phd-scripts/Unpublished/XFEM2/1D_Solver/GetF.m

function [] = GetF()
% set up grid
gd=0.;
numElem=4;
eLen=0.25;
for i=1:numElem+1
    ndCrd(i)=gd;
    gd=gd+eLen;
end
for i=1:numElem
    elemNod(i,1)=i;
    elemNod(i,2)=i+1;
end
% Initial level set
dpos=0.1;
for i=1:numElem+1
    lSet(i)=sign(ndCrd(i)-dpos)*abs(dpos-ndCrd(i));
end
lSet'
for tstep=1:1
    % Velocity BC
    F=zeros(numElem+1,1);
    for i=1:numElem
        if sign(lSet(elemNod(i,1)))~=sign(lSet(elemNod(i,2)))
            F(elemNod(i,1))= 0.0005;
            F(elemNod(i,2))= 0.0005;
        end
    end
    % Assemble 'Stiffness' Matrices
    A=zeros(numElem+1);
    for i=1:numElem
        pos(1)=-1/sqrt(3);
        pos(2)=1/sqrt(3);
        AfL=zeros(2);
        AfLGLS=zeros(2);
        for j=1:2
            shp(1)=(1-pos(j))/2.;
            shp(2)=(1+pos(j))/2.;
            dshp(1)=-0.5;
            dshp(2)=0.5;
            rset=shp(1)*lSet(elemNod(i,1))+shp(2)*lSet(elemNod(i,2));
            dls=dshp(1)*lSet(elemNod(i,1))+dshp(2)*lSet(elemNod(i,2));
            AfL=AfL+shp'*sign(rset)*(dls*dshp);
            AfLGLS=AfLGLS+(dshp'*dls)*(0.25/abs(dls))*(dls*dshp);
        end
        for k=1:2;
            for j=1:2;
               A(elemNod(i,j),elemNod(i,k))=A(elemNod(i,j),elemNod(i,k))+AfL(j,k)+AfLGLS(j,k)
            end
        end
    end
    % Apply BCs
    RHS=zeros(numElem+1,1);
    Sub=A*F;
    iindex=0;
    for i=1:numElem+1
        if F(i)==0.
            iindex=iindex+1;
            RHSred(iindex)=RHS(i)-Sub(i);
            Fred=0.;
            jindex=0;
            for j=1:numElem+1
                if F(j)==0.
                    jindex=jindex+1;
                    Ared(iindex,jindex)=A(i,j);
                end
            end
        end
    end
    % Solve for Fred
    Fred=(Ared^-1)*RHSred';
    % Get F
    iindex=0;
    for i=1:numElem+1
        if F(i)==0.
            iindex=iindex+1;
            F(i)=Fred(iindex);
        end
    end
    % Update level set
    mMat=zeros(numElem+1);
    mMatGLS=zeros(numElem+1);
    f1=zeros(numElem+1,1);
    f2=zeros(numElem+1,1);
    f3=zeros(numElem+1,1);
    h=0.25;
    visc=0.000;
    for i=1:numElem
        pos(1)=-1/sqrt(3);
        pos(2)=1/sqrt(3); 
        mMatL=zeros(2);
        mMatGLSL=zeros(2);
        f1L=zeros(2,1);
        f2L=zeros(2,1);
        f3L=zeros(2,1);
        for j=1:2
            shp(1)=(1-pos(j))/2.;
            shp(2)=(1+pos(j))/2.;
            dshp(1)=-0.5;
            dshp(2)=0.5;    
            Floc=shp(1)*F(elemNod(i,1))+shp(2)*F(elemNod(i,2));
            rset=shp(1)*lSet(elemNod(i,1))+shp(2)*lSet(elemNod(i,2));
            dls=dshp(1)*lSet(elemNod(i,1))+dshp(2)*lSet(elemNod(i,2));
            mMatL=mMatL+shp'*shp;
            mMatGLSL=mMatGLSL+((dshp'*(dls/abs(dls)))*Floc*(h/abs(Floc)))*shp;
            f1L=f1L+shp'*Floc*abs(dls);
            f2L=f2L+(dshp'*(dls/abs(dls))*Floc)*(h/abs(Floc))*Floc*abs(dls);
            vs=h*((abs(visc+Floc*abs(dls)))/(abs(Floc*dls)+h));
            f3L=f3L+vs*dshp'*dls;
        end
        for k=1:2;
            for j=1:2;
               mMat(elemNod(i,j),elemNod(i,k))=mMat(elemNod(i,j),elemNod(i,k))+mMatL(j,k);
               mMatGLS(elemNod(i,j),elemNod(i,k))=mMatGLS(elemNod(i,j),elemNod(i,k))+mMatGLSL(j,k);           
            end
            f1(elemNod(i,k))=f1(elemNod(i,k))+f1L(k);
            f2(elemNod(i,k))=f2(elemNod(i,k))+f2L(k);
            f3(elemNod(i,k))=f3(elemNod(i,k))+f3L(k);       
        end
    end
    dt=0.01;
    lSet=lSet-((((mMat+mMatGLS)^-1)/dt)*(f1+f2+f3))';
    lSet';
end