrMsgTxt("length of Site is zero");\r
+ /*\r
+// cerr << "dimOfVec : (" << vec[0] << " " << vec[1] << " " << vec[2]\r
+// << ") alle Werte 0 \n";*/\r
+ return -1;\r
+ }\r
+\r
+}\r
+\r
+// Gibt von [0 1 2] die Fehlende Zahl zurueck\r
+inline int dimOfThird(int a, int b) {\r
+ return ((-(a + b) % 3) + 3) % 3;\r
+}\r
+\r
+void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {\r
+/*\r
+// initeQuad();\r
+// cout << Quad[1].nod[0];\r
+*/\r
+ int i, j, k; //Schleifenindizes\r
+ double tmp; //Zwischenspeicherung der Einzelnen Werte\r
+ int count;\r
+\r
+ //Sicherheitsabfragen zu Datengroessen\r
+ if ((nrhs != 4))\r
+ mexErrMsgTxt(\r
+ "expected (coordinates(Nx3),elements(Mx4),zeta(double),type(int))");\r
+ if (nlhs > 1)\r
+ mexErrMsgTxt("has only one output argument");\r
+\r
+ int cm = mxGetM(prhs[0]);\r
+ int cn = mxGetN(prhs[0]);\r
+ if (cn != 3)\r
+ mexErrMsgTxt("expected coordinates (Nx3)");\r
+// cout << " Koordinaten:" << cm << endl;\r
+\r
+ int em = mxGetM(prhs[1]);\r
+ int en = mxGetN(prhs[1]);\r
+ if (en != 4)\r
+ mexErrMsgTxt("expected elements (Mx4)");\r
+// cout << " Elemente:" << em << endl;\r
+\r
+ //Auslesen der Parameter\r
+\r
+ plhs[0] = mxCreateDoubleMatrix(em, em, mxREAL);\r
+ double * A = mxGetPr(plhs[0]);\r
+ double * C = mxGetPr(prhs[0]);\r
+ double * E = mxGetPr(prhs[1]);\r
+\r
+ int type = (int) *(mxGetPr(prhs[3]));\r
+ double * zeta = mxGetPr(prhs[2]);\r
+\r
+ //Initialisieren der Hilfsvektoren\r
+\r
+ double * x0 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
+ double * x1 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
+ double * x2 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
+ double * x3 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
+ double * xa = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
+ double * xb = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
+\r
+ double * y0 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
+ double * y1 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
+ double * y2 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
+ double * y3 = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
+ double * ya = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
+ double * yb = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
+\r
+ double * d = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
+ double * dt = mxGetPr(mxCreateDoubleMatrix(3, 1, mxREAL));\r
+\r
+ // Welche Funktion soll verwendet werden\r
+ double(*ctypeP)(double, double, double, double, double, double, double,\r
+ double*);\r
+ double(*ctypeO)(double, double, double, double, double, double, double,\r
+ double*);\r
+\r
+ //Art der Berechnung bestimmen\r
+// cout << " Typ:" << type << endl;\r
+ switch (type) {\r
+ default:\r
+ ctypeP = cParO1;\r
+ ctypeO = NULL;\r
+ break;\r
+ case 0:\r
+ ctypeP = cParO0;\r
+ ctypeO = NULL;\r
+ break;\r
+ case 2:\r
+ ctypeP = cParO2;\r
+ ctypeO = NULL;\r
+ break;\r
+ case 3:\r
+ ctypeP = cParO3;\r
+ ctypeO = NULL;\r
+ break;\r
+ }\r
+\r
+ //LageInformationen\r
+ int rx, rxa, rxb, ry, rya, ryb;\r
+\r
+// cout << " Progress: #";\r
+ count = 0;\r
+ //Ausrechnen\r
+ for (j = 0; j < em; ++j) {\r
+ x0[0] = C[(int) E[j] - 1];\r
+ x0[1] = C[cm + (int) E[j] - 1];\r
+ x0[2] = C[2 * cm + (int) E[j] - 1];\r
+\r
+ x1[0] = C[(int) E[em + j] - 1];\r
+ x1[1] = C[cm + (int) E[em + j] - 1];\r
+ x1[2] = C[2 * cm + (int) E[em + j] - 1];\r
+\r
+ x2[0] = C[(int) E[2 * em + j] - 1];\r
+ x2[1] = C[cm + (int) E[2 * em + j] - 1];\r
+ x2[2] = C[2 * cm + (int) E[2 * em + j] - 1];\r
+\r
+ x3[0] = C[(int) E[3 * em + j] - 1];\r
+ x3[1] = C[cm + (int) E[3 * em + j] - 1];\r
+ x3[2] = C[2 * cm + (int) E[3 * em + j] - 1];\r
+\r
+ for (i = 0; i < 3; ++i)\r
+ xa[i] = x1[i] - x0[i];\r
+\r
+ for (i = 0; i < 3; ++i)\r
+ xb[i] = x3[i] - x0[i];\r
+\r
+ // Lageeigenschaften des Flaechenstuecks\r
+\r
+ rxa = dimOfVec(xa);\r
+ rxb = dimOfVec(xb);\r
+ rx = dimOfThird(rxa, rxb);\r
+\r
+ //kleinste Ecke finden und fuer \delta verwenden\r
+\r
+ if (xa[rxa] > 0) {\r
+ if (xb[rxb] > 0) {\r
+ for (i = 0; i < 3; ++i)\r
+ dt[i] = -x0[i];\r
+ } else {\r
+ for (i = 0; i < 3; ++i)\r
+ dt[i] = -x3[i];\r
+ }\r
+ } else {\r
+ if (xb[rxb] > 0) {\r
+ for (i = 0; i < 3; ++i)\r
+ dt[i] = -x1[i];\r
+ } else {\r
+ for (i = 0; i < 3; ++i)\r
+ dt[i] = -x2[i];\r
+ }\r
+ }\r
+\r
+ for (k = 0; k <= j; ++k) {\r
+ y0[0] = C[(int) E[k] - 1];\r
+ y0[1] = C[cm + (int) E[k] - 1];\r
+ y0[2] = C[2 * cm + (int) E[k] - 1];\r
+\r
+ y1[0] = C[(int) E[em + k] - 1];\r
+ y1[1] = C[cm + (int) E[em + k] - 1];\r
+ y1[2] = C[2 * cm + (int) E[em + k] - 1];\r
+\r
+ y2[0] = C[(int) E[2 * em + k] - 1];\r
+ y2[1] = C[cm + (int) E[2 * em + k] - 1];\r
+ y2[2] = C[2 * cm + (int) E[2 * em + k] - 1];\r
+\r
+ y3[0] = C[(int) E[3 * em + k] - 1];\r
+ y3[1] = C[cm + (int) E[3 * em + k] - 1];\r
+ y3[2] = C[2 * cm + (int) E[3 * em + k] - 1];\r
+\r
+ for (i = 0; i < 3; ++i)\r
+ ya[i] = y1[i] - y0[i];\r
+\r
+ for (i = 0; i < 3; ++i)\r
+ yb[i] = y3[i] - y0[i];\r
+\r
+ // Lageeigenschaften des Flaechenstuecks\r
+\r
+ rya = dimOfVec(ya);\r
+ ryb = dimOfVec(yb);\r
+ ry = dimOfThird(rya, ryb);\r
+\r
+ //kleinste Ecke finden und fuer \delta verwenden\r
+\r
+ if (ya[rya] > 0) {\r
+ if (yb[ryb] > 0) {\r
+ for (i = 0; i < 3; ++i)\r
+ d[i] = dt[i] + y0[i];\r
+ } else {\r
+ for (i = 0; i < 3; ++i)\r
+ d[i] = dt[i] + y3[i];\r
+ }\r
+ } else {\r
+ if (yb[ryb] > 0) {\r
+ for (i = 0; i < 3; ++i)\r
+ d[i] = dt[i] + y1[i];\r
+ } else {\r
+ for (i = 0; i < 3; ++i)\r
+ d[i] = dt[i] + y2[i];\r
+ }\r
+ }\r
+\r
+ if (rx == ry) {\r
+ if (rxa == rya) {\r
+ tmp = ctypeP(fabs(xa[rxa]), fabs(xb[rxb]), fabs(ya[rxa]),\r
+ fabs(yb[rxb]), d[rxa], d[rxb], d[rx], zeta);\r
+\r
+ } else {\r
+ tmp = ctypeP(fabs(xa[rxa]), fabs(xb[rxb]), fabs(yb[rxa]),\r
+ fabs(ya[rxb]), d[rxa], d[rxb], d[rx], zeta);\r
+ }\r
+\r
+ } else {\r
+\r
+ if (rxa == rya) {\r
+ tmp = ctypeO(fabs(xb[rxb]), fabs(xa[rxa]), fabs(ya[rya]),\r
+ fabs(yb[ryb]), d[rxb], d[rxa], d[rx], zeta);\r
+ } else if (rxa == ryb) {\r
+ tmp = ctypeO(fabs(xb[rxb]), fabs(xa[rxa]), fabs(yb[ryb]),\r
+ fabs(ya[rya]), d[rxb], d[rxa], d[rx], zeta);\r
+ } else if (rxb == rya) {\r
+ tmp = ctypeO(fabs(xa[rxa]), fabs(xb[rxb]), fabs(ya[rya]),\r
+ fabs(yb[ryb]), d[rxa], d[rxb], d[rx], zeta);\r
+ } else {\r
+ tmp = ctypeO(fabs(xa[rxa]), fabs(xb[rxb]), fabs(yb[ryb]),\r
+ fabs(ya[rya]), d[rxa], d[rxb], d[rx], zeta);\r
+ }\r
+\r
+ }\r
+ A[(k * em) + j] = 1. / (4 * M_PI) * tmp;\r
+ if (k != j)\r
+ A[(j * em) + k] = 1. / (4 * M_PI) * tmp;\r
+/* if (count++ > ((em * (em + 1)) / 2) / 10) {\r
+ count = 0;\r
+// mexPrintf("#");\r
+// cout << "#";\r
+// cout.flush();\r
+ }*/\r
+\r
+ }\r
+\r
+ }\r
+// cout << endl;\r
+ //Rueckgabe (eventuell zurueck schreiben)\r
+/* mxFree(x0);\r
+ mxFree(x1);\r
+ mxFree(x3);\r
+ mxFree(xa);\r
+ mxFree(xb);\r
+ mxFree(y0);\r
+ mxFree(y1);\r
+ mxFree(y3);\r
+ mxFree(ya);\r
+ mxFree(yb);\r
+ mxFree(d);\r
+ mxFree(dt);\r
+*/\r
+ return;\r
+}\r
format longG
% Matrix MEX Funktion neu Compilieren
-mex mex_build_AU.cpp slpRectangle.cpp
+mex mex_build_V.cpp slpRectangle.cpp
% Test ausführen