function [] = FESolveSimp()
% MATLAB based 1-D XFEM Solver
% J. Grogan (2012)
clear all
% Define Geometry
len=10.;
% Define Section Properties
rho=1.;
% Generate Mesh
numElem=10;
charlen=len/numElem;
ndCoords=linspace(0,len,numElem+1);
numNodes=size(ndCoords,2);
indx=1:numElem;
elemNodes(:,1)=indx;
elemNodes(:,2)=indx+1;
% dofs per node
ndof=1;
% Initial temperatures
Tnew=zeros(numNodes,1);
Bound=zeros(numNodes,1);
Tnew(1)=1.;
Bound(1)=1.;
% Define Time Step
dtime=0.01;
tsteps=10;
time=0.;
% Loop through time steps
for ts=1:tsteps
    K=zeros(numNodes,numNodes);
    M=zeros(numNodes,numNodes);
    % Loop Through Elements
    for e=1:numElem
        Ke=zeros(2*ndof);
        Me=zeros(2*ndof);
        crdn1=ndCoords(elemNodes(e,1));
        crdn2=ndCoords(elemNodes(e,2));
        elen=abs(crdn2-crdn1);
        ajacob=elen/2.;     
        gpx(1)=-1/sqrt(3.);
        gpx(2)=1/sqrt(3.);
        w(1)=1.;
        w(2)=1.;         
        % Loop Through Int Points
        for i=1:2;
            c=gpx(i);
            phi(1)=(1.-c)/2.;
            phi(2)=(1.+c)/2.;
            cond=1.;
            spec=1.;          
            phic(1)=-0.5;
            phic(2)=0.5;               
            phix(1)=phic(1)/ajacob;
            phix(2)=phic(2)/ajacob;
            we=ajacob*w(i);
            Ke=Ke+we*cond*phix'*phix;
            Me=Me+(we*rho*spec*phi'*phi)/dtime;
        end 
        % Assemble Global Matrices
        gnum=elemNodes(e,1);
        for i=1:2;
            for j=1:2;
                K(gnum+j-1,gnum+i-1)=K(gnum+j-1,gnum+i-1)+Ke(j,i);
                M(gnum+j-1,gnum+i-1)=M(gnum+j-1,gnum+i-1)+Me(j,i);
            end
        end
    end
    %Remove NON-ENHANCED DOFs(Reduce Matrices)
    iindex=0.; 
    A=K+M;
    Sub=A*Bound; 
    RHS=M*Tnew-Sub;   
    % Apply Boundary Conditions       
    for i=1:numNodes; 
        if Bound(i)==0.;
            iindex=iindex+1;
            RHSR(iindex)=RHS(i);
            jindex=0;
            for j=1:numNodes;                  
               if Bound(j)==0.; 
                    jindex=jindex+1;
                    AR(iindex,jindex)=A(i,j);   
               end
            end
         end
    end         
    %Solve
    Tnewr=(AR^-1)*RHSR';
    % Restore Matrices
    iindex=0;
    for i=1:numNodes; 
        if Bound(i)==0.;          
              iindex=iindex+1;
              Tnew(i)=Tnewr(iindex);
        end       
    end       
    Tnew
end