void ComputeElecField(double t, const dTensor2& node, const dTensorBC3& qvals,
dTensorBC3& aux, dTensorBC3& Evals)
{
void ConvertBC(const dTensor2& node, const int mbc1, const int mbc2,
const double tmp1, const double tmp2, const dTensorBC3& Fvals,
double& gamma, double& beta);
void PoissonSolve(const int mstart, const dTensor2& node,
const double gamma, const double beta,
const dTensorBC3& Fvals, dTensorBC3& qvals);
const int melems = qvals.getsize(1);
const int meqn = qvals.getsize(2);
const int kmax = qvals.getsize(3);
const int mbc = qvals.getmbc();
dTensorBC3 fvals(melems, 1 , kmax, mbc); // right hand side function
// phi(mx,1,kmax1d) = 'electric' field
// phi(mx,2,kmax1d) = potential (not unique!)
dTensorBC3 phi(melems, 2, kmax, mbc); // Electric field and potential
for(int i=1; i<= melems; i++)
for(int k=1; k<=kmax; k++)
{
fvals.set(i, 1, k, qvals.get(i,1,k) - aux.get(i,1,k) );
}
//////////////////////////////////////////////////////////////////////////
// Solve for electric field and potential
//////////////////////////////////////////////////////////////////////////
// periodic boundary conditions: alpha = beta = 0;
// gamma = delta will be forced provided \int f = 0.
double gamma, beta;
ConvertBC(node, 1, 1, 0.0, 0.0, fvals, gamma, beta);
PoissonSolve(1, node, gamma, beta, fvals, phi);
//////////////////////////////////////////////////////////////////////////
// Save results into Evals
//////////////////////////////////////////////////////////////////////////
for(int i = 1; i <= melems; i++ )
for(int k=1; k <= kmax; k++ )
{ Evals.set(i, 1, k, phi.get(i, 1, k) ); }
}// end of Compute Electric Field
void ComputeElecPotential(double t, const dTensor2& node, const dTensorBC3& qvals,
dTensorBC3& aux, dTensorBC3& phi)
{
/////////////////////////////////////////////////////////////////////////
// This function is only ever called in Output.cpp -- the purpose is to
// print the moments for both the electric potential, as well as the
// electric field
/////////////////////////////////////////////////////////////////////////
// --------------------- Function Declarations -------------------------//
void ConvertBC(const dTensor2& node, const int mbc1, const int mbc2,
const double tmp1, const double tmp2, const dTensorBC3& Fvals,
double& gamma, double& beta);
void PoissonSolve(const int mstart, const dTensor2& node,
const double gamma, const double beta,
const dTensorBC3& Fvals, dTensorBC3& qvals);
// --------------------- Function Declarations -------------------------//
// --------------------- Local Variables -------------------------------//
const int melems = qvals.getsize(1);
const int meqn = qvals.getsize(2);
const int kmax = qvals.getsize(3);
const int mbc = qvals.getmbc();
dTensorBC3 fvals(melems, 2 , kmax, mbc, 1); // right hand side function
for(int i=1; i<= melems; i++)
for(int k=1; k<=kmax; k++)
{
double tmp = qvals.get(i,1,k);
fvals.set(i, 1, k, tmp - aux.get(i,1,k) );
}
//////////////////////////////////////////////////////////////////////////
// Solve for electric field and potential
//////////////////////////////////////////////////////////////////////////
// periodic boundary conditions: alpha = beta = 0;
// gamma = delta will be forced provided \int f = 0.
double gamma, beta;
ConvertBC(node, 1, 1, 0.0, 0.0, fvals, gamma, beta);
PoissonSolve(1, node, gamma, beta, fvals, phi);
}
void L2Project_interface(int mopt, int run,int istart, int iend,
const dTensor2& node,
const dTensorBC3& qin,
const dTensorBC3& auxin,
const dTensor4 qI,
const dTensor4 auxI,dTensor4& Implicit,double dt,
const dTensor1 interf2global,
const dTensorBC1 global2interf,
const dTensor2 dxi,
dTensorBC3& Fout,
dTensor4& FI,
void (*Func)(const dTensor1&, const dTensor2&, const dTensor2&, dTensor2&))
{
const int kmax = dogParams.get_space_order();
const int meqn = qin.getsize(2);
const int maux = auxin.getsize(2);
const int mlength = Fout.getsize(2);
const int mpoints = Fout.getsize(3);
int mtmp = iMax(1,6-mopt);//iMax(1,mpoints-mopt);
dTensor1 wgt(mtmp), spts(mtmp),rspts(mtmp),lspts(mtmp);
dTensor2 phi(mtmp,kmax), phi_x(mtmp,kmax), rIphi_x(mtmp,kmax), lIphi_x(mtmp,kmax);
// -----------------
// Quick error check
// -----------------
if (meqn<1 || maux <0 || mpoints<1 || mpoints>6 || mlength<1
|| mopt < 0 || mopt > 1)
{
printf(" Error in L2project.cpp ... \n");
printf(" meqn = %i\n",meqn);
printf(" maux = %i\n",maux);
printf(" mpoints = %i\n",mpoints);
printf(" mlength = %i\n",mlength);
printf(" istart = %i\n",istart);
printf(" iend = %i\n",iend);
printf(" mopts = %i\n",mopt);
printf("\n");
exit(1);
}
// ---------------------------------------------
// Check for trivial case in the case of mopt==1
// ---------------------------------------------
if ( mpoints == mopt )
{ Fout.setall(0.); }
else
{
// Set quadrature weights and points
void SetQuadPts(dTensor1&,dTensor1&);
SetQuadPts(wgt,spts);
// Sample basis function at quadrature points
void SampleBasis(const dTensor1&,dTensor2&);
SampleBasis(spts,phi);
// Sample gradient of basis function at quadrature points
void SampleBasisGrad(const dTensor1&,dTensor2&);
void SampleBasisGrad_variable(const dTensor1&,dTensor2&,double);
SampleBasisGrad(spts,phi_x);
// ----------------------------------
// Loop over all elements of interest
// ----------------------------------
const double xlow = dogParamsCart1.get_xlow();
const double dx = dogParamsCart1.get_dx();
#pragma omp parallel for
for (int i=istart; i<=iend; i++)
{
if(abs(global2interf.get(i))<1.0e-1)
{
double xc = xlow + (double(i)-0.5)*dx;
// Each of these three items needs to be private to each thread ..
dTensor1 xpts(mtmp);
dTensor2 qvals(mtmp,meqn);
dTensor2 auxvals(mtmp,maux);
dTensor2 fvals(mtmp,mlength);
// Loop over each quadrature point
for (int m=1; m<=mtmp; m++)
{
// grid point x
xpts.set( m, xc + 0.5*dx*spts.get(m) );
// Solution values (q) at each grid point
for (int me=1; me<=meqn; me++)
{
qvals.set(m,me, 0.0 );
for (int k=1; k<=mpoints; k++)
{
qvals.set(m,me, qvals.get(m,me)
+ phi.get(m,k) * qin.get(i,me,k) );
}
}
// Auxiliary values (aux) at each grid point
for (int ma=1; ma<=maux; ma++)
{
auxvals.set(m,ma, 0.0 );
for (int k=1; k<=mpoints; k++)
{
auxvals.set(m,ma, auxvals.get(m,ma)
+ phi.get(m,k) * auxin.get(i,ma,k) );
}
}
}
// Call user-supplied function to set fvals
Func(xpts,qvals,auxvals,fvals);
// Evaluate integrals
if (mopt==0) // project onto Legendre basis
{
for (int m1=1; m1<=mlength; m1++)
for (int m2=1; m2<=mpoints; m2++)
{
double tmp = 0.0;
for (int k=1; k<=mtmp; k++)
{
tmp += wgt.get(k)*fvals.get(k,m1)*phi.get(k,m2);
}
Fout.set(i,m1,m2, 0.5*tmp );
}
}
else // project onto derivatives of Legendre basis
{
for (int m1=1; m1<=mlength; m1++)
for (int m2=1; m2<=mpoints; m2++)
{
double tmp = 0.0;
for (int k=1; k<=mtmp; k++)
{
tmp += wgt.get(k)*fvals.get(k,m1)*phi_x.get(k,m2);
}
Fout.set(i,m1,m2, 0.5*tmp );
}
}
}
else if(run==1)
{
int iint=int(global2interf.get(i));
double xc1 = xlow + (double(i)-1.0)*dx+0.5*dxi.get(iint,1);
double xc2 = xlow + (double(i)-1.0)*dx+dxi.get(iint,1)+0.5*dxi.get(iint,2);
double dxl=dxi.get(iint,1);
double dxr=dxi.get(iint,2);
// Each of these three items needs to be private to each thread ..
dTensor1 xptsl(mtmp);
dTensor2 qvalsl(mtmp,meqn);
dTensor2 auxvalsl(mtmp,maux);
dTensor2 fvalsl(mtmp,mlength);
dTensor1 xptsr(mtmp);
dTensor2 qvalsr(mtmp,meqn);
dTensor2 auxvalsr(mtmp,maux);
dTensor2 fvalsr(mtmp,mlength);
//SampleBasisGrad_variable(lspts,lIphi_x,dxl);
//SampleBasisGrad_variable(rspts,rIphi_x,dxr);
//SampleBasisGrad_variable(lspts,lIphi_x,1.0);
//SampleBasisGrad_variable(rspts,rIphi_x,1.0);
SampleBasisGrad_variable(spts,lIphi_x,1.0);
SampleBasisGrad_variable(spts,rIphi_x,1.0);
// Loop over each quadrature point
for (int m=1; m<=mtmp; m++)
{
// grid point x
xptsl.set( m, xc1 + 0.5*dxl*spts.get(m) );
xptsr.set( m, xc2 + 0.5*dxr*spts.get(m) );
// Solution values (q) at each grid point
for (int me=1; me<=meqn; me++)
{
qvalsl.set(m,me, 0.0 );
qvalsr.set(m,me, 0.0 );
for (int k=1; k<=mpoints; k++)
{
qvalsl.set(m,me, qvalsl.get(m,me)
+ phi.get(m,k) * qI.get(1,iint,me,k) );
qvalsr.set(m,me, qvalsr.get(m,me)
+ phi.get(m,k) * qI.get(2,iint,me,k) );
}
}
// Auxiliary values (aux) at each grid point
for (int ma=1; ma<=maux; ma++)
{
auxvalsl.set(m,ma, 0.0 );
auxvalsr.set(m,ma, 0.0 );
for (int k=1; k<=mpoints; k++)
{
auxvalsl.set(m,ma, auxvalsl.get(m,ma)
+ phi.get(m,k) * auxI.get(1,iint,ma,k) );
auxvalsr.set(m,ma, auxvalsr.get(m,ma)
+ phi.get(m,k) * auxI.get(2,iint,ma,k) );
}
}
//printf("xcl=%e xtryl= %e \n",xc1,dxl);
//printf("xcr=%e xtryr= %e \n",xc2,dxr);
}
// Call user-supplied function to set fvals
Func(xptsl,qvalsl,auxvalsl,fvalsl);
Func(xptsr,qvalsr,auxvalsr,fvalsr);
/*
for (int m=1; m<=mtmp; m++)
{
printf("xtryl= %e \n",xptsl.get(m));
printf("xtryr= %e \n",xptsr.get(m));
printf("qtryl= %e \n",qvalsl.get(m,1));
printf("qtryr= %e \n",qvalsr.get(m,1));
}*/
//printf("i=%d iint=%d q= %e %e \n",i,iint,qI.get(1,iint,1,1),qI.get(1,iint,1,2));
//printf("2i=%d iint=%d q= %e %e \n",i,iint,Iq.qget(2,iint,1,1),qI.get(2,iint,1,2));
/*
for (inti m=1; m<=mtmp; m++)
{
printf("Points HERE! %d %e %e %e %e \n",m,xptsl.get(m),fvalsl.get(m,1),xptsr.get(m),fvalsl.get(m,1));
}*/
// Evaluate integrals
if (mopt==0) // project onto Legendre basis
{
for (int m1=1; m1<=mlength; m1++)
for (int m2=1; m2<=mpoints; m2++)
{
double tmpl = 0.0;
double tmpr = 0.0;
for (int k=1; k<=mtmp; k++)
{
tmpl += wgt.get(k)*fvalsl.get(k,m1)*phi.get(k,m2);
tmpr += wgt.get(k)*fvalsr.get(k,m1)*phi.get(k,m2);
}
FI.set(1,iint,m1,m2, 0.5*tmpl );
FI.set(2,iint,m1,m2, 0.5*tmpr );
}
}
else // project onto derivatives of Legendre basis
{
double Ul=auxI.get(1,iint,1,1);
double Ur=auxI.get(2,iint,1,1);
/*
for (int m1=1; m1<=mlength; m1++)
for (int m2=1; m2<=mpoints; m2++)
{
double tmpl = 0.0;
double tmpr = 0.0;
for (int k=1; k<=mtmp; k++)
{
tmpl += wgt.get(k)*fvalsl.get(k,m1)*lIphi_x.get(k,m2);
tmpr += wgt.get(k)*fvalsr.get(k,m1)*rIphi_x.get(k,m2);
}
FI.set(1,iint,m1,m2, 0.5*tmpl );
FI.set(2,iint,m1,m2, 0.5*tmpr );
}*/
for (int m2=1; m2<=mpoints; m2++)
for (int m3=1; m3<=mpoints; m3++)
{
double tmponl = 0.0;
double tmponr = 0.0;
double tmpIl = 0.0;
double tmpIr = 0.0;
for (int k=1; k<=mtmp; k++)
{
tmpIl += wgt.get(k)*Ul*phi.get(k,m3)*lIphi_x.get(k,m2);
tmpIr += wgt.get(k)*Ur*phi.get(k,m3)*rIphi_x.get(k,m2);
tmponl += wgt.get(k)*Ul*phi.get(k,m3)*phi_x.get(k,m2);
tmponr += wgt.get(k)*Ur*phi.get(k,m3)*phi_x.get(k,m2);
}
// Implicit.set(iint,m1,m2,m3, Implicit.get(iint,m1,m2,m3)-0.5*tmpIl );
//Implicit.set(iint,m1,kmax+m2,kmax+m3, Implicit.get(iint,m1,kmax+m2,kmax+m3)-0.5*tmpIr );
//Implicit.set(iint,m1,m2,m3, Implicit.get(iint,m1,m2,m3)+0.5*tmpIl );
//Implicit.set(iint,m1,kmax+m2,kmax+m3, Implicit.get(iint,m1,kmax+m2,kmax+m3)+0.5*tmpIr );
Implicit.set(iint,1,m2,m3, Implicit.get(iint,1,m2,m3)-0.5*tmpIl );
Implicit.set(iint,1,kmax+m2,kmax+m3, Implicit.get(iint,1,kmax+m2,kmax+m3)-0.5*tmpIl );
Implicit.set(iint,1,2*kmax+m2,2*kmax+m3, Implicit.get(iint,1,2*kmax+m2,2*kmax+m3)-0.5*tmpIl );
Implicit.set(iint,1,3*kmax+m2,3*kmax+m3, Implicit.get(iint,1,3*kmax+m2,3*kmax+m3)-0.5*tmpIr );
Implicit.set(iint,1,4*kmax+m2,4*kmax+m3, Implicit.get(iint,1,4*kmax+m2,4*kmax+m3)-0.5*tmpIr );
Implicit.set(iint,1,5*kmax+m2,5*kmax+m3, Implicit.get(iint,1,5*kmax+m2,5*kmax+m3)-0.5*tmpIr );
//if(abs(tmpIl)>1.0e-12 || abs(tmpIr)>1.0e-12)
//{printf("HERE2!!!! %e %e \n",0.5*tmpIl,0.5*tmpIr);}
}
/*
for(int m2=1;m2<=mpoints;m2++)
{
double tmp1=0.0;
double tmp2=0.0;
for (int m3=1;m3<=mpoints;m3++)
{
double tmpIl = 0.0;
double tmpIr = 0.0;
for (int k=1; k<=mtmp; k++)
{
tmpIl += wgt.get(k)*Ul*phi.get(k,m3)*lIphi_x.get(k,m2);
tmpIr += wgt.get(k)*Ur*phi.get(k,m3)*rIphi_x.get(k,m2);
}
tmp1=tmp1+0.5*tmpIl*qI.get(1,iint,1,m3);
tmp2=tmp2+0.5*tmpIr*qI.get(2,iint,1,m3);
}
//printf("HERE left! %e \n",tmp1-FI.get(1,1,1,m2));
//printf("HERE right! %e \n",tmp2-FI.get(2,1,1,m2));
}*/
}
}
}
}
}
static int trim_ns(bam1_t *b, void *data) {
int ret = 0;
opts_t *op((opts_t *)data);
std::vector<uint8_t> aux(bam_get_aux(b), bam_get_aux(b) + bam_get_l_aux(b));
int tmp;
uint8_t *const seq(bam_get_seq(b));
uint32_t *const cigar(bam_get_cigar(b));
//op->n_cigar = b->core.n_cigar;
op->resize(b->l_data); // Make sure it's big enough to hold everything.
memcpy(op->data, b->data, b->core.l_qname);
// Get #Ns at the beginning
for(tmp = 0; bam_seqi(seq, tmp) == dlib::htseq::HTS_N; ++tmp);
const int n_start(tmp);
if(tmp == b->core.l_qseq - 1) // all bases are N -- garbage read
ret |= op->skip_all_ns;
// Get #Ns at the end
for(tmp = b->core.l_qseq - 1; bam_seqi(seq, tmp) == dlib::htseq::HTS_N; --tmp);
const int n_end(b->core.l_qseq - 1 - tmp);
// Get new length for read
int final_len(b->core.l_qseq - n_end - n_start);
if(final_len < 0) final_len = 0;
if(final_len < op->min_trimmed_len) // Too short.
ret |= 1;
// Copy in qual and all of aux.
if(n_end) {
if((tmp = bam_cigar_oplen(cigar[b->core.n_cigar - 1]) - n_end) == 0) {
LOG_DEBUG("Entire cigar operation is the softclip. Decrease the number of new cigar operations.\n");
--b->core.n_cigar;
} else {
LOG_DEBUG("Updating second cigar operation in-place.\n");
cigar[b->core.n_cigar - 1] = bam_cigar_gen(tmp, BAM_CSOFT_CLIP);
}
}
// Get new n_cigar.
if((tmp = bam_cigar_oplen(*cigar) - n_start) == 0) {
memcpy(op->data + b->core.l_qname, cigar + 1, (--b->core.n_cigar) << 2); // << 2 for 4 bit per cigar op
} else {
if(n_start) *cigar = bam_cigar_gen(tmp, BAM_CSOFT_CLIP);
memcpy(op->data + b->core.l_qname, cigar, b->core.n_cigar << 2);
}
uint8_t *opseq(op->data + b->core.l_qname + (b->core.n_cigar << 2)); // Pointer to the seq region of new data field.
for(tmp = 0; tmp < final_len >> 1; ++tmp)
opseq[tmp] = (bam_seqi(seq, ((tmp << 1) + n_start)) << 4) | (bam_seqi(seq, (tmp << 1) + n_start + 1));
if(final_len & 1)
opseq[tmp] = (bam_seqi(seq, ((tmp << 1) + n_start)) << 4);
tmp = bam_get_l_aux(b);
memcpy(opseq + ((final_len + 1) >> 1), bam_get_qual(b) + n_start, final_len + tmp);
// Switch data strings
std::swap(op->data, b->data);
b->core.l_qseq = final_len;
memcpy(bam_get_aux(b), aux.data(), aux.size());
b->l_data = (bam_get_aux(b) - b->data) + aux.size();
if(n_end) bam_aux_append(b, "NE", 'i', sizeof(int), (uint8_t *)&n_end);
if(n_start) bam_aux_append(b, "NS", 'i', sizeof(int), (uint8_t *)&n_start);
const uint32_t *pvar((uint32_t *)dlib::array_tag(b, "PV"));
tmp = b->core.flag & BAM_FREVERSE ? n_end: n_start;
if(pvar) {
std::vector<uint32_t>pvals(pvar + tmp, pvar + final_len + tmp);
bam_aux_del(b, (uint8_t *)(pvar) - 6);
dlib::bam_aux_array_append(b, "PV", 'I', sizeof(uint32_t), final_len, (uint8_t *)pvals.data());
}
const uint32_t *fvar((uint32_t *)dlib::array_tag(b, "FA"));
if(fvar) {
std::vector<uint32_t>fvals(fvar + tmp, fvar + final_len + tmp);
bam_aux_del(b, (uint8_t *)(fvar) - 6);
dlib::bam_aux_array_append(b, "FA", 'I', sizeof(uint32_t), final_len, (uint8_t *)fvals.data());
}
return ret;
}
// All-purpose routine for computing the L2-projection
// of various functions onto the gradient of the Legendre basis
// (Unstructured grid version)
//
void L2ProjectGrad_Unst(
const dTensor2* vel_vec,
const int istart,
const int iend,
const int QuadOrder,
const int BasisOrder_qin,
const int BasisOrder_auxin,
const int BasisOrder_fout,
const mesh& Mesh,
const dTensor3* qin,
const dTensor3* auxin,
dTensor3* fout,
void (*Func)(const dTensor2* vel_vec,
const dTensor2&,const dTensor2&,
const dTensor2&,dTensor3&))
{
// starting and ending indeces
const int NumElems = Mesh.get_NumElems();
assert_ge(istart,1);
assert_le(iend,NumElems);
// qin variable
assert_eq(NumElems,qin->getsize(1));
const int meqn = qin->getsize(2);
const int kmax_qin = qin->getsize(3);
assert_eq(kmax_qin,(BasisOrder_qin*(BasisOrder_qin+1))/2);
// auxin variable
assert_eq(NumElems,auxin->getsize(1));
const int maux = auxin->getsize(2);
const int kmax_auxin = auxin->getsize(3);
assert_eq(kmax_auxin,(BasisOrder_auxin*(BasisOrder_auxin+1))/2);
// fout variables
assert_eq(NumElems,fout->getsize(1));
const int mcomps_out = fout->getsize(2);
const int kmax_fout = fout->getsize(3);
assert_eq(kmax_fout,(BasisOrder_fout*(BasisOrder_fout+1))/2);
// number of quadrature points
assert_ge(QuadOrder,1);
assert_le(QuadOrder,5);
int mpoints;
switch ( QuadOrder )
{
case 1:
mpoints = 0;
break;
case 2:
mpoints = 1;
break;
case 3:
mpoints = 6;
break;
case 4:
mpoints = 7;
break;
case 5:
mpoints = 16;
break;
}
// trivial case
if ( QuadOrder==1 )
{
for (int i=istart; i<=iend; i++)
for (int m=1; m<=mcomps_out; m++)
for (int k=1; k<=kmax_fout; k++)
{ fout->set(i,m,k, 0.0 ); }
}
else
{
const int kmax = iMax(iMax(kmax_qin,kmax_auxin),kmax_fout);
dTensor2 spts(mpoints,2);
dTensor1 wgts(mpoints);
dTensor2 xpts(mpoints,2);
dTensor2 qvals(mpoints,meqn);
dTensor2 auxvals(mpoints,maux);
dTensor3 fvals(mpoints,mcomps_out,2);
dTensor2 mu(mpoints,kmax); // monomial basis (non-orthogonal)
dTensor2 phi(mpoints,kmax); // Legendre basis (orthogonal)
dTensor2 mu_xi(mpoints,kmax_fout); // xi-derivative of monomial basis (non-orthogonal)
dTensor2 mu_eta(mpoints,kmax_fout); // eta-derivative of monomial basis (non-orthogonal)
dTensor2 phi_xi(mpoints,kmax_fout); // xi-derivative of Legendre basis (orthogonal)
dTensor2 phi_eta(mpoints,kmax_fout); // eta-derivative of Legendre basis (orthogonal)
dTensor2 phi_x(mpoints,kmax_fout); // x-derivative of Legendre basis (orthogonal)
dTensor2 phi_y(mpoints,kmax_fout); // y-derivative of Legendre basis (orthogonal)
switch ( QuadOrder )
{
case 2:
spts.set(1,1, 0.0 );
spts.set(1,2, 0.0 );
wgts.set(1, 0.5 );
break;
case 3:
spts.set(1,1, 0.112615157582632 );
spts.set(1,2, 0.112615157582632 );
spts.set(2,1, -0.225230315165263 );
spts.set(2,2, 0.112615157582632 );
spts.set(3,1, 0.112615157582632 );
spts.set(3,2, -0.225230315165263 );
spts.set(4,1, -0.241757119823562 );
spts.set(4,2, -0.241757119823562 );
spts.set(5,1, 0.483514239647126 );
spts.set(5,2, -0.241757119823562 );
spts.set(6,1, -0.241757119823562 );
spts.set(6,2, 0.483514239647126 );
wgts.set(1, 0.1116907948390055 );
wgts.set(2, 0.1116907948390055 );
wgts.set(3, 0.1116907948390055 );
wgts.set(4, 0.0549758718276610 );
wgts.set(5, 0.0549758718276610 );
wgts.set(6, 0.0549758718276610 );
break;
case 4:
spts.set(1,1, 0.000000000000000 );
spts.set(1,2, 0.000000000000000 );
spts.set(2,1, 0.136808730771782 );
spts.set(2,2, 0.136808730771782 );
spts.set(3,1, -0.273617461543563 );
spts.set(3,2, 0.136808730771782 );
spts.set(4,1, 0.136808730771782 );
spts.set(4,2, -0.273617461543563 );
spts.set(5,1, -0.232046826009877 );
spts.set(5,2, -0.232046826009877 );
spts.set(6,1, 0.464093652019754 );
spts.set(6,2, -0.232046826009877 );
spts.set(7,1, -0.232046826009877 );
spts.set(7,2, 0.464093652019754 );
wgts.set(1, 0.1125000000000000 );
wgts.set(2, 0.0661970763942530 );
wgts.set(3, 0.0661970763942530 );
wgts.set(4, 0.0661970763942530 );
wgts.set(5, 0.0629695902724135 );
wgts.set(6, 0.0629695902724135 );
wgts.set(7, 0.0629695902724135 );
break;
case 5:
spts.set(1,1, 0.000000000000000 );
spts.set(1,2, 0.000000000000000 );
spts.set(2,1, 0.125959254959390 );
spts.set(2,2, 0.125959254959390 );
spts.set(3,1, -0.251918509918779 );
spts.set(3,2, 0.125959254959390 );
spts.set(4,1, 0.125959254959390 );
spts.set(4,2, -0.251918509918779 );
spts.set(5,1, -0.162764025581573 );
spts.set(5,2, -0.162764025581573 );
spts.set(6,1, 0.325528051163147 );
spts.set(6,2, -0.162764025581573 );
spts.set(7,1, -0.162764025581573 );
spts.set(7,2, 0.325528051163147 );
spts.set(8,1, -0.282786105016302 );
spts.set(8,2, -0.282786105016302 );
spts.set(9,1, 0.565572210032605 );
spts.set(9,2, -0.282786105016302 );
spts.set(10,1, -0.282786105016302 );
spts.set(10,2, 0.565572210032605 );
spts.set(11,1, -0.324938555923375 );
spts.set(11,2, -0.070220503698695 );
spts.set(12,1, -0.324938555923375 );
spts.set(12,2, 0.395159059622071 );
spts.set(13,1, -0.070220503698695 );
spts.set(13,2, -0.324938555923375 );
spts.set(14,1, -0.070220503698695 );
spts.set(14,2, 0.395159059622071 );
spts.set(15,1, 0.395159059622071 );
spts.set(15,2, -0.324938555923375 );
spts.set(16,1, 0.395159059622071 );
spts.set(16,2, -0.070220503698695 );
wgts.set(1, 0.0721578038388935 );
wgts.set(2, 0.0475458171336425 );
wgts.set(3, 0.0475458171336425 );
wgts.set(4, 0.0475458171336425 );
wgts.set(5, 0.0516086852673590 );
wgts.set(6, 0.0516086852673590 );
wgts.set(7, 0.0516086852673590 );
wgts.set(8, 0.0162292488115990 );
wgts.set(9, 0.0162292488115990 );
wgts.set(10, 0.0162292488115990 );
wgts.set(11, 0.0136151570872175 );
wgts.set(12, 0.0136151570872175 );
wgts.set(13, 0.0136151570872175 );
wgts.set(14, 0.0136151570872175 );
wgts.set(15, 0.0136151570872175 );
wgts.set(16, 0.0136151570872175 );
break;
}
// Loop over each quadrature point and construct monomial polys
for (int m=1; m<=mpoints; m++)
{
// coordinates
const double xi = spts.get(m,1);
const double xi2 = xi*xi;
const double xi3 = xi2*xi;
const double xi4 = xi3*xi;
const double eta = spts.get(m,2);
const double eta2 = eta*eta;
const double eta3 = eta2*eta;
const double eta4 = eta3*eta;
// monomial basis functions at each gaussian quadrature point
switch( kmax )
{
case 15: // fifth order
mu.set(m, 15, eta4 );
mu.set(m, 14, xi4 );
mu.set(m, 13, xi2*eta2 );
mu.set(m, 12, eta3*xi );
mu.set(m, 11, xi3*eta );
case 10: // fourth order
mu.set(m, 10, eta3 );
mu.set(m, 9, xi3 );
mu.set(m, 8, xi*eta2 );
mu.set(m, 7, eta*xi2 );
case 6: // third order
mu.set(m, 6, eta2 );
mu.set(m, 5, xi2 );
mu.set(m, 4, xi*eta );
case 3: // second order
mu.set(m, 3, eta );
mu.set(m, 2, xi );
case 1: // first order
mu.set(m, 1, 1.0 );
break;
}
// Loop over each quadrature point and construct Legendre polys
for (int i=1; i<=kmax; i++)
{
double tmp = 0.0;
for (int j=1; j<=i; j++)
{ tmp = tmp + Mmat[i-1][j-1]*mu.get(m,j); }
phi.set(m,i, tmp );
}
// Gradient of monomial basis functions at each gaussian quadrature point
switch( kmax_fout )
{
case 15: // fifth order
mu_xi.set( m,15, 0.0 );
mu_xi.set( m,14, 4.0*xi3 );
mu_xi.set( m,13, 2.0*xi*eta2 );
mu_xi.set( m,12, eta3 );
mu_xi.set( m,11, 3.0*xi2*eta );
mu_eta.set( m,15, 4.0*eta3 );
mu_eta.set( m,14, 0.0 );
mu_eta.set( m,13, 2.0*xi2*eta );
mu_eta.set( m,12, 3.0*eta2*xi );
mu_eta.set( m,11, xi3 );
case 10: // fourth order
mu_xi.set( m,10, 0.0 );
mu_xi.set( m,9, 3.0*xi2 );
mu_xi.set( m,8, eta2 );
mu_xi.set( m,7, 2.0*eta*xi );
mu_eta.set( m,10, 3.0*eta2 );
mu_eta.set( m,9, 0.0 );
mu_eta.set( m,8, 2.0*eta*xi );
mu_eta.set( m,7, xi2 );
case 6: // third order
mu_xi.set( m,6, 0.0 );
mu_xi.set( m,5, 2.0*xi );
mu_xi.set( m,4, eta );
mu_eta.set( m,6, 2.0*eta );
mu_eta.set( m,5, 0.0 );
mu_eta.set( m,4, xi );
case 3: // second order
mu_xi.set( m,3, 0.0 );
mu_xi.set( m,2, 1.0 );
mu_eta.set( m,3, 1.0 );
mu_eta.set( m,2, 0.0 );
case 1: // first order
mu_xi.set( m,1, 0.0 );
mu_eta.set( m,1, 0.0 );
break;
}
// Loop over each quadrature point and construct Legendre polys
for (int i=1; i<=kmax_fout; i++)
{
double tmp1 = 0.0;
double tmp2 = 0.0;
for (int j=1; j<=i; j++)
{
tmp1 = tmp1 + Mmat[i-1][j-1]*mu_xi.get(m,j);
tmp2 = tmp2 + Mmat[i-1][j-1]*mu_eta.get(m,j);
}
phi_xi.set(m,i, tmp1 );
phi_eta.set(m,i, tmp2 );
}
}
// -------------------------------------------------------------
// Loop over every grid cell indexed by user supplied parameters
// described by istart...iend
// -------------------------------------------------------------
#pragma omp parallel for
for (int i=istart; i<=iend; i++)
{
// Find center of current cell
const int i1 = Mesh.get_tnode(i,1);
const int i2 = Mesh.get_tnode(i,2);
const int i3 = Mesh.get_tnode(i,3);
const double x1 = Mesh.get_node(i1,1);
const double y1 = Mesh.get_node(i1,2);
const double x2 = Mesh.get_node(i2,1);
const double y2 = Mesh.get_node(i2,2);
const double x3 = Mesh.get_node(i3,1);
const double y3 = Mesh.get_node(i3,2);
const double xc = (x1+x2+x3)/3.0;
const double yc = (y1+y2+y3)/3.0;
// Compute q, aux and fvals at each Gaussian Quadrature point
// for this current cell indexed by (i,j)
// Save results into dTensor2 qvals, auxvals and fvals.
for (int m=1; m<=mpoints; m++)
{
// convert phi_xi and phi_eta derivatives
// to phi_x and phi_y derivatives through Jacobian
for (int k=1; k<=kmax_fout; k++)
{
phi_x.set(m,k, Mesh.get_jmat(i,1,1)*phi_xi.get(m,k)
+ Mesh.get_jmat(i,1,2)*phi_eta.get(m,k) );
phi_y.set(m,k, Mesh.get_jmat(i,2,1)*phi_xi.get(m,k)
+ Mesh.get_jmat(i,2,2)*phi_eta.get(m,k) );
}
// point on the unit triangle
const double s = spts.get(m,1);
const double t = spts.get(m,2);
// point on the physical triangle
xpts.set(m,1, xc + (x2-x1)*s + (x3-x1)*t );
xpts.set(m,2, yc + (y2-y1)*s + (y3-y1)*t );
// Solution values (q) at each grid point
for (int me=1; me<=meqn; me++)
{
qvals.set(m,me, 0.0 );
for (int k=1; k<=kmax_qin; k++)
{
qvals.set(m,me, qvals.get(m,me)
+ phi.get(m,k) * qin->get(i,me,k) );
}
}
// Auxiliary values (aux) at each grid point
for (int ma=1; ma<=maux; ma++)
{
auxvals.set(m,ma, 0.0 );
for (int k=1; k<=kmax_auxin; k++)
{
auxvals.set(m,ma, auxvals.get(m,ma)
+ phi.get(m,k) * auxin->get(i,ma,k) );
}
}
}
// Call user-supplied function to set fvals
Func(vel_vec, xpts, qvals, auxvals, fvals);
// Evaluate integral on current cell (project onto Legendre basis)
// using Gaussian Quadrature for the integration
for (int m1=1; m1<=mcomps_out; m1++)
for (int m2=1; m2<=kmax_fout; m2++)
{
double tmp = 0.0;
for (int k=1; k<=mpoints; k++)
{
tmp = tmp + wgts.get(k)*
( fvals.get(k,m1,1)*phi_x.get(k,m2) +
fvals.get(k,m1,2)*phi_y.get(k,m2) );
}
fout->set(i, m1, m2, 2.0*tmp );
}
}
}
}
// Modified version of the all purpose routine L2Project specifically written
// for projecting the "time-averaged" flux function onto the basis function.
//
// This routine also returns the coefficients of the Lax Wendroff Flux
// Function when expanded with legendre basis functions, and therefore the
// basis expansions produced by this routine can be used for all of the
// Riemann solves.
//
// ---------------------------------------------------------------------
// Inputs should have the following sizes:
// TODO - document the inputs here
// ---------------------------------------------------------------------
void L2ProjectLxW_Unst( const int mterms,
const double alpha, const double beta_dt, const double charlie_dt,
const int istart, const int iend, // Start-stop indices
const int QuadOrder,
const int BasisOrder_qin,
const int BasisOrder_auxin,
const int BasisOrder_fout,
const mesh& Mesh,
const dTensor3* qin, const dTensor3* auxin, // state vector
dTensor3* F, dTensor3* G, // time-averaged Flux function
void FluxFunc (const dTensor2& xpts,
const dTensor2& Q, const dTensor2& Aux, dTensor3& flux),
void DFluxFunc (const dTensor2& xpts,
const dTensor2& Q, const dTensor2& aux, dTensor4& Dflux),
void D2FluxFunc (const dTensor2& xpts,
const dTensor2& Q, const dTensor2& aux, dTensor5& D2flux) )
{
if( fabs( alpha ) < 1e-14 && fabs( beta_dt ) < 1e-14 && fabs( charlie_dt ) < 1e-14 )
{
F->setall(0.);
G->setall(0.);
return;
}
// starting and ending indices
const int NumElems = Mesh.get_NumElems();
assert_ge(istart,1);
assert_le(iend,NumElems);
// qin variable
assert_eq(NumElems,qin->getsize(1));
const int meqn = qin->getsize(2);
const int kmax_qin = qin->getsize(3);
assert_eq(kmax_qin,(BasisOrder_qin*(BasisOrder_qin+1))/2);
// auxin variable
assert_eq(NumElems,auxin->getsize(1));
const int maux = auxin->getsize(2);
const int kmax_auxin = auxin->getsize(3);
assert_eq(kmax_auxin,(BasisOrder_auxin*(BasisOrder_auxin+1))/2);
// fout variables
assert_eq(NumElems, F->getsize(1));
const int mcomps_out = F->getsize(2);
const int kmax_fout = F->getsize(3);
assert_eq(kmax_fout, (BasisOrder_fout*(BasisOrder_fout+1))/2 );
// number of quadrature points
assert_ge(QuadOrder, 1);
assert_le(QuadOrder, 5);
// Number of quadrature points
int mpoints;
switch( QuadOrder )
{
case 1:
mpoints = 1;
break;
case 2:
mpoints = 3;
break;
case 3:
mpoints = 6;
break;
case 4:
mpoints = 12;
break;
case 5:
mpoints = 16;
break;
}
const int kmax = iMax(iMax(kmax_qin, kmax_auxin), kmax_fout);
dTensor2 phi(mpoints, kmax); // Legendre basis (orthogonal)
dTensor2 spts(mpoints, 2); // List of quadrature points
dTensor1 wgts(mpoints); // List of quadrature weights
setQuadPoints_Unst( QuadOrder, wgts, spts );
// ---------------------------------------------------------------------- //
// Evaluate the basis functions at each point
SetLegendreAtPoints_Unst(spts, phi);
// ---------------------------------------------------------------------- //
// ---------------------------------------------------------------------- //
// First-order derivatives
dTensor2 phi_xi (mpoints, kmax );
dTensor2 phi_eta(mpoints, kmax );
SetLegendreGrad_Unst( spts, phi_xi, phi_eta );
// ---------------------------------------------------------------------- //
// ---------------------------------------------------------------------- //
// Second-order derivatives
dTensor2 phi_xi2 (mpoints, kmax );
dTensor2 phi_xieta(mpoints, kmax );
dTensor2 phi_eta2 (mpoints, kmax );
LegendreDiff2_Unst(spts, &phi_xi2, &phi_xieta, &phi_eta2 );
// ---------------------------------------------------------------------- //
// ------------------------------------------------------------- //
// Loop over every grid cell indexed by user supplied parameters //
// described by istart...iend, jstart...jend //
// ------------------------------------------------------------- //
#pragma omp parallel for
for (int i=istart; i<=iend; i++)
{
// These need to be defined locally. Each mesh element carries its
// own change of basis matrix, so these need to be recomputed for
// each element. The canonical derivatives, phi_xi, and phi_eta can
// be computed and shared for each element.
// First-order derivatives
dTensor2 phi_x(mpoints, kmax_fout); // x-derivative of Legendre basis (orthogonal)
dTensor2 phi_y(mpoints, kmax_fout); // y-derivative of Legendre basis (orthogonal)
// Second-order derivatives
dTensor2 phi_xx(mpoints, kmax_fout); // xx-derivative of Legendre basis (orthogonal)
dTensor2 phi_xy(mpoints, kmax_fout); // xy-derivative of Legendre basis (orthogonal)
dTensor2 phi_yy(mpoints, kmax_fout); // yy-derivative of Legendre basis (orthogonal)
//find center of current cell
const int i1 = Mesh.get_tnode(i,1);
const int i2 = Mesh.get_tnode(i,2);
const int i3 = Mesh.get_tnode(i,3);
// Corners:
const double x1 = Mesh.get_node(i1,1);
const double y1 = Mesh.get_node(i1,2);
const double x2 = Mesh.get_node(i2,1);
const double y2 = Mesh.get_node(i2,2);
const double x3 = Mesh.get_node(i3,1);
const double y3 = Mesh.get_node(i3,2);
// Center of current cell:
const double xc = (x1+x2+x3)/3.0;
const double yc = (y1+y2+y3)/3.0;
// Variables that need to be written to, and therefore are
// created for each thread
dTensor2 xpts (mpoints, 2);
dTensor2 qvals (mpoints, meqn);
dTensor2 auxvals(mpoints, maux);
// local storage for Flux function its Jacobian, and the Hessian:
dTensor3 fvals(mpoints, meqn, 2); // flux function (vector)
dTensor4 A(mpoints, meqn, meqn, 2); // Jacobian of flux
dTensor5 H(mpoints, meqn, meqn, meqn, 2); // Hessian of flux
// Compute q, aux and fvals at each Gaussian Quadrature point
// for this current cell indexed by (i,j)
// Save results into dTensor2 qvals, auxvals and fvals.
for (int m=1; m<= mpoints; m++)
{
// convert phi_xi and phi_eta derivatives
// to phi_x and phi_y derivatives through Jacobian
//
// Note that:
//
// pd_x = J11 pd_xi + J12 pd_eta and
// pd_y = J21 pd_xi + J22 pd_eta.
//
// Squaring these operators yields the second derivatives.
for (int k=1; k<=kmax_fout; k++)
{
phi_x.set(m,k, Mesh.get_jmat(i,1,1)*phi_xi.get(m,k)
+ Mesh.get_jmat(i,1,2)*phi_eta.get(m,k) );
phi_y.set(m,k, Mesh.get_jmat(i,2,1)*phi_xi.get(m,k)
+ Mesh.get_jmat(i,2,2)*phi_eta.get(m,k) );
phi_xx.set(m,k, Mesh.get_jmat(i,1,1)*Mesh.get_jmat(i,1,1)*phi_xi2.get(m,k)
+ Mesh.get_jmat(i,1,1)*Mesh.get_jmat(i,1,2)*phi_xieta.get(m,k)
+ Mesh.get_jmat(i,1,2)*Mesh.get_jmat(i,1,2)*phi_eta2.get(m,k)
);
phi_xy.set(m,k, Mesh.get_jmat(i,1,1)*Mesh.get_jmat(i,2,1)*phi_xi2.get(m,k)
+(Mesh.get_jmat(i,1,2)*Mesh.get_jmat(i,2,1)
+ Mesh.get_jmat(i,1,1)*Mesh.get_jmat(i,2,2))*phi_xieta.get(m,k)
+ Mesh.get_jmat(i,1,2)*Mesh.get_jmat(i,2,2)*phi_eta2.get(m,k)
);
phi_yy.set(m,k, Mesh.get_jmat(i,2,1)*Mesh.get_jmat(i,2,1)*phi_xi2.get(m,k)
+ Mesh.get_jmat(i,2,1)*Mesh.get_jmat(i,2,2)*phi_xieta.get(m,k)
+ Mesh.get_jmat(i,2,2)*Mesh.get_jmat(i,2,2)*phi_eta2.get(m,k)
);
}
// point on the unit triangle
const double s = spts.get(m,1);
const double t = spts.get(m,2);
// point on the physical triangle
xpts.set(m,1, xc + (x2-x1)*s + (x3-x1)*t );
xpts.set(m,2, yc + (y2-y1)*s + (y3-y1)*t );
// Solution values (q) at each grid point
for (int me=1; me<=meqn; me++)
{
qvals.set(m,me, 0.0 );
for (int k=1; k<=kmax_qin; k++)
{
qvals.set(m,me, qvals.get(m,me)
+ phi.get(m,k) * qin->get(i,me,k) );
}
}
// Auxiliary values (aux) at each grid point
for (int ma=1; ma<=maux; ma++)
{
auxvals.set(m,ma, 0.0 );
for (int k=1; k<=kmax_auxin; k++)
{
auxvals.set(m,ma, auxvals.get(m,ma)
+ phi.get(m,k) * auxin->get(i,ma,k) );
}
}
}
// ----------------------------------------------------------------- //
//
// Part I:
//
// Project the flux function onto the basis
// functions. This is the term of order O( 1 ) in the
// "time-averaged" Taylor expansion of f and g.
//
// ----------------------------------------------------------------- //
// Call user-supplied function to set fvals
FluxFunc(xpts, qvals, auxvals, fvals);
// Evaluate integral on current cell (project onto Legendre basis)
// using Gaussian Quadrature for the integration
//
// TODO - do we want to optimize this by looking into using transposes,
// as has been done in the 2d/cart code? (5/14/2014) -DS
for (int me=1; me<=mcomps_out; me++)
for (int k=1; k<=kmax; k++)
{
double tmp1 = 0.0;
double tmp2 = 0.0;
for (int mp=1; mp <= mpoints; mp++)
{
tmp1 += wgts.get(mp)*fvals.get(mp, me, 1)*phi.get(mp, k);
tmp2 += wgts.get(mp)*fvals.get(mp, me, 2)*phi.get(mp, k);
}
F->set(i, me, k, 2.0*tmp1 );
G->set(i, me, k, 2.0*tmp2 );
}
// ----------------------------------------------------------------- //
//
// Part II:
//
// Project the derivative of the flux function onto the basis
// functions. This is the term of order O( \dt ) in the
// "time-averaged" Taylor expansion of f and g.
//
// ----------------------------------------------------------------- //
// ----------------------------------------------------------------- //
// Compute pointwise values for fx+gy:
//
// We can't multiply fvals of f, and g,
// by alpha, otherwise we compute the wrong derivative here!
//
dTensor2 fx_plus_gy( mpoints, meqn ); fx_plus_gy.setall(0.);
for( int mp=1; mp <= mpoints; mp++ )
for( int me=1; me <= meqn; me++ )
{
double tmp = 0.;
for( int k=2; k <= kmax; k++ )
{
tmp += F->get( i, me, k ) * phi_x.get( mp, k );
tmp += G->get( i, me, k ) * phi_y.get( mp, k );
}
fx_plus_gy.set( mp, me, tmp );
}
// Call user-supplied Jacobian to set f'(q) and g'(q):
DFluxFunc( xpts, qvals, auxvals, A );
// place-holders for point values of
// f'(q)( fx + gy ) and g'(q)( fx + gy ):
dTensor2 dt_times_fdot( mpoints, meqn );
dTensor2 dt_times_gdot( mpoints, meqn );
// Compute point values for f'(q) * (fx+gy) and g'(q) * (fx+gy):
for( int mp=1; mp <= mpoints; mp++ )
for( int m1=1; m1 <= meqn; m1++ )
{
double tmp1 = 0.;
double tmp2 = 0.;
for( int m2=1; m2 <= meqn; m2++ )
{
tmp1 += A.get(mp, m1, m2, 1 ) * fx_plus_gy.get(mp, m2);
tmp2 += A.get(mp, m1, m2, 2 ) * fx_plus_gy.get(mp, m2);
}
dt_times_fdot.set( mp, m1, -beta_dt*tmp1 );
dt_times_gdot.set( mp, m1, -beta_dt*tmp2 );
}
// --- Third-order terms --- //
//
// These are the terms that are O( \dt^2 ) in the "time-averaged"
// flux function.
dTensor2 f_tt( mpoints, meqn ); f_tt.setall(0.);
dTensor2 g_tt( mpoints, meqn ); g_tt.setall(0.);
if( mterms > 2 )
{
// Construct the Hessian at each (quadrature) point
D2FluxFunc( xpts, qvals, auxvals, H );
// Second-order derivative terms
dTensor2 qx_vals (mpoints, meqn); qx_vals.setall(0.);
dTensor2 qy_vals (mpoints, meqn); qy_vals.setall(0.);
dTensor2 fxx_vals(mpoints, meqn); fxx_vals.setall(0.);
dTensor2 gxx_vals(mpoints, meqn); gxx_vals.setall(0.);
dTensor2 fxy_vals(mpoints, meqn); fxy_vals.setall(0.);
dTensor2 gxy_vals(mpoints, meqn); gxy_vals.setall(0.);
dTensor2 fyy_vals(mpoints, meqn); fyy_vals.setall(0.);
dTensor2 gyy_vals(mpoints, meqn); gyy_vals.setall(0.);
for( int m=1; m <= mpoints; m++ )
for( int me=1; me <= meqn; me++ )
{
// Can start at k=1, because derivative of a constant is
// zero.
double tmp_qx = 0.;
double tmp_qy = 0.;
for( int k=2; k <= kmax; k++ )
{
tmp_qx += phi_x.get(m,k) * qin->get(i,me,k);
tmp_qy += phi_y.get(m,k) * qin->get(i,me,k);
}
qx_vals.set(m,me, tmp_qx );
qy_vals.set(m,me, tmp_qy );
// First non-zero terms start at third-order.
for( int k=4; k <= kmax; k++ )
{
fxx_vals.set(m,me, fxx_vals.get(m,me) + phi_xx.get(m,k)*F->get(i,me,k) );
gxx_vals.set(m,me, gxx_vals.get(m,me) + phi_xx.get(m,k)*G->get(i,me,k) );
fxy_vals.set(m,me, fxy_vals.get(m,me) + phi_xy.get(m,k)*F->get(i,me,k) );
gxy_vals.set(m,me, gxy_vals.get(m,me) + phi_xy.get(m,k)*G->get(i,me,k) );
fyy_vals.set(m,me, fyy_vals.get(m,me) + phi_yy.get(m,k)*F->get(i,me,k) );
gyy_vals.set(m,me, gyy_vals.get(m,me) + phi_yy.get(m,k)*G->get(i,me,k) );
}
}
// ----------------------------------- //
// Part I: Compute (f_x + g_y)_{,t}
// ----------------------------------- //
// Compute terms that get multiplied by \pd2{ f }{ q } and \pd2{ g }{ q }.
dTensor2 fx_plus_gy_t( mpoints, meqn );
for( int m = 1; m <= mpoints; m++ )
for( int me = 1; me <= meqn; me++ )
{
double tmp = 0.;
// Terms that get multiplied by the Hessian:
for( int m1=1; m1 <= meqn; m1++ )
for( int m2=1; m2 <= meqn; m2++ )
{
tmp += H.get(m,me,m1,m2,1)*qx_vals.get(m,m1)*fx_plus_gy.get(m,m2);
tmp += H.get(m,me,m1,m2,2)*qy_vals.get(m,m1)*fx_plus_gy.get(m,m2);
}
// Terms that get multiplied by f'(q) and g'(q):
for( int m1=1; m1 <= meqn; m1++ )
{
tmp += A.get(m,me,m1,1)*( fxx_vals.get(m,m1)+gxy_vals.get(m,m1) );
tmp += A.get(m,me,m1,2)*( fxy_vals.get(m,m1)+gyy_vals.get(m,m1) );
}
fx_plus_gy_t.set( m, me, tmp );
}
// ----------------------------------- //
// Part II: Compute
// f'(q) * fx_plus_gy_t and
// g'(q) * fx_plus_gy_t
// ----------------------------------- //
// Add in the third term that gets multiplied by A:
for( int m=1; m <= mpoints; m++ )
for( int m1=1; m1 <= meqn; m1++ )
{
double tmp1 = 0.;
double tmp2 = 0.;
for( int m2=1; m2 <= meqn; m2++ )
{
tmp1 += A.get(m,m1,m2,1)*fx_plus_gy_t.get(m,m2);
tmp2 += A.get(m,m1,m2,2)*fx_plus_gy_t.get(m,m2);
}
f_tt.set( m, m1, tmp1 );
g_tt.set( m, m1, tmp2 );
}
// ----------------------------------------------- //
// Part III: Add in contributions from
// f''(q) * (fx_plus_gy, fx_plus_gy ) and
// g''(q) * (fx_plus_gy, fx_plus_gy ).
// ----------------------------------------------- //
for( int m =1; m <= mpoints; m++ )
for( int me =1; me <= meqn; me++ )
{
double tmp1 = 0.;
double tmp2 = 0.;
// Terms that get multiplied by the Hessian:
for( int m1=1; m1 <= meqn; m1++ )
for( int m2=1; m2 <= meqn; m2++ )
{
tmp1 += H.get(m,me,m1,m2,1)*fx_plus_gy.get(m,m1)*fx_plus_gy.get(m,m2);
tmp2 += H.get(m,me,m1,m2,2)*fx_plus_gy.get(m,m1)*fx_plus_gy.get(m,m2);
}
f_tt.set( m, me, f_tt.get(m,me) + tmp1 );
g_tt.set( m, me, g_tt.get(m,me) + tmp2 );
}
} // End of computing "third"-order terms
// ---------------------------------------------------------- //
//
// Construct basis coefficients (integrate_on_current_cell)
//
// ---------------------------------------------------------- //
for (int me=1; me<=mcomps_out; me++)
for (int k=1; k<=kmax; k++)
{
double tmp1 = 0.0;
double tmp2 = 0.0;
for (int mp=1; mp<=mpoints; mp++)
{
tmp1 += wgts.get(mp)*phi.get(mp,k)*(
dt_times_fdot.get(mp, me) + charlie_dt*f_tt.get(mp, me) );
tmp2 += wgts.get(mp)*phi.get(mp,k)*(
dt_times_gdot.get(mp, me) + charlie_dt*g_tt.get(mp, me) );
}
F->set(i,me,k, F->get(i,me,k) + 2.0*tmp1 );
G->set(i,me,k, G->get(i,me,k) + 2.0*tmp2 );
}
}
}