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remhos_tools.cpp
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remhos_tools.cpp
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// Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at
// the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights
// reserved. See files LICENSE and NOTICE for details.
//
// This file is part of CEED, a collection of benchmarks, miniapps, software
// libraries and APIs for efficient high-order finite element and spectral
// element discretizations for exascale applications. For more information and
// source code availability see http://github.com/ceed.
//
// The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
// a collaborative effort of two U.S. Department of Energy organizations (Office
// of Science and the National Nuclear Security Administration) responsible for
// the planning and preparation of a capable exascale ecosystem, including
// software, applications, hardware, advanced system engineering and early
// testbed platforms, in support of the nation's exascale computing imperative.
#include "remhos_tools.hpp"
using namespace std;
namespace mfem
{
SmoothnessIndicator::SmoothnessIndicator(int type_id,
ParMesh &subcell_mesh,
ParFiniteElementSpace &pfes_DG_,
ParGridFunction &u,
DofInfo &dof_info)
: type(type_id), param(type == 1 ? 5.0 : 3.0),
fec_sub(1, pfes_DG_.GetMesh()->Dimension(), BasisType::Positive),
pfes_CG_sub(&subcell_mesh, &fec_sub),
pfes_DG(pfes_DG_)
{
// TODO assemble SI matrices every RK stage for remap.
MFEM_VERIFY(type_id == 1 || type_id == 2, "Bad smoothness indicator id!");
BilinearForm massH1(&pfes_CG_sub);
massH1.AddDomainIntegrator(new MassIntegrator);
massH1.Assemble();
massH1.Finalize();
Mmat = massH1.SpMat();
ConstantCoefficient neg_one(-1.0);
BilinearForm lap(&pfes_CG_sub);
lap.AddDomainIntegrator(new DiffusionIntegrator(neg_one));
lap.AddBdrFaceIntegrator(new DGDiffusionIntegrator(neg_one, 0., 0.));
lap.Assemble();
lap.Finalize();
LaplaceOp = lap.SpMat();
MassMixed = new SparseMatrix(pfes_CG_sub.GetVSize(), pfes_DG.GetVSize());
MassInt = new MassIntegrator;
BilinearForm mlH1(&pfes_CG_sub);
mlH1.AddDomainIntegrator(new LumpedIntegrator(new MassIntegrator));
mlH1.Assemble();
mlH1.Finalize();
mlH1.SpMat().GetDiag(lumpedMH1);
Vector lumped_hv(pfes_CG_sub.GetTrueVSize());
pfes_CG_sub.Dof_TrueDof_Matrix()->MultTranspose(lumpedMH1, lumped_hv);
pfes_CG_sub.GetProlongationMatrix()->Mult(lumped_hv, lumpedMH1);
// Stores the index for the dof of H1-conforming for each node.
// If the node is on the boundary, the entry is -1.
const int dim = pfes_DG.GetMesh()->Dimension(),
nd = pfes_DG.GetFE(0)->GetDof(),
ne = pfes_DG.GetMesh()->GetNE();
DG2CG.SetSize(ne*nd);
Array<int> vdofs;
int e, i, j, e_id;
for (e = 0; e < ne; e++)
{
for (i = 0; i < dof_info.numSubcells; i++)
{
e_id = e*dof_info.numSubcells + i;
pfes_CG_sub.GetElementVDofs(e_id, vdofs);
// Switchero - numbering CG vs DG.
DG2CG(e*nd + dof_info.Sub2Ind(i, 0)) = vdofs[0];
DG2CG(e*nd + dof_info.Sub2Ind(i, 1)) = vdofs[1];
if (dim > 1)
{
DG2CG(e*nd + dof_info.Sub2Ind(i, 2)) = vdofs[3];
DG2CG(e*nd + dof_info.Sub2Ind(i, 3)) = vdofs[2];
}
if (dim == 3)
{
DG2CG(e*nd + dof_info.Sub2Ind(i, 4)) = vdofs[4];
DG2CG(e*nd + dof_info.Sub2Ind(i, 5)) = vdofs[5];
DG2CG(e*nd + dof_info.Sub2Ind(i, 6)) = vdofs[7];
DG2CG(e*nd + dof_info.Sub2Ind(i, 7)) = vdofs[6];
}
}
// Domain boundaries.
for (i = 0; i < dof_info.numBdrs; i++)
{
for (j = 0; j < dof_info.numFaceDofs; j++)
{
if (dof_info.NbrDof(e,i,j) < 0)
{
DG2CG(e*nd+dof_info.BdrDofs(j,i)) = -1;
}
}
}
}
ComputeVariationalMatrix(dof_info);
IntegrationRule *ir;
IntegrationRule irX;
QuadratureFunctions1D qf;
qf.ClosedUniform(pfes_DG.GetFE(0)->GetOrder() + 1, &irX);
Vector shape(nd);
if (dim == 1) { ir = &irX; }
if (dim == 2) { ir = new IntegrationRule(irX, irX); }
if (dim == 3) { ir = new IntegrationRule(irX, irX, irX); }
ShapeEval.SetSize(nd, nd); // nd equals ir->GetNPoints().
for (i = 0; i < ir->GetNPoints(); i++)
{
const IntegrationPoint &ip = ir->IntPoint(i);
pfes_DG.GetFE(0)->CalcShape(ip, shape);
ShapeEval.SetCol(i, shape);
}
ShapeEval.Transpose();
// Print the values of the smoothness indicator.
ParGridFunction si_val;
ComputeSmoothnessIndicator(u, si_val);
{
ofstream smth("si_init.gf");
smth.precision(8);
si_val.SaveAsOne(smth);
}
if (dim > 1) { delete ir; }
}
SmoothnessIndicator::~SmoothnessIndicator()
{
delete MassInt;
delete MassMixed;
}
void SmoothnessIndicator::ComputeSmoothnessIndicator(const Vector &u,
ParGridFunction &si_vals_u)
{
si_vals_u.SetSpace(&pfes_CG_sub);
ParGridFunction g(&pfes_CG_sub);
const int N = g.Size();
Vector gmin(N), gmax(N);
ApproximateLaplacian(u, g);
ComputeFromSparsity(Mmat, g, gmin, gmax);
if (type == 1)
{
const double eps = 1.0e-50;
for (int e = 0; e < N; e++)
{
si_vals_u(e) = 1.0 - pow( (abs(gmin(e) - gmax(e)) + eps) /
(abs(gmin(e)) + abs(gmax(e)) + eps), param);
}
}
else if (type == 2)
{
const double eps = 1.0e-15;
for (int e = 0; e < N; e++)
{
si_vals_u(e) = min(1.0, param *
max(0., gmin(e)*gmax(e)) /
(max(gmin(e)*gmin(e),gmax(e)*gmax(e)) + eps) );
}
}
}
void SmoothnessIndicator::UpdateBounds(int dof_id, double u_HO,
const ParGridFunction &si_vals,
double &u_min, double &u_max)
{
const double tmp = (DG2CG(dof_id) < 0.0) ? 1.0 : si_vals(DG2CG(dof_id));
u_min = max(0.0, tmp * u_HO + (1.0 - tmp) * u_min);
u_max = min(1.0, tmp * u_HO + (1.0 - tmp) * u_max);
}
void SmoothnessIndicator::ComputeVariationalMatrix(DofInfo &dof_info)
{
Mesh *subcell_mesh = pfes_CG_sub.GetMesh();
const int dim = subcell_mesh->Dimension();
const int nd = pfes_DG.GetFE(0)->GetDof(), ne = pfes_DG.GetMesh()->GetNE();
int k, m, e_id;
DenseMatrix elmat1;
Array <int> te_vdofs, tr_vdofs;
tr_vdofs.SetSize(dof_info.numDofsSubcell);
for (k = 0; k < ne; k++)
{
for (m = 0; m < dof_info.numSubcells; m++)
{
e_id = k*dof_info.numSubcells + m;
const FiniteElement *el = pfes_CG_sub.GetFE(e_id);
ElementTransformation *tr = subcell_mesh->GetElementTransformation(e_id);
MassInt->AssembleElementMatrix(*el, *tr, elmat1);
pfes_CG_sub.GetElementVDofs(e_id, te_vdofs);
// Switchero - numbering CG vs DG.
tr_vdofs[0] = k*nd + dof_info.Sub2Ind(m, 0);
tr_vdofs[1] = k*nd + dof_info.Sub2Ind(m, 1);
if (dim > 1)
{
tr_vdofs[2] = k*nd + dof_info.Sub2Ind(m, 3);
tr_vdofs[3] = k*nd + dof_info.Sub2Ind(m, 2);
}
if (dim == 3)
{
tr_vdofs[4] = k*nd + dof_info.Sub2Ind(m, 4);
tr_vdofs[5] = k*nd + dof_info.Sub2Ind(m, 5);
tr_vdofs[6] = k*nd + dof_info.Sub2Ind(m, 7);
tr_vdofs[7] = k*nd + dof_info.Sub2Ind(m, 6);
}
MassMixed->AddSubMatrix(te_vdofs, tr_vdofs, elmat1);
}
}
MassMixed->Finalize();
}
void SmoothnessIndicator::ApproximateLaplacian(const Vector &x,
ParGridFunction &y)
{
const int nd = pfes_DG.GetFE(0)->GetDof(), ne = pfes_DG.GetMesh()->GetNE();
int k, i, j, N = lumpedMH1.Size();
Array<int> eldofs;
Vector xDofs(nd), tmp(nd), xEval(ne*nd);
Vector rhs_tv(pfes_CG_sub.GetTrueVSize()), z_tv(pfes_CG_sub.GetTrueVSize());
eldofs.SetSize(nd);
y.SetSize(N);
Vector rhs(N), z(N);
// Approximate inversion, corresponding to Neumann series truncated after
// first two summands.
int iter, max_iter = 2;
const double abs_tol = 1.e-10;
double resid;
for (k = 0; k < ne; k++)
{
for (j = 0; j < nd; j++) { eldofs[j] = k*nd + j; }
x.GetSubVector(eldofs, xDofs);
ShapeEval.Mult(xDofs, tmp);
xEval.SetSubVector(eldofs, tmp);
}
MassMixed->Mult(xEval, rhs);
pfes_CG_sub.Dof_TrueDof_Matrix()->MultTranspose(rhs, rhs_tv);
pfes_CG_sub.GetProlongationMatrix()->Mult(rhs_tv, rhs);
y = 0.;
// Project x to a CG space (result is in y).
for (iter = 1; iter <= max_iter; iter++)
{
Mmat.Mult(y, z);
pfes_CG_sub.Dof_TrueDof_Matrix()->MultTranspose(z, z_tv);
z_tv -= rhs_tv;
pfes_CG_sub.GetProlongationMatrix()->Mult(z_tv, z);
double loc_res = z_tv.Norml2();
loc_res *= loc_res;
MPI_Allreduce(&loc_res, &resid, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
resid = sqrt(resid);
if (resid <= abs_tol) { break; }
y.HostReadWrite();
z.HostReadWrite();
const double *h_lumpedMH1 = lumpedMH1.HostRead();
for (i = 0; i < N; i++)
{
y(i) -= z(i) / h_lumpedMH1[i];
}
}
LaplaceOp.Mult(y, rhs);
pfes_CG_sub.Dof_TrueDof_Matrix()->MultTranspose(rhs, rhs_tv);
pfes_CG_sub.GetProlongationMatrix()->Mult(rhs_tv, rhs);
y = 0.;
for (iter = 1; iter <= max_iter; iter++)
{
Mmat.Mult(y, z);
pfes_CG_sub.Dof_TrueDof_Matrix()->MultTranspose(z, z_tv);
z_tv -= rhs_tv;
pfes_CG_sub.GetProlongationMatrix()->Mult(z_tv, z);
double loc_res = z_tv.Norml2();
loc_res *= loc_res;
MPI_Allreduce(&loc_res, &resid, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
resid = sqrt(resid);
if (resid <= abs_tol) { break; }
y.HostReadWrite();
z.HostReadWrite();
const double * h_lumpedMH1 = lumpedMH1.HostRead();
for (i = 0; i < N; i++)
{
y(i) -= z(i) / h_lumpedMH1[i];
}
}
}
void SmoothnessIndicator::ComputeFromSparsity(const SparseMatrix &K,
const ParGridFunction &x,
Vector &x_min, Vector &x_max)
{
const int *I = K.GetI(), *J = K.GetJ(), loc_size = K.Size();
int end;
for (int i = 0, k = 0; i < loc_size; i++)
{
x_min(i) = numeric_limits<double>::infinity();
x_max(i) = -x_min(i);
for (end = I[i+1]; k < end; k++)
{
const double x_j = x(J[k]);
x_max(i) = max(x_max(i), x_j);
x_min(i) = min(x_min(i), x_j);
}
}
GroupCommunicator &gcomm = x.ParFESpace()->GroupComm();
Array<double> minvals(x_min.GetData(), x_min.Size()),
maxvals(x_max.GetData(), x_max.Size());
gcomm.Reduce<double>(minvals, GroupCommunicator::Min);
gcomm.Bcast(minvals);
gcomm.Reduce<double>(maxvals, GroupCommunicator::Max);
gcomm.Bcast(maxvals);
}
DofInfo::DofInfo(ParFiniteElementSpace &pfes_sltn, int btype)
: bounds_type(btype),
pmesh(pfes_sltn.GetParMesh()), pfes(pfes_sltn),
fec_bounds(std::max(pfes.GetOrder(0), 1),
pmesh->Dimension(), BasisType::GaussLobatto),
pfes_bounds(pmesh, &fec_bounds),
x_min(&pfes_bounds), x_max(&pfes_bounds)
{
int n = pfes.GetVSize();
int ne = pmesh->GetNE();
xi_min.SetSize(n);
xi_max.SetSize(n);
xe_min.SetSize(ne);
xe_max.SetSize(ne);
ExtractBdrDofs(pfes.GetOrder(0),
pfes.GetFE(0)->GetGeomType(), BdrDofs);
numFaceDofs = BdrDofs.Height();
numBdrs = BdrDofs.Width();
FillNeighborDofs(); // Fill NbrDof.
FillSubcell2CellDof(); // Fill Sub2Ind.
}
void DofInfo::ComputeMatrixSparsityBounds(const Vector &el_min,
const Vector &el_max,
Vector &dof_min, Vector &dof_max,
Array<bool> *active_el)
{
ParMesh *pmesh = pfes.GetParMesh();
L2_FECollection fec_bounds(0, pmesh->Dimension());
ParFiniteElementSpace pfes_bounds(pmesh, &fec_bounds);
ParGridFunction x_min(&pfes_bounds), x_max(&pfes_bounds);
const int NE = pmesh->GetNE();
const int ndofs = dof_min.Size() / NE;
x_min.HostReadWrite();
x_max.HostReadWrite();
x_min = el_min;
x_max = el_max;
x_min.ExchangeFaceNbrData(); x_max.ExchangeFaceNbrData();
const Vector &minv = x_min.FaceNbrData(), &maxv = x_max.FaceNbrData();
const Table &el_to_el = pmesh->ElementToElementTable();
Array<int> face_nbr_el;
for (int i = 0; i < NE; i++)
{
double el_min = x_min(i), el_max = x_max(i);
el_to_el.GetRow(i, face_nbr_el);
for (int n = 0; n < face_nbr_el.Size(); n++)
{
if (face_nbr_el[n] < NE)
{
// Local neighbor.
el_min = std::min(el_min, x_min(face_nbr_el[n]));
el_max = std::max(el_max, x_max(face_nbr_el[n]));
}
else
{
// MPI face neighbor.
el_min = std::min(el_min, minv(face_nbr_el[n] - NE));
el_max = std::max(el_max, maxv(face_nbr_el[n] - NE));
}
}
for (int j = 0; j < ndofs; j++)
{
dof_min(i*ndofs + j) = el_min;
dof_max(i*ndofs + j) = el_max;
}
}
}
void DofInfo::ComputeOverlapBounds(const Vector &el_min,
const Vector &el_max,
Vector &dof_min, Vector &dof_max,
Array<bool> *active_el)
{
GroupCommunicator &gcomm = pfes_bounds.GroupComm();
Array<int> dofsCG;
const int NE = pfes.GetNE();
// Form min/max at each CG dof, considering element overlaps.
x_min = std::numeric_limits<double>::infinity();
x_max = - std::numeric_limits<double>::infinity();
for (int i = 0; i < NE; i++)
{
// Inactive elements don't affect the bounds.
if (active_el && (*active_el)[i] == false) { continue; }
x_min.HostReadWrite();
x_max.HostReadWrite();
pfes_bounds.GetElementDofs(i, dofsCG);
for (int j = 0; j < dofsCG.Size(); j++)
{
x_min(dofsCG[j]) = std::min(x_min(dofsCG[j]), el_min(i));
x_max(dofsCG[j]) = std::max(x_max(dofsCG[j]), el_max(i));
}
}
Array<double> minvals(x_min.GetData(), x_min.Size());
Array<double> maxvals(x_max.GetData(), x_max.Size());
gcomm.Reduce<double>(minvals, GroupCommunicator::Min);
gcomm.Bcast(minvals);
gcomm.Reduce<double>(maxvals, GroupCommunicator::Max);
gcomm.Bcast(maxvals);
// Use (x_min, x_max) to fill (dof_min, dof_max) for each DG dof.
const TensorBasisElement *fe_cg =
dynamic_cast<const TensorBasisElement *>(pfes_bounds.GetFE(0));
const Array<int> &dof_map = fe_cg->GetDofMap();
const int ndofs = dof_map.Size();
for (int i = 0; i < NE; i++)
{
// Comment about the case when active_el != null, i.e., when this function
// is used to compute the bounds of s:
//
// Note that this loop goes over all elements, including inactive ones.
// The following happens in an inactive element:
// - If a DOF is on the boundary with an active element, it will get the
// value that's propagated by the continuous functions x_min and x_max.
// - Otherwise, the DOF would get the inf values.
// This is the mechanism that allows new elements, that switch from
// inactive to active, to get some valid bounds. More specifically, this
// function is called on the old state, but the result from it is used
// to limit the new state, which has different active elements.
pfes_bounds.GetElementDofs(i, dofsCG);
for (int j = 0; j < dofsCG.Size(); j++)
{
dof_min(i*ndofs + j) = x_min(dofsCG[dof_map[j]]);
dof_max(i*ndofs + j) = x_max(dofsCG[dof_map[j]]);
}
}
}
void DofInfo::ComputeElementsMinMax(const Vector &u,
Vector &u_min, Vector &u_max,
Array<bool> *active_el,
Array<bool> *active_dof) const
{
const int NE = pfes.GetNE(), ndof = pfes.GetFE(0)->GetDof();
int dof_id;
u.HostRead(); u_min.HostReadWrite(); u_max.HostReadWrite();
for (int k = 0; k < NE; k++)
{
u_min(k) = numeric_limits<double>::infinity();
u_max(k) = -numeric_limits<double>::infinity();
// Inactive elements don't affect the bounds.
if (active_el && (*active_el)[k] == false) { continue; }
for (int i = 0; i < ndof; i++)
{
dof_id = k*ndof + i;
// Inactive dofs don't affect the bounds.
if (active_dof && (*active_dof)[dof_id] == false) { continue; }
u_min(k) = min(u_min(k), u(dof_id));
u_max(k) = max(u_max(k), u(dof_id));
}
}
}
void DofInfo::FillNeighborDofs()
{
// Use the first mesh element as indicator.
const FiniteElement &dummy = *pfes.GetFE(0);
const int dim = pmesh->Dimension();
int i, j, k, ne = pmesh->GetNE();
int nd = dummy.GetDof(), p = dummy.GetOrder();
Array <int> bdrs, orientation;
pmesh->ExchangeFaceNbrData();
Table *face_to_el = pmesh->GetFaceToAllElementTable();
NbrDof.SetSize(ne, numBdrs, numFaceDofs);
// Permutations of BdrDofs, taking into account all possible orientations.
// Assumes BdrDofs are ordered in xyz order, which is true for 3D hexes,
// but it isn't true for 2D quads.
// TODO: check other FEs, function ExtractBoundaryDofs().
int orient_cnt = 1;
if (dim == 2) { orient_cnt = 2; }
if (dim == 3) { orient_cnt = 8; }
const int dof1D_cnt = p+1;
DenseTensor fdof_ids(numFaceDofs, numBdrs, orient_cnt);
for (int ori = 0; ori < orient_cnt; ori++)
{
for (int face_id = 0; face_id < numBdrs; face_id++)
{
for (int fdof_id = 0; fdof_id < numFaceDofs; fdof_id++)
{
// Index of fdof_id in the current orientation.
const int ori_fdof_id = GetLocalFaceDofIndex(dim, face_id, ori,
fdof_id, dof1D_cnt);
fdof_ids(ori)(ori_fdof_id, face_id) = BdrDofs(fdof_id, face_id);
}
}
}
for (k = 0; k < ne; k++)
{
if (dim == 1)
{
pmesh->GetElementVertices(k, bdrs);
for (i = 0; i < numBdrs; i++)
{
const int nbr_cnt = face_to_el->RowSize(bdrs[i]);
if (nbr_cnt == 1)
{
// No neighbor element.
NbrDof(k, i, 0) = -1;
continue;
}
int el1_id, el2_id, nbr_id;
pmesh->GetFaceElements(bdrs[i], &el1_id, &el2_id);
if (el2_id < 0)
{
// This element is in a different mpi task.
el2_id = -1 - el2_id + ne;
}
nbr_id = (el1_id == k) ? el2_id : el1_id;
NbrDof(k,i,0) = nbr_id*nd + BdrDofs(0, (i+1) % 2);
}
}
else if (dim==2)
{
pmesh->GetElementEdges(k, bdrs, orientation);
for (i = 0; i < numBdrs; i++)
{
const int nbr_cnt = face_to_el->RowSize(bdrs[i]);
if (nbr_cnt == 1)
{
// No neighbor element.
for (j = 0; j < numFaceDofs; j++) { NbrDof(k, i, j) = -1; }
continue;
}
int el1_id, el2_id, nbr_id;
pmesh->GetFaceElements(bdrs[i], &el1_id, &el2_id);
if (el2_id < 0)
{
// This element is in a different mpi task.
el2_id = -1 - el2_id + ne;
}
nbr_id = (el1_id == k) ? el2_id : el1_id;
int el1_info, el2_info;
pmesh->GetFaceInfos(bdrs[i], &el1_info, &el2_info);
const int face_id_nbr = (nbr_id == el1_id) ? el1_info / 64
: el2_info / 64;
for (j = 0; j < numFaceDofs; j++)
{
// Here it is utilized that the orientations of the face for
// the two elements are opposite of each other.
NbrDof(k,i,j) = nbr_id*nd + BdrDofs(numFaceDofs - 1 - j,
face_id_nbr);
}
}
}
else if (dim==3)
{
pmesh->GetElementFaces(k, bdrs, orientation);
for (int f = 0; f < numBdrs; f++)
{
const int nbr_cnt = face_to_el->RowSize(bdrs[f]);
if (nbr_cnt == 1)
{
// No neighbor element.
for (j = 0; j < numFaceDofs; j++) { NbrDof(k, f, j) = -1; }
continue;
}
int el1_id, el2_id, nbr_id;
pmesh->GetFaceElements(bdrs[f], &el1_id, &el2_id);
if (el2_id < 0)
{
// This element is in a different mpi task.
el2_id = -1 - el2_id + ne;
}
nbr_id = (el1_id == k) ? el2_id : el1_id;
// Local index and orientation of the face, when considered in
// the neighbor element.
int el1_info, el2_info;
pmesh->GetFaceInfos(bdrs[f], &el1_info, &el2_info);
const int face_id_nbr = (nbr_id == el1_id) ? el1_info / 64
: el2_info / 64;
const int face_or_nbr = (nbr_id == el1_id) ? el1_info % 64
: el2_info % 64;
for (j = 0; j < numFaceDofs; j++)
{
// What is the index of the j-th dof on the face, given its
// orientation.
const int loc_face_dof_id =
GetLocalFaceDofIndex(dim, face_id_nbr, face_or_nbr,
j, dof1D_cnt);
// What is the corresponding local dof id on the element,
// given the face orientation.
const int nbr_dof_id =
fdof_ids(face_or_nbr)(loc_face_dof_id, face_id_nbr);
NbrDof(k, f, j) = nbr_id*nd + nbr_dof_id;
}
}
}
}
delete face_to_el;
}
void DofInfo::FillSubcell2CellDof()
{
const int dim = pmesh->Dimension(), p = pfes.GetFE(0)->GetOrder();
if (dim==1)
{
numSubcells = p;
numDofsSubcell = 2;
}
else if (dim==2)
{
numSubcells = p*p;
numDofsSubcell = 4;
}
else if (dim==3)
{
numSubcells = p*p*p;
numDofsSubcell = 8;
}
Sub2Ind.SetSize(numSubcells, numDofsSubcell);
int aux;
for (int m = 0; m < numSubcells; m++)
{
for (int j = 0; j < numDofsSubcell; j++)
{
if (dim == 1) { Sub2Ind(m,j) = m + j; }
else if (dim == 2)
{
aux = m + m/p;
switch (j)
{
case 0: Sub2Ind(m,j) = aux; break;
case 1: Sub2Ind(m,j) = aux + 1; break;
case 2: Sub2Ind(m,j) = aux + p+1; break;
case 3: Sub2Ind(m,j) = aux + p+2; break;
}
}
else if (dim == 3)
{
aux = m + m/p + (p+1)*(m/(p*p));
switch (j)
{
case 0: Sub2Ind(m,j) = aux; break;
case 1: Sub2Ind(m,j) = aux + 1; break;
case 2: Sub2Ind(m,j) = aux + p+1; break;
case 3: Sub2Ind(m,j) = aux + p+2; break;
case 4: Sub2Ind(m,j) = aux + (p+1)*(p+1); break;
case 5: Sub2Ind(m,j) = aux + (p+1)*(p+1)+1; break;
case 6: Sub2Ind(m,j) = aux + (p+1)*(p+1)+p+1; break;
case 7: Sub2Ind(m,j) = aux + (p+1)*(p+1)+p+2; break;
}
}
}
}
}
Assembly::Assembly(DofInfo &_dofs, LowOrderMethod &_lom,
const GridFunction &inflow,
ParFiniteElementSpace &pfes, ParMesh *submesh, int mode)
: exec_mode(mode), inflow_gf(inflow), x_gf(&pfes),
VolumeTerms(NULL),
fes(&pfes), SubFes0(NULL), SubFes1(NULL),
subcell_mesh(submesh), dofs(_dofs), lom(_lom)
{
Mesh *mesh = fes->GetMesh();
int k, i, m, dim = mesh->Dimension(), ne = fes->GetNE();
Array <int> bdrs, orientation;
FaceElementTransformations *Trans;
bdrInt.SetSize(ne, dofs.numBdrs, dofs.numFaceDofs*dofs.numFaceDofs);
bdrInt = 0.;
if (lom.subcell_scheme)
{
VolumeTerms = lom.VolumeTerms;
SubcellWeights.SetSize(dofs.numSubcells, dofs.numDofsSubcell, ne);
SubFes0 = lom.SubFes0;
SubFes1 = lom.SubFes1;
}
// Initialization for transport mode.
if (exec_mode == 0)
{
for (k = 0; k < ne; k++)
{
if (dim==1) { mesh->GetElementVertices(k, bdrs); }
else if (dim==2) { mesh->GetElementEdges(k, bdrs, orientation); }
else if (dim==3) { mesh->GetElementFaces(k, bdrs, orientation); }
for (i = 0; i < dofs.numBdrs; i++)
{
Trans = mesh->GetFaceElementTransformations(bdrs[i]);
ComputeFluxTerms(k, i, Trans, lom);
}
if (lom.subcell_scheme)
{
for (m = 0; m < dofs.numSubcells; m++)
{
ComputeSubcellWeights(k, m);
}
}
}
}
}
void Assembly::ComputeFluxTerms(const int e_id, const int BdrID,
FaceElementTransformations *Trans,
LowOrderMethod &lom)
{
Mesh *mesh = fes->GetMesh();
int i, j, l, dim = mesh->Dimension();
double aux, vn;
const FiniteElement &el = *fes->GetFE(e_id);
Vector vval, nor(dim), shape(el.GetDof());
for (l = 0; l < lom.irF->GetNPoints(); l++)
{
const IntegrationPoint &ip = lom.irF->IntPoint(l);
IntegrationPoint eip1;
Trans->Face->SetIntPoint(&ip);
if (dim == 1)
{
Trans->Loc1.Transform(ip, eip1);
nor(0) = 2.*eip1.x - 1.0;
}
else
{
CalcOrtho(Trans->Face->Jacobian(), nor);
}
if (Trans->Elem1No != e_id)
{
Trans->Loc2.Transform(ip, eip1);
el.CalcShape(eip1, shape);
Trans->Elem2->SetIntPoint(&eip1);
lom.coef->Eval(vval, *Trans->Elem2, eip1);
nor *= -1.;
}
else
{
Trans->Loc1.Transform(ip, eip1);
el.CalcShape(eip1, shape);
Trans->Elem1->SetIntPoint(&eip1);
lom.coef->Eval(vval, *Trans->Elem1, eip1);
}
nor /= nor.Norml2();
if (exec_mode == 0)
{
// Transport.
vn = std::min(0., vval * nor);
}
else
{
// Remap.
vn = std::max(0., vval * nor);
vn *= -1.0;
}
const double w = ip.weight * Trans->Face->Weight();
for (i = 0; i < dofs.numFaceDofs; i++)
{
aux = w * shape(dofs.BdrDofs(i,BdrID)) * vn;
for (j = 0; j < dofs.numFaceDofs; j++)
{
bdrInt(e_id, BdrID, i*dofs.numFaceDofs+j) -=
aux * shape(dofs.BdrDofs(j,BdrID));
}
}
}
}
void Assembly::ComputeSubcellWeights(const int k, const int m)
{
DenseMatrix elmat; // These are essentially the same.
const int e_id = k*dofs.numSubcells + m;
const FiniteElement *el0 = SubFes0->GetFE(e_id);
const FiniteElement *el1 = SubFes1->GetFE(e_id);
ElementTransformation *tr = subcell_mesh->GetElementTransformation(e_id);
VolumeTerms->AssembleElementMatrix2(*el1, *el0, *tr, elmat);
for (int j = 0; j < elmat.Width(); j++)
{
// Using the fact that elmat has just one row.
SubcellWeights(k)(m,j) = elmat(0,j);
}
}
void Assembly::LinearFluxLumping(const int k, const int nd, const int BdrID,
const Vector &x, Vector &y, const Vector &x_nd,
const Vector &alpha) const
{
int i, j, dofInd;
double xNeighbor;
Vector xDiff(dofs.numFaceDofs);
const int size_x = x.Size();
for (j = 0; j < dofs.numFaceDofs; j++)
{
dofInd = k*nd+dofs.BdrDofs(j,BdrID);
const int nbr_dof_id = dofs.NbrDof(k, BdrID, j);
// Note that if the boundary is outflow, we have bdrInt = 0 by definition,
// s.t. this value will not matter.
if (nbr_dof_id < 0) { xNeighbor = inflow_gf(dofInd); }
else
{
xNeighbor = (nbr_dof_id < size_x) ? x(nbr_dof_id)
: x_nd(nbr_dof_id - size_x);
}
xDiff(j) = xNeighbor - x(dofInd);
}
for (i = 0; i < dofs.numFaceDofs; i++)
{
dofInd = k*nd+dofs.BdrDofs(i,BdrID);
for (j = 0; j < dofs.numFaceDofs; j++)
{
// alpha=0 is the low order solution, alpha=1, the Galerkin solution.
// 0 < alpha < 1 can be used for limiting within the low order method.
y(dofInd) += bdrInt(k, BdrID, i*dofs.numFaceDofs + j) *
(xDiff(i) + (xDiff(j)-xDiff(i)) *
alpha(dofs.BdrDofs(i,BdrID)) *
alpha(dofs.BdrDofs(j,BdrID)));
}
}
}
void Assembly::NonlinFluxLumping(const int k, const int nd,
const int BdrID, const Vector &x,
Vector &y, const Vector &x_nd,
const Vector &alpha) const
{
int i, j, dofInd;
double xNeighbor, SumCorrP = 0., SumCorrN = 0., eps = 1.E-15;
const int size_x = x.Size();
Vector xDiff(dofs.numFaceDofs), BdrTermCorr(dofs.numFaceDofs);
BdrTermCorr = 0.;
for (j = 0; j < dofs.numFaceDofs; j++)
{
dofInd = k*nd+dofs.BdrDofs(j,BdrID);
const int nbr_dof_id = dofs.NbrDof(k, BdrID, j);
// Note that if the boundary is outflow, we have bdrInt = 0 by definition,
// s.t. this value will not matter.
if (nbr_dof_id < 0) { xNeighbor = inflow_gf(dofInd); }
else
{
xNeighbor = (nbr_dof_id < size_x) ? x(nbr_dof_id)
: x_nd(nbr_dof_id - size_x);
}
xDiff(j) = xNeighbor - x(dofInd);
}
y.HostReadWrite();
bdrInt.HostRead();
xDiff.HostReadWrite();
for (i = 0; i < dofs.numFaceDofs; i++)
{
dofInd = k*nd+dofs.BdrDofs(i,BdrID);
for (j = 0; j < dofs.numFaceDofs; j++)
{
y(dofInd) += bdrInt(k, BdrID, i*dofs.numFaceDofs + j) * xDiff(i);
BdrTermCorr(i) += bdrInt(k, BdrID,
i*dofs.numFaceDofs + j) * (xDiff(j)-xDiff(i));
}
BdrTermCorr(i) *= alpha(dofs.BdrDofs(i,BdrID));
SumCorrP += max(0., BdrTermCorr(i));
SumCorrN += min(0., BdrTermCorr(i));
}
for (i = 0; i < dofs.numFaceDofs; i++)
{
dofInd = k*nd+dofs.BdrDofs(i,BdrID);
if (SumCorrP + SumCorrN > eps)
{
BdrTermCorr(i) = min(0., BdrTermCorr(i)) -
max(0., BdrTermCorr(i)) * SumCorrN / SumCorrP;
}
else if (SumCorrP + SumCorrN < -eps)
{
BdrTermCorr(i) = max(0., BdrTermCorr(i)) -
min(0., BdrTermCorr(i)) * SumCorrP / SumCorrN;
}
y(dofInd) += BdrTermCorr(i);
}
}
void PrecondConvectionIntegrator::AssembleElementMatrix(
const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
{
int i, nd = el.GetDof(), dim = el.GetDim();
#ifdef MFEM_THREAD_SAFE
DenseMatrix dshape, adjJ, Q_ir;
Vector shape, vec2, BdFidxT;
#endif
elmat.SetSize(nd);
dshape.SetSize(nd,dim);
adjJ.SetSize(dim);
shape.SetSize(nd);
vec2.SetSize(dim);
BdFidxT.SetSize(nd);
double w;
Vector vec1;
DenseMatrix mass(nd,nd), conv(nd,nd), lumpedM(nd,nd), tmp(nd,nd);
const IntegrationRule *ir = IntRule;
if (ir == NULL)
{
int order = Trans.OrderGrad(&el) + Trans.Order() + el.GetOrder();
order = max(order, 2 * el.GetOrder() + Trans.OrderW());
ir = &IntRules.Get(el.GetGeomType(), order);
}
Q.Eval(Q_ir, Trans, *ir);
conv = mass = 0.0;
for (i = 0; i < ir->GetNPoints(); i++)