void MatMult(const FullMatrix& A,
const dTensor1& invec,
dTensor1& outvec)
{
for (int i=1; i<=A.get_NumRows(); i++)
{
int jmax = A.get_NZrow(i);
double tmp = 0.0;
for (int j=1; j<=jmax; j++)
{
int ind = A.get_Index(i,j);
double val = A.get_Value(i,j);
tmp = tmp + val*invec.get(ind);
}
outvec.set(i, tmp );
}
}
void ConstructA_CG2(const mesh& Mesh, FullMatrix& A)
{
const int NumPhysElems = Mesh.get_NumPhysElems();
const int NumBndNodes = Mesh.get_SubNumBndNodes();
const int Asize = Mesh.get_SubNumPhysNodes();
assert_eq(Asize,A.get_NumRows());
assert_eq(Asize,A.get_NumCols());
dTensor1 A1(6);
dTensor1 A2(6);
dTensor1 A3(6);
dTensor1 A4(6);
dTensor1 A5(6);
dTensor1 A6(6);
A1.set(1, -oneninth );
A1.set(2, 4.0*oneninth );
A1.set(3, -oneninth );
A1.set(4, 4.0*oneninth );
A1.set(5, 4.0*oneninth );
A1.set(6, -oneninth );
A2.set(1, -onethird );
A2.set(2, 0.0 );
A2.set(3, onethird );
A2.set(4, -4.0*onethird );
A2.set(5, 4.0*onethird );
A2.set(6, 0.0 );
A3.set(1, -onethird );
A3.set(2, -4.0*onethird );
A3.set(3, 0.0 );
A3.set(4, 0.0 );
A3.set(5, 4.0*onethird );
A3.set(6, onethird );
A4.set(1, 4.0 );
A4.set(2, -4.0 );
A4.set(3, 0.0 );
A4.set(4, -4.0 );
A4.set(5, 4.0 );
A4.set(6, 0.0 );
A5.set(1, 2.0 );
A5.set(2, -4.0 );
A5.set(3, 2.0 );
A5.set(4, 0.0 );
A5.set(5, 0.0 );
A5.set(6, 0.0 );
A6.set(1, 2.0 );
A6.set(2, 0.0 );
A6.set(3, 0.0 );
A6.set(4, -4.0 );
A6.set(5, 0.0 );
A6.set(6, 2.0 );
dTensor2 spts(3,2);
spts.set(1,1, 1.0/3.0 );
spts.set(1,2, -1.0/6.0 );
spts.set(2,1, -1.0/6.0 );
spts.set(2,2, -1.0/6.0 );
spts.set(3,1, -1.0/6.0 );
spts.set(3,2, 1.0/3.0 );
dTensor1 wgts(3);
wgts.set(1, 1.0/6.0 );
wgts.set(2, 1.0/6.0 );
wgts.set(3, 1.0/6.0 );
// Loop over all elements in the mesh
for (int i=1; i<=NumPhysElems; i++)
{
// Information for element i
iTensor1 tt(6);
for (int k=1; k<=6; k++)
{ tt.set(k, Mesh.get_node_subs(i,k) ); }
// Evaluate gradients of the Lagrange polynomials on Gauss quadrature points
dTensor2 gpx(6,3);
dTensor2 gpy(6,3);
for (int m=1; m<=3; m++)
{
double xi = spts.get(m,1);
double eta = spts.get(m,2);
for (int k=1; k<=6; k++)
{
double gp_xi = A2.get(k) + 2.0*A5.get(k)*xi + A4.get(k)*eta;
double gp_eta = A3.get(k) + A4.get(k)*xi + 2.0*A6.get(k)*eta;
gpx.set(k,m, Mesh.get_jmat(i,1,1)*gp_xi
+ Mesh.get_jmat(i,1,2)*gp_eta );
gpy.set(k,m, Mesh.get_jmat(i,2,1)*gp_xi
+ Mesh.get_jmat(i,2,2)*gp_eta );
}
}
// Entries of the stiffness matrix A
double Area = Mesh.get_area_prim(i);
for (int j=1; j<=6; j++)
for (int k=1; k<=6; k++)
{
double tmp = A.get(tt.get(j),tt.get(k));
for (int m=1; m<=3; m++)
{
tmp = tmp + 2.0*Area*wgts.get(m)*(gpx.get(j,m)*gpx.get(k,m)+gpy.get(j,m)*gpy.get(k,m));
}
A.set(tt.get(j),tt.get(k), tmp );
}
}
// Replace boundary node equations by Dirichlet boundary condition enforcement
for (int i=1; i<=NumBndNodes; i++)
{
const int j=Mesh.get_sub_bnd_node(i);
for (int k=1; k<=A.get_NumCols(); k++)
{
A.set(j,k, 0.0 );
}
for (int k=1; k<=A.get_NumRows(); k++)
{
A.set(k,j, 0.0 );
}
A.set(j,j, 1.0 );
}
// Get sparse structure representation
A.Sparsify();
}
void ConjugateGradient(const int MaxIters,
const double TOL,
const FullMatrix& A,
const dTensor1& rhs,
dTensor1& phi)
{
double DotProd(const dTensor1& avec,
const dTensor1& bvec);
void MatMult(const FullMatrix& A,
const dTensor1& invec,
dTensor1& outvec);
const int size = A.get_NumRows();
int NumIters = 0;
int mflag = 0;
dTensor1 r(size);
dTensor1 d(size);
dTensor1 Ad(size);
for (int i=1; i<=size; i++)
{ phi.set(i, 0.0 ); }
MatMult(A,phi,r);
for (int i=1; i<=size; i++)
{ r.set(i, rhs.get(i)-r.get(i) ); }
for (int i=1; i<=size; i++)
{ d.set(i, r.get(i) ); }
double rhs_norm = sqrt(DotProd(rhs,rhs));
if (fabs(rhs_norm)<=1.0e-12)
{ rhs_norm = 1.0; }
//printf(" rhs_norm = %e\n",rhs_norm);
double rdotr = DotProd(r,r);
//printf(" sqrt(rdotr) = %e\n",sqrt(rdotr));
double rel_res_norm = sqrt(rdotr)/rhs_norm;
if(rel_res_norm < TOL)
{ mflag = 1; }
NumIters = 1;
while(mflag==0)
{
MatMult(A,d,Ad);
double alpha = rdotr/DotProd(d,Ad);
for (int i=1; i<=size; i++)
{ phi.set(i, phi.get(i)+alpha*d.get(i) ); }
for (int i=1; i<=size; i++)
{ r.set(i, r.get(i)-alpha*Ad.get(i) ); }
double rdotr_old = rdotr;
rdotr = DotProd(r,r);
rel_res_norm = sqrt(rdotr)/rhs_norm;
if(rel_res_norm < TOL)
{ mflag = 1; }
//printf(" NumIters = %i, rel_res_norm = %e\n",NumIters,rel_res_norm);
if (NumIters==MaxIters)
{ mflag = 1; }
if (mflag==0)
{
double beta = rdotr/rdotr_old;
for (int i=1; i<=size; i++)
{ d.set(i, r.get(i)+beta*d.get(i) ); }
NumIters = NumIters+1;
}
}
printf(" |----------------------------\n");
printf(" | Conjugate Gradient Results:\n");
printf(" |----------------------------\n");
printf(" | MaxIters = %i\n",MaxIters);
printf(" | TOL = %e\n",TOL);
printf(" | NumIters = %i\n",NumIters);
printf(" | residual = %e\n",rel_res_norm);
printf(" |----------------------------\n");
printf("\n");
}
