function [] = FESolve()
% MATLAB based FE Solver
% J. Grogan (2012)
clear all
% Define Geometry
len=1.;
% Define Section Properties
rho=1.;
spec=1.;
cond=1.;
% Generate Mesh
numElem=10;
ndCoords=linspace(0,len,numElem+1);
numNodes=size(ndCoords,2);
indx=1:numElem;
elemNodes(:,1)=indx;
elemNodes(:,2)=indx+1;
% Initialize Conditions
Tnew=zeros(numNodes,1);
Tnew(1)=1.;
% Define Time Step
dtime=.1;
tsteps=10;
time=0.;
% Loop through time steps
for ts=1:tsteps;
    time=time+dtime;
    K=zeros(numNodes,numNodes);
    M=zeros(numNodes,numNodes);
    % Loop Through Elements
    for e=1:numElem;
        Ke=zeros(2);
        Me=zeros(2);
        gpx(1)=-1./sqrt(3.);
        gpx(2)=1./sqrt(3.);
        ajacob=abs(ndCoords(elemNodes(e,2))-ndCoords(elemNodes(e,1)))/2.;
        % Loop Through Int Points
        for i=1:2;
            c=gpx(i);
            phi(1)=(1.-c)/2.;
            phi(2)=(1.+c)/2.;
            phic(1)=-0.5;
            phic(2)=0.5;
            phix(1)=phic(1)/ajacob;
            phix(2)=phic(2)/ajacob;
            we=ajacob;
            Ke=Ke+we*cond*phix'*phix;
            Me=Me+(we*rho*spec*phi'*phi)/dtime;
        end
        % Assemble Global Matrices
        K(elemNodes(e,1),elemNodes(e,1))=K(elemNodes(e,1),elemNodes(e,1))+Ke(1,1);
        K(elemNodes(e,1),elemNodes(e,2))=K(elemNodes(e,1),elemNodes(e,2))+Ke(1,2);
        K(elemNodes(e,2),elemNodes(e,1))=K(elemNodes(e,2),elemNodes(e,1))+Ke(2,1);
        K(elemNodes(e,2),elemNodes(e,2))=K(elemNodes(e,2),elemNodes(e,2))+Ke(2,2);    
        M(elemNodes(e,1),elemNodes(e,1))=M(elemNodes(e,1),elemNodes(e,1))+Me(1,1);
        M(elemNodes(e,1),elemNodes(e,2))=M(elemNodes(e,1),elemNodes(e,2))+Me(1,2);
        M(elemNodes(e,2),elemNodes(e,1))=M(elemNodes(e,2),elemNodes(e,1))+Me(2,1);
        M(elemNodes(e,2),elemNodes(e,2))=M(elemNodes(e,2),elemNodes(e,2))+Me(2,2);      
    end
    %Apply Boundary Conditions (Reduce Matrices)
    T1=1;
    RHS=M*Tnew;
    for i=1:numNodes-1;
        for j=1:numNodes-1;
            Kred(i,j)=K(i+1,j+1);
            Mred(i,j)=M(i+1,j+1);
        end
        Subr(i)=(K(i+1,1)+M(i+1,1))*T1;
        RHSr(i)=RHS(i+1);
    end          
    %Solve
    StiffI=(Mred+Kred)^-1;
    Tnewr=StiffI*(RHSr'-Subr');
    for i=1:numNodes-1;
        Tnew(i+1)=Tnewr(i);
    end
    Tnew(1)=1.;
    Tnew
end