136 lines
5.4 KiB
Matlab
136 lines
5.4 KiB
Matlab
clc
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clear all
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% 算例配置（改材料/模态数请编辑 case_config.m）
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[phy, cfg] = case_config();
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% 四面体体积分：高斯积分节点与权重
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IntegralOrder=cfg.IntegralOrder;
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xt = [0.25,...
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0.0919710780526,0.0919710780526,0.0919710780526,0.724086765841,...
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0.319793627829,0.319793627829,0.319793627829,0.0406191165118,...
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0.0563508326895,0.0563508326895,0.44364916731,0.0563508326895,...
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0.44364916731,0.44364916731];
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yt = [0.25,...
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0.0919710780526,0.0919710780526,0.724086765841,0.0919710780526,...
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0.319793627829,0.319793627829,0.0406191165118,0.319793627829,...
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0.0563508326895,0.44364916731,0.0563508326895,0.44364916731,...
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0.0563508326895,0.44364916731];
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zt = [0.25,...
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0.0919710780526,0.724086765841,0.0919710780526,0.0919710780526,...
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0.319793627829,0.0406191165118,0.319793627829,0.319793627829,...
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0.44364916731,0.0563508326895,0.0563508326895,0.44364916731,...
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0.44364916731,0.0563508326895];
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pt = [0.0197530864198,...
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0.0119895139632,0.0119895139632,0.0119895139632,0.0119895139632,...
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0.011511367871,0.011511367871,0.011511367871,0.011511367871,...
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0.00881834215168,0.00881834215168,0.00881834215168,0.00881834215168,...
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0.00881834215168,0.00881834215168];
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model=mphload(cfg.mphFile);
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[m1, m2]=mphmeshstats(model);
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NbrNodes=max(size(m2.vertex)); % 顶点数
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NbrElements=max(size(m2.elem{2})); % 四面体数
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Nodes=m2.vertex; % 顶点坐标 3*n
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Domains=m2.elementity{2}; % 四面体区域索引 n*1
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Elements=m2.elem{2}+1; % 四面体顶点索引 4*n（COMSOL 0-based -> MATLAB 1-based）
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% 四面体顶点重新排序，节点按从小到大顺序排列
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Elements = sort(Elements);
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el2no=Elements;
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% 面排序
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f1=el2no([1 1 1 2],:);
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f2=el2no([2 2 3 3],:);
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f3=el2no([3 4 4 4],:);
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f_array=[f1(:) f2(:) f3(:)];
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% Faces 全局面 n*3；FacesOfElements 四面体面索引 4N*1
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[Faces,~,FacesOfElements]=unique(f_array,'rows');
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NbrFaces=max(size(Faces)); % 面数
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% 边排序
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n1=el2no([1 1 1 2 2 3],:);
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n2=el2no([2 3 4 3 4 4],:);
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el_ed2no_array=[n1(:) n2(:)];
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% Edges 全局边 n*2；EdgesOfElements 四面体边索引 6N*1
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[Edges,~,EdgesOfElements]=unique(el_ed2no_array,'rows');
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NbrEdges=max(size(Edges)); % 边数
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epsilon=phy.eps; % 相对介电常数
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Dof=NbrEdges*2+NbrFaces*2; % 自由度：二阶矢量基，边数*2+面数*2
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A=zeros(Dof,Dof);
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B=zeros(Dof,Dof);
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for n=1:NbrElements
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% 网格坐标
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x=zeros(4,1);y=zeros(4,1);z=zeros(4,1);
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x(1)=Nodes(1,Elements(1,n));y(1)=Nodes(2,Elements(1,n));z(1)=Nodes(3,Elements(1,n));
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x(2)=Nodes(1,Elements(2,n));y(2)=Nodes(2,Elements(2,n));z(2)=Nodes(3,Elements(2,n));
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x(3)=Nodes(1,Elements(3,n));y(3)=Nodes(2,Elements(3,n));z(3)=Nodes(3,Elements(3,n));
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x(4)=Nodes(1,Elements(4,n));y(4)=Nodes(2,Elements(4,n));z(4)=Nodes(3,Elements(4,n));
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% 边长度
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l=zeros(6,1);
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l(1)=sqrt((x(1)-x(2))*(x(1)-x(2))+(y(1)-y(2))*(y(1)-y(2))+(z(1)-z(2))*(z(1)-z(2)));
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l(2)=sqrt((x(1)-x(3))*(x(1)-x(3))+(y(1)-y(3))*(y(1)-y(3))+(z(1)-z(3))*(z(1)-z(3)));
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l(3)=sqrt((x(4)-x(1))*(x(4)-x(1))+(y(4)-y(1))*(y(4)-y(1))+(z(4)-z(1))*(z(4)-z(1)));
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l(4)=sqrt((x(2)-x(3))*(x(2)-x(3))+(y(2)-y(3))*(y(2)-y(3))+(z(2)-z(3))*(z(2)-z(3)));
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l(5)=sqrt((x(4)-x(2))*(x(4)-x(2))+(y(4)-y(2))*(y(4)-y(2))+(z(4)-z(2))*(z(4)-z(2)));
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l(6)=sqrt((x(4)-x(3))*(x(4)-x(3))+(y(4)-y(3))*(y(4)-y(3))+(z(4)-z(3))*(z(4)-z(3)));
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ll=zeros(20,1); % 基函数归一化系数
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ll(1)=l(1);ll(2)=l(1);ll(3)=l(2);ll(4)=l(2);ll(5)=l(3);ll(6)=l(3);
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ll(7)=l(4);ll(8)=l(4);ll(9)=l(5);ll(10)=l(5);ll(11)=l(6);ll(12)=l(6);
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ll(13)=1.5*l(1);ll(14)=1.5*l(2);ll(15)=1.5*l(1);ll(16)=1.5*l(3);
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ll(17)=1.5*l(2);ll(18)=1.5*l(3);ll(19)=1.5*l(4);ll(20)=1.5*l(5);
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% 雅可比矩阵
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Jac=zeros(3,3);
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Jac(1,1)=x(1)-x(4);Jac(1,2)=y(1)-y(4);Jac(1,3)=z(1)-z(4);
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Jac(2,1)=x(2)-x(4);Jac(2,2)=y(2)-y(4);Jac(2,3)=z(2)-z(4);
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Jac(3,1)=x(3)-x(4);Jac(3,2)=y(3)-y(4);Jac(3,3)=z(3)-z(4);
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InvJac=inv(Jac);
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DetJac=abs(det(Jac));
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TJac=Jac'/DetJac;
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% 计算高斯节点对应的基函数
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tempE=zeros(1,3);E=zeros(20,3,IntegralOrder);curlE=zeros(20,3,IntegralOrder);
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for i=1:IntegralOrder
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for j=1:20
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tempE(:)=BF_E(xt(i),yt(i),zt(i),j)*ll(j);
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E(j,:,i)=(InvJac*tempE(:))';
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tempE(:)=BF_CurlE(xt(i),yt(i),zt(i),j)*ll(j);
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curlE(j,:,i)=(TJac*tempE(:))';
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end
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end
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% 计算映射数组（局部 DOF -> 全局 DOF）
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map=zeros(20,1);
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for i=1:6
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map(i*2-1)=EdgesOfElements((n-1)*6+i);
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map(i*2)=EdgesOfElements((n-1)*6+i)+NbrEdges;
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end
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for i=1:4
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map(12+i*2-1)=2*NbrEdges+FacesOfElements((n-1)*4+i);
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map(12+i*2)=FacesOfElements((n-1)*4+i)+NbrFaces+2*NbrEdges;
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end
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% 双循环计算子矩阵
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Ae=zeros(20,20);Be=zeros(20,20);
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for i=1:20
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for j=1:20
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for k=1:IntegralOrder
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Ae(i,j)=Ae(i,j)+pt(k)*DetJac*(curlE(i,1,k)*curlE(j,1,k)+curlE(i,2,k)*curlE(j,2,k)+curlE(i,3,k)*curlE(j,3,k));
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Be(i,j)=Be(i,j)+pt(k)*DetJac*(E(i,1,k)*E(j,1,k)+E(i,2,k)*E(j,2,k)+E(i,3,k)*E(j,3,k));
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end
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end
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end
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% 矩阵组装
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for i=1:20
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for j=1:20
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A(map(i),map(j))= A(map(i),map(j))+Ae(i,j);
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B(map(i),map(j))= B(map(i),map(j))+Be(i,j);
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end
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end
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end
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% 广义本征值求解：A*x = lambda*B*x，lambda = k0^2
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[V,D] = eigs(A,B,cfg.NbrMode,cfg.eigsSigma);
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k0=diag(sqrt(D)) |