331 lines
9.9 KiB
Mathematica
331 lines
9.9 KiB
Mathematica
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function [] = F2DLevelSetFMM()
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clear all
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% Define Main Solution Mesh
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NumX=32;
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NumY=32;
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delX=0.25;
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delY=0.25;
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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(0:0.25:8);
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Z=zeros(33);
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for i=1:1089
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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=1:10
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% Identify Narrow Band Elements
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NBElems=0;
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NBNodes=0;
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NGlobal=zeros(numNodes);
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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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for j=1:4
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if NGlobal(Element(i,j))==0
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NBNodes=NBNodes+1;
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NGlobal(Element(i,j))=NBNodes;
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NLocal(NBNodes)=Element(i,j);
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end
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end
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NBElems=NBElems+1;
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NBelem(NBElems,1)=NGlobal(Element(i,1));
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NBelem(NBElems,2)=NGlobal(Element(i,2));
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NBelem(NBElems,3)=NGlobal(Element(i,3));
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NBElems=NBElems+1;
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NBelem(NBElems,1)=NGlobal(Element(i,1));
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NBelem(NBElems,2)=NGlobal(Element(i,3));
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NBelem(NBElems,3)=NGlobal(Element(i,4));
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end
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end
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% Get local Level Set
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for i=1:NBNodes
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lSetLocal(i)=lSet(NLocal(i));
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end
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% Velocity BC
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F=zeros(NBNodes,1);
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for i=1:NBElems
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L1=sign(lSetLocal(NBelem(i,1)));
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L2=sign(lSetLocal(NBelem(i,2)));
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L3=sign(lSetLocal(NBelem(i,3)));
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if L1 ~= L2 || L1 ~= L3
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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(NBNodes);
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for i=1:NBElems
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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(NLocal(NBelem(i,1)),1);
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y1=Node(NLocal(NBelem(i,1)),2);
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x2=Node(NLocal(NBelem(i,2)),1);
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y2=Node(NLocal(NBelem(i,2)),2);
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x3=Node(NLocal(NBelem(i,3)),1);
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y3=Node(NLocal(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=[lSetLocal(NBelem(i,1));lSetLocal(NBelem(i,2));lSetLocal(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(NBNodes,1);
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Sub=A*F;
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iindex=0;
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for i=1:NBNodes
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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:NBNodes
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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:NBNodes
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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(NBNodes);
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mMatGLS=zeros(NBNodes);
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f1=zeros(NBNodes,1);
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f2=zeros(NBNodes,1);
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f3=zeros(NBNodes,1);
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h2=0.00001;
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visc=0.0005;
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for i=1:NBElems
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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(NLocal(NBelem(i,1)),1);
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y1=Node(NLocal(NBelem(i,1)),2);
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x2=Node(NLocal(NBelem(i,2)),1);
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y2=Node(NLocal(NBelem(i,2)),2);
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x3=Node(NLocal(NBelem(i,3)),1);
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y3=Node(NLocal(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=[lSetLocal(NBelem(i,1));lSetLocal(NBelem(i,2));lSetLocal(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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lSetLocal=lSetLocal-((((mMat+mMatGLS)^-1)*dt)*(f1+f2+f3))';
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newlSet=lSetLocal;
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% Reinitialize LS
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nstat=zeros(NBNodes,1);
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for i=1:NBElems
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L1=sign(lSetLocal(NBelem(i,1)));
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L2=sign(lSetLocal(NBelem(i,2)));
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L3=sign(lSetLocal(NBelem(i,3)));
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if L1 ~= L2 || L1 ~= L3
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for j=1:3
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nstat(NBelem(i,j))=1;
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end
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end
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end
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maincheck=0;
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while(maincheck==0)
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lmin=1000.;
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avlmin=1000.;
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eindex=0;
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nindex=0;
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maincheck=1;
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for i=1:NBElems
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if nstat(NBelem(i,1))+nstat(NBelem(i,2))+nstat(NBelem(i,3))==2
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maincheck=0;
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check=0;
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ltot=0.;
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for j=1:3
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if nstat(NBelem(i,j))==0
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if abs(lSetLocal(NBelem(i,j)))<=lmin
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check=1;
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tempindex=j;
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end
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end
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ltot=ltot+abs(lSetLocal(NBelem(i,j)));
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end
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if check==1 & ltot/3.<=avlmin
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eindex=i;
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nindex=tempindex;
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lmin=lSetLocal(NBelem(eindex,nindex));
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avlmin=ltot/3.;
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end
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end
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end
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if maincheck==0
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% Find New LS for point
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xp=Node(NLocal(NBelem(eindex,nindex)),1);
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yp=Node(NLocal(NBelem(eindex,nindex)),2);
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count=0;
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for i=1:3
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if i~=nindex
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count=count+1;
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x(count)=Node(NLocal(NBelem(eindex,i)),1);
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y(count)=Node(NLocal(NBelem(eindex,i)),2);
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lloc(count)=newlSet(NBelem(eindex,i));
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end
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end
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delxa=x(1)-xp;
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delya=y(1)-yp;
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delxb=x(2)-xp;
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delyb=y(2)-yp;
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N=[delxa delya; delxb delyb];
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M=N^-1;
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A=(M(1)*M(1)+M(2)*M(2));
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B=(M(3)*M(3)+M(4)*M(4));
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C=2.*(M(1)*M(3)+M(2)*M(4));
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a=A+B+C;
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b=-2.*lloc(1)*A-2.*lloc(2)*B-C*(lloc(1)+lloc(2));
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c=lloc(1)*lloc(1)*A+lloc(2)*lloc(2)*B+lloc(1)*lloc(2)*C-1.;
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templ1=(-b+sqrt(b*b-4.*a*c))/(2.*a);
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templ2=(-b-sqrt(b*b-4.*a*c))/(2.*a);
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if abs(templ1)>abs(templ2)
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newlSet(NBelem(eindex,nindex))=templ1;
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else
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newlSet(NBelem(eindex,nindex))=templ2;
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end
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nstat(NBelem(eindex,nindex))=1;
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end
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end
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% lSetLocal=newlSet;
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% Update Global Level Set
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for i=1:NBNodes
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lSet(NLocal(i))=lSetLocal(i);
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end
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end
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lSet'
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[X Y]=meshgrid(0:0.25:8);
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Z=zeros(33);
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for i=1:1089
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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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