234 lines
6.5 KiB
Mathematica
234 lines
6.5 KiB
Mathematica
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function [] = 2DLevelSetFMM()
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clear all
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% Define Main Solution Mesh
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NumX=3;
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NumY=1;
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delX=1.;
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delY=1.;
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for j=1:NumY+1
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for i=1:NumX+1
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index=i+(NumX+1)*(j-1);
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Node(index,1)=single((i-1.))*delX;
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Node(index,2)=single((j-1.))*delY;
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end
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end
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numNodes=(NumX+1)*(NumY+1);
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for j=1:NumY
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for i=1:NumX
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index=i+NumX*(j-1);
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Element(index,1)=i+(NumX+1)*(j-1);
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Element(index,2)=i+(NumX+1)*(j-1)+1;
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Element(index,3)=i+(NumX+1)*(j)+1;
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Element(index,4)=i+(NumX+1)*(j);
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end
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end
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numElem=(NumX)*(NumY);
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% Define Initial Level Set
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%centx=4.;
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%centy=4.;
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%rad=2.1;
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%for i=1:numNodes;
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% dist=sqrt((Node(i,1)-centx)*(Node(i,1)-centx)+(Node(i,2)-centy)*(Node(i,2)-centy));
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% lSet(i)=dist-rad;
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%end
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for i=1:numNodes;
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dist=Node(i,1)-0.1;
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lSet(i)=dist;
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end
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% Plot initial level set
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%[X Y]=meshgrid(0:1.:8);
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%Z=zeros(9);
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%for i=1:81
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% Z(i)=lSet(i);
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%end
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%surf(X,Y,Z)
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% LS Algorithm Parameters
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lSet'
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bandwidth=10.;
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% Loop through timesteps
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for tstep=1:1
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% Identify Narrow Band Elements
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NBindex=0;
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for i=1:numElem
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check=0;
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for iNd=1:4
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if abs(lSet(Element(i,iNd)))<=bandwidth*delX
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check=1;
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end
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end
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% If an element is in the narrow band split it into triangles
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if check==1
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NBindex=NBindex+1;
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NBelem(NBindex,1)=Element(i,1);
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NBelem(NBindex,2)=Element(i,2);
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NBelem(NBindex,3)=Element(i,3);
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NBindex=NBindex+1;
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NBelem(NBindex,1)=Element(i,1);
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NBelem(NBindex,2)=Element(i,3);
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NBelem(NBindex,3)=Element(i,4);
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end
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end
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% Velocity BC
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F=zeros(numNodes,1);
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for i=1:NBindex
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if sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,2)))||sign(lSet(NBelem(i,1)))~=sign(lSet(NBelem(i,3)))
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F(NBelem(i,1))= 1.;
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F(NBelem(i,2))= 1.;
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F(NBelem(i,3))= 1.;
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end
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end
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% Assemble 'Stiffness' Matrices
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A=zeros(numNodes);
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for i=1:NBindex
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gx(1)=2./3.;
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gx(2)=1./6.;
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gx(3)=1./6.;
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hx(1)=1./6.;
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hx(2)=1./6.;
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hx(3)=2./3.;
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AfL=zeros(3);
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AfLGLS=zeros(3);
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x1=Node(NBelem(i,1),1);
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y1=Node(NBelem(i,1),2);
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x2=Node(NBelem(i,2),1);
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y2=Node(NBelem(i,2),2);
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x3=Node(NBelem(i,3),1);
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y3=Node(NBelem(i,3),2);
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for j=1:3
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g=gx(j);
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h=hx(j);
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phi(1)=1.-g-h;
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phi(2)=g;
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phi(3)=h;
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phig(1)=-1.;
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phig(2)=1.;
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phig(3)=0.;
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phih(1)=-1.;
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phih(2)=0.;
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phih(3)=1.;
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djac=2*abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
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for k=1:3
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phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
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phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
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end
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delphi=[phix;phiy];
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nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
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set=phi*nodalLset;
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delset=delphi*nodalLset;
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AfL=AfL+(phi'*sign(set))*(delset'*delphi)/3.;
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AfLGLS=AfLGLS+(delphi'*delset)*(1./norm(delset))*(delset'*delphi)/3.;
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end
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sum=AfL+AfLGLS;
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for k=1:3;
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for j=1:3;
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A(NBelem(i,j),NBelem(i,k))=A(NBelem(i,j),NBelem(i,k))+sum(j,k);
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end
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end
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end
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% Apply BCs
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RHS=zeros(numNodes,1);
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Sub=A*F;
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iindex=0;
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for i=1:numNodes
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if F(i)==0.
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iindex=iindex+1;
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RHSred(iindex)=RHS(i)-Sub(i);
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Fred=0.;
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jindex=0;
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for j=1:numNodes
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if F(j)==0.
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jindex=jindex+1;
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Ared(iindex,jindex)=A(i,j);
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end
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end
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end
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end
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% Solve for Fred
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Fred=(Ared^-1)*RHSred';
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% Get F
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iindex=0;
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for i=1:numNodes
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if F(i)==0.
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iindex=iindex+1;
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F(i)=Fred(iindex);
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end
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end
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% Update level set
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mMat=zeros(numNodes);
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mMatGLS=zeros(numNodes);
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f1=zeros(numNodes,1);
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f2=zeros(numNodes,1);
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f3=zeros(numNodes,1);
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h2=0.00001;
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visc=0.0005;
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for i=1:NBindex
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mMatL=zeros(3);
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mMatGLSL=zeros(3);
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f1L=zeros(3,1);
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f2L=zeros(3,1);
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f3L=zeros(3,1);
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gx(1)=2./3.;
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gx(2)=1./6.;
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gx(3)=1./6.;
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hx(1)=1./6.;
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hx(2)=1./6.;
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hx(3)=2./3.;
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x1=Node(NBelem(i,1),1);
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y1=Node(NBelem(i,1),2);
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x2=Node(NBelem(i,2),1);
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y2=Node(NBelem(i,2),2);
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x3=Node(NBelem(i,3),1);
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y3=Node(NBelem(i,3),2);
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for j=1:3
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g=gx(j);
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h=hx(j);
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phi(1)=1.-g-h;
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phi(2)=g;
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phi(3)=h;
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phig(1)=-1.;
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phig(2)=1.;
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phig(3)=0.;
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phih(1)=-1.;
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phih(2)=0.;
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phih(3)=1.;
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djac=abs(x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2));
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for k=1:3
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phix(k)=(1./djac)*((-y1+y3)*phig(k)+(y1-y2)*phih(k));
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phiy(k)=(1./djac)*((x1-x3)*phig(k)+(-x1+x2)*phih(k));
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end
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delphi=[phix;phiy];
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nodalLset=[lSet(NBelem(i,1));lSet(NBelem(i,2));lSet(NBelem(i,3))];
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nodalF=[F(NBelem(i,1));F(NBelem(i,2));F(NBelem(i,3))];
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delset=delphi*nodalLset;
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Floc=phi*nodalF;
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mMatL=mMatL+(phi'*phi)/3.;
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mMatGLSL=mMatGLSL+((delphi'*(delset/norm(delset)))*Floc*(h2/abs(Floc)))*phi/3.;
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f1L=f1L+phi'*Floc*norm(delset)/3.;
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f2L=f2L+(delphi'*(delset/norm(delset))*Floc)*(h2/abs(Floc))*Floc*norm(delset)/3.;
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vs=h2*((abs(visc+Floc*norm(delset)))/(norm(Floc*delset)+h2));
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f3L=f3L+vs*delphi'*delset/3.;
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end
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for k=1:3;
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for j=1:3;
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mMat(NBelem(i,j),NBelem(i,k))=mMat(NBelem(i,j),NBelem(i,k))+mMatL(j,k);
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mMatGLS(NBelem(i,j),NBelem(i,k))=mMatGLS(NBelem(i,j),NBelem(i,k))+mMatGLSL(j,k);
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end
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f1(NBelem(i,k))=f1(NBelem(i,k))+f1L(k);
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f2(NBelem(i,k))=f2(NBelem(i,k))+f2L(k);
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f3(NBelem(i,k))=f3(NBelem(i,k))+f3L(k);
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end
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end
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dt=0.01;
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lSet=lSet-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
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end
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lSet'
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%[X Y]=meshgrid(0:1.:8);
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%Z=zeros(9);
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%for i=1:81
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% Z(i)=lSet(i);
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%end
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%surf(X,Y,Z)
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