153 lines
4.4 KiB
Matlab
153 lines
4.4 KiB
Matlab
function [A,B,EdgesOfElements,PECInd,Dof,r]=EigenModeMatrixAssembly...
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(Nodes,Elements,Domain,lam0,epsilonr,mur)
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%Description:Assembling matrices of finite element method for mode analysis
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%Gauss quadrature points
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[xt,yt,pt,IntegralOrder]=Get2DGuassPoints(2);
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%Processsing mesh
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el2no=Elements';
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n1=el2no([1 1 2],:);
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n2=el2no([2 3 3],:);
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el_ed2no_array=[n1(:) n2(:)];
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[Edges,~,EdgesOfElements]=unique(el_ed2no_array,'rows');
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NbrEdges=length(Edges);
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NbrNodes=length(Nodes);
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NbrElement=max(size(Elements));
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%PEC Boundary conditions
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NumEdges=zeros(NbrEdges,1);
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for i=1:length(EdgesOfElements)
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temp=EdgesOfElements(i);
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NumEdges(temp)=NumEdges(temp)+1;
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end
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PECEdge=find(NumEdges==1);
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PECEdges=Edges(PECEdge,:);
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PECNode=[PECEdges(:,1);PECEdges(:,2)];
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PECNode=unique(PECNode);
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PECNode=sort(PECNode);
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PECInd=[PECNode;PECEdge+NbrNodes];
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%variable initialization
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k0=2*pi/lam0;
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Dof=NbrEdges+NbrNodes;
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NbrNonZero=NbrElement*9;
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NumA=0;
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Ai=zeros(NbrNonZero,1);
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Aj=zeros(NbrNonZero,1);
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Av=complex(zeros(NbrNonZero,1));
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NumB=0;
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Bi=zeros(NbrNonZero*4,1);
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Bj=zeros(NbrNonZero*4,1);
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Bv=complex(zeros(NbrNonZero*4,1));
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%Loop over meshes
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for n=1:NbrElement
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%coordinate of nodes
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x=zeros(3,1);y=zeros(3,1);l=zeros(3,1);
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x(1)=Nodes(Elements(n,1),1);y(1)=Nodes(Elements(n,1),2);
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x(2)=Nodes(Elements(n,2),1);y(2)=Nodes(Elements(n,2),2);
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x(3)=Nodes(Elements(n,3),1);y(3)=Nodes(Elements(n,3),2);
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l(1)=sqrt((x(1)-x(2))*(x(1)-x(2))+(y(1)-y(2))*(y(1)-y(2)));
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l(2)=sqrt((x(1)-x(3))*(x(1)-x(3))+(y(1)-y(3))*(y(1)-y(3)));
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l(3)=sqrt((x(3)-x(2))*(x(3)-x(2))+(y(3)-y(2))*(y(3)-y(2)));
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%Jac matrics
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Jac=zeros(3,3);
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Jac(1,1)=x(2)-x(1);Jac(1,2)=y(2)-y(1);
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Jac(2,1)=x(3)-x(1);Jac(2,2)=y(3)-y(1);Jac(3,3)=1;
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InvJac=inv(Jac);
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DetJac=abs(det(Jac));
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TJac=Jac'/det(Jac);
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%basis functions
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Et=zeros(3,3,IntegralOrder);curlEt=zeros(3,3,IntegralOrder);
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Ez=zeros(3,3,IntegralOrder);gradEz=zeros(3,3,IntegralOrder);
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temp=zeros(3,1);
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for i=1:IntegralOrder
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for j=1:3
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[temp(1),temp(2)]=BF_Et(j,xt(i),yt(i));temp(3)=0;
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Et(j,:,i)=InvJac*temp*l(j);
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temp(3)=BF_curlEt(j,xt(i),yt(i));temp(1)=0;temp(2)=0;
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curlEt(j,:,i)=TJac*temp*l(j);
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temp(3)=BF_Ez(j,xt(i),yt(i));temp(1)=0;temp(2)=0;
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Ez(j,:,i)=temp;
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[temp(1),temp(2)]=BF_gradEz(j,xt(i),yt(i));temp(3)=0;
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gradEz(j,:,i)=InvJac*temp;
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end
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end
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%material
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domain=Domain(n);
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mu=mur(domain);
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epsilon=epsilonr(domain);
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%Submatrix
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St=zeros(3,3);Tte=zeros(3,3);
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Sz=zeros(3,3);Tz=zeros(3,3);
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G=zeros(3,3);Ttu=zeros(3,3);
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for i=1:3
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for j=1:3
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for k=1:IntegralOrder
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St(i,j)=St(i,j)+pt(k)*DetJac/mu*dot(curlEt(i,:,k),curlEt(j,:,k));
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Tte(i,j)=Tte(i,j)+pt(k)*DetJac*k0*k0*epsilon*dot(Et(i,:,k),Et(j,:,k));
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Sz(i,j)=Sz(i,j)+pt(k)*DetJac/mu*dot(gradEz(i,:,k),gradEz(j,:,k));
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Tz(i,j)=Tz(i,j)+pt(k)*DetJac*k0*k0*epsilon*dot(Ez(i,:,k),Ez(j,:,k));
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G(i,j)=G(i,j)+pt(k)*DetJac/mu*dot(Et(i,:,k),gradEz(j,:,k));
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Ttu(i,j)=Ttu(i,j)+pt(k)*DetJac/mu*dot(Et(i,:,k),Et(j,:,k));
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end
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end
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end
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Gt=G';
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for i=1:3
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for j=1:3
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MappingIndexSi=Elements(n,i);
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MappingIndexSj=Elements(n,j);
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MappingIndexVi=EdgesOfElements((n-1)*3+i)+NbrNodes;
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MappingIndexVj=EdgesOfElements((n-1)*3+j)+NbrNodes;
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NumA=NumA+1;
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Ai(NumA)=MappingIndexVi;
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Aj(NumA)=MappingIndexVj;
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Av(NumA)=St(i,j)-Tte(i,j);
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NumB=NumB+1;
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Bi(NumB)=MappingIndexVi;
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Bj(NumB)=MappingIndexVj;
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Bv(NumB)=Ttu(i,j);
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NumB=NumB+1;
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Bi(NumB)=MappingIndexSi;
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Bj(NumB)=MappingIndexSj;
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Bv(NumB)=Sz(i,j)-Tz(i,j);
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NumB=NumB+1;
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Bi(NumB)=MappingIndexVi;
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Bj(NumB)=MappingIndexSj;
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Bv(NumB)=G(i,j);
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NumB=NumB+1;
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Bi(NumB)=MappingIndexSi;
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Bj(NumB)=MappingIndexVj;
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Bv(NumB)=Gt(i,j);
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end
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end
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end
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%Assembling matrices
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A = sparse(Ai,Aj,Av);
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B = sparse(Bi,Bj,Bv);
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%Processing PEC
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Free_ind=1:Dof;
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Free_ind(PECInd)=[];
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A=A(Free_ind,Free_ind);
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B=B(Free_ind,Free_ind);
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%Matrix reordering
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r=symrcm(B);
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B=B(r,r);
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A=A(r,r);
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end |