双二次Lagrange 有限元计算特征值程序（基于iFEM）

 function lambda = c0P2(h)
 %% Mesh
 [node,elem] = squarequadmesh([,,,],h);
 elem = elem(:,[,,,]);
   showmesh(node,elem);
   findnode(node);
   findquadelem(node,elem);
 %% Construct Data Structure
 [elem2dof,edge,inDof] = c0dofP2(elem);
 elem2dof=double(elem2dof);
 N = size(node,);  NT = size(elem,);
 Ndof = N+NT+size(edge,);
 A=sparse(Ndof,Ndof);
 B=sparse(Ndof,Ndof);
 %% Assemble stiffness matrix
 % Since Dphi_i*Dphi_j is quadratic,
 % numerical quadrature rule is used here
 option.quadorder = ;   % default order
 [pts,weight] = quadquadpts(option.quadorder);
 pts=pts*-;
 x=pts(:,);y=pts(:,);
 h1=h/;h2=h1;
 area=h2*h1;
 %% Assemble Matrix
 for i=:
     for j=i:
 DuDv=area*(Dxphi(x,y,h1,i).*Dxphi(x,y,h1,j)...
           +Dyphi(x,y,h2,i).*Dyphi(x,y,h2,j))'*weight;
 uv=area*(phi(x,y,i).*phi(x,y,j))'*weight;
       if i==j
 A = A + sparse(elem2dof(:,i),elem2dof(:,j),DuDv,Ndof,Ndof);
 B = B + sparse(elem2dof(:,i),elem2dof(:,j),uv,Ndof,Ndof);
       else
 A = A + sparse([elem2dof(:,i);elem2dof(:,j)],...
                [elem2dof(:,j);elem2dof(:,i)],DuDv,Ndof,Ndof);
 B = B + sparse([elem2dof(:,i);elem2dof(:,j)],...
                [elem2dof(:,j);elem2dof(:,i)],uv,Ndof,Ndof);
       end
     end
 end
 %% Solve Ax = lambda Bx, and its first solution is *pi^
 lambda=eigs(A(inDof,inDof),B(inDof,inDof),,'sm');
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % subfunction Dxphi
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     function s = Dxphi(xi,eta,L1,i) % gradient of basis phi for x
     switch i
         case
             s = (eta.*(.*xi - ).*(eta - ))/(*L1);
         case
             s = (eta.*(.*xi + ).*(eta - ))/(*L1);
         case
             s = (eta.*(.*xi + ).*(eta + ))/(*L1);
         case
             s = (eta.*(.*xi - ).*(eta + ))/(*L1);
         case
             s = -(eta.*xi.*(eta - ))/L1;
         case
             s = -((eta.^ - ).*(*xi + ))/(*L1);
         case
             s = -(eta.*xi.*(eta + ))/L1;
         case
             s = -((eta.^ - ).*(.*xi - ))/(*L1);
         case
             s = (*xi.*(eta.^ - ))/L1;
     end
     end
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % subfunction Dxphi
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     function s = Dyphi(xi,eta,L2,i) % gradient of basis phi for y
      switch i
      case
          s = (xi.*(.*eta - ).*(xi - ))/(*L2);
      case
          s = (xi.*(.*eta - ).*(xi + ))/(*L2);
      case
          s = (xi.*(.*eta + ).*(xi + ))/(*L2);
      case
          s = (xi.*(.*eta + ).*(xi - ))/(*L2);
     case
         s = -((.*eta - ).*(xi.^ - ))/(*L2);
     case
         s = -(eta.*xi.*(xi + ))/L2;
     case
         s =-((*eta + ).*(xi.^ - ))/(*L2);
     case
         s = -(eta.*xi.*(xi - ))/L2;
     case
         s = (*eta.*(xi.^ - ))/L2;
      end
     end

 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % subfunction phi
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     function s = phi(xi,eta,i) % gradient of basis phi
     switch i
         case
             s = (eta.*xi.*(eta - ).*(xi - ))/;
         case
             s = (eta.*xi.*(eta - ).*(xi + ))/;
         case
             s = (eta.*xi.*(eta + ).*(xi + ))/;
         case
             s = (eta.*xi.*(eta + ).*(xi - ))/;
         case
             s = -(eta.*(xi.^ - ).*(eta - ))/;
         case
             s = -(xi.*(eta.^ - ).*(xi + ))/;
         case
             s = -(eta.*(xi.^ - ).*(eta + ))/;
         case
             s = -(xi.*(eta.^ - ).*(xi - ))/;
         case
             s = (eta.^ - ).*(xi.^ - );
     end
     end
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 end

lambda = c0P2(h)

 function [elem2dof,edge,inDof] = c0dofP2(elem)
 totalEdge=sort([elem(:,[,]);elem(:,[,]);elem(:,[,]);elem(:,[,])],);
 [edge, i2, j] = myunique(totalEdge);
 N = max(elem(:));
 NT = size(elem,);
 NE = size(edge,);
 elem2edge = reshape(j,NT,);
 elem2dof = uint32([elem N+elem2edge (N+NE+:N+NE+NT)']);
 i1(j(*NT:-:)) = *NT:-:;
 i1 = i1';
 bdEdgeIdx = (i1 == i2);
 isBdDof = false(N+NE+NT,);
 isBdDof(edge(bdEdgeIdx,:)) = true;   % nodal
 idx = find(bdEdgeIdx);
 isBdDof(N+idx) = true;
 inDof = find(~isBdDof);
 end

[elem2dof,edge,inDof] = c0dofP2(elem)

http://files.cnblogs.com/files/wangshixi12/%E5%8F%8C%E4%BA%8C%E6%AC%A1Lagrange%E6%9C%89%E9%99%90%E5%85%83.rar