//---------------------------------------------------------
void CSN::show_alloc() const
//---------------------------------------------------------
{
umMSG(1, "\nAllocations in Numeric object:\n");
umMSG(1, " L : %8d (csc) \n", L.size());
umMSG(1, " U : %8d (csc) \n", U.size());
umMSG(1, " pinv : %8d (int) \n", pinv.size());
umMSG(1, " B : %8d (dbl) \n\n", B.size());
}
//---------------------------------------------------------
void VertexAngles
(
const DVec& x1, const DVec& x2, const DVec& x3,
const DVec& y1, const DVec& y2, const DVec& y3,
DVec& a1, DVec& a2, DVec& a3
)
//---------------------------------------------------------
{
//------------------------------------------
// Expand definitions from ElmTools
//------------------------------------------
// a1 = acos ( -a23() / sqrt(a22()*a33()) );
// a2 = acos ( -a13() / sqrt(a11()*a33()) );
// a3 = acos ( -a12() / sqrt(a11()*a22()) );
DVec g2x=(y3-y1), g2y=(x1-x3), g3x=(y1-y2), g3y=(x2-x1);
DVec det = g3y*g2x - g3x*g2y;
DVec d = 1.0/det;
g2x *= d; g2y *= d; g3x *= d; g3y *= d;
DVec g1x = - g2x - g3x;
DVec g1y = - g2y - g3y;
a1 = acos( -(g2x*g3x + g2y*g3y) / sqrt((sqr(g2x)+sqr(g2y)) * (sqr(g3x)+sqr(g3y)) ));
a2 = acos( -(g1x*g3x + g1y*g3y) / sqrt((sqr(g1x)+sqr(g1y)) * (sqr(g3x)+sqr(g3y)) ));
a3 = acos( -(g1x*g2x + g1y*g2y) / sqrt((sqr(g1x)+sqr(g1y)) * (sqr(g2x)+sqr(g2y)) ));
#if (0)
// check that the angles in each element sum to 180
int Ni = x1.size(); double sum=0.0;
umMSG(1, "\nChecking sum of angles in %d element\n", Ni);
for (int i=1; i<=Ni; ++i) {
sum = fabs(a1(i)) + fabs(a2(i)) + fabs(a3(i));
if ( fabs(sum-M_PI) > 1e-15) {
umMSG(1, "element %4d: %12.5e\n", i, fabs(sum-M_PI));
}
}
#endif
}
//---------------------------------------------------------
void CSS::show_alloc() const
//---------------------------------------------------------
{
umMSG(1, "\nAllocations in Symbolic object:\n");
umMSG(1, " pinv : %8d (int) \n", pinv.size());
umMSG(1, " Q : %8d (int) \n", Q.size());
umMSG(1, " parent: %8d (int) \n", parent.size());
umMSG(1, " cp : %8d (int) \n", cp.size());
umMSG(1, " leftmost: %8d (int) \n", leftmost.size());
umMSG(1, " m2: %d lnz: %g unz: %g \n\n", m2, lnz, unz);
}
//---------------------------------------------------------
void MaxwellNonCon2D::AdjustMesh_P()
//---------------------------------------------------------
{
umMSG(1, "Adjusting mesh for non-conforming (P) elements\n");
Nfaces = 3;
tiConnect2D(EToV, EToE,EToF);
// make boundary conditions all "Wall" type
BCType = int(BC_Wall) * EToE.eq(outer(Range(1,K),Ones(Nfaces)));
IVec Norder(K);
if (1) {
// generate a random order for each element
Norder = ceil(10.0*rand(K));
} else if (0) {
Norder = 5;
} else {
Norder(1) = 1;
Norder(2) = 1;
Norder(3) = 2;
Norder(4) = 2;
Norder(5) = 3;
Norder(6) = 3;
Norder(Range(7,K)) = 4;
}
// Build mesh, each element having arbitrary order
BuildPNonCon2D(Norder, K, VX, VY, EToV, BCType, m_PInfo);
xx.resize(max_pinf_id);
yy.resize(max_pinf_id);
for (int N1=1; N1<=Nmax; ++N1) {
const PInfo& pinf = (*m_PInfo[N1]);
if (pinf.K > 0) {
const IVec& pids = dynamic_cast<const IVec&>(pinf.ids);
xx(pids) = pinf.x;
yy(pids) = pinf.y;
}
}
}
//---------------------------------------------------------
void CurvedINS2D::Run()
//---------------------------------------------------------
{
ti0=timer.read();
// function [Ux, Uy, PR, time] = CurvedINS2D(...
// Ux, Uy, PR, FinalTime, nu, simtype, ExactSolution, BCfunction);
// Purpose: integrate the incompressible Navier-Stokes equations to FinalTime
InitRun(); // initialize timers & counters
// choose order to integrate exactly
int Nint = (int)ceil(3.0*N/2.0);
// build cubature nodes for all elements
CubatureOrder = 2*(Nint+1); CubatureVolumeMesh2D(CubatureOrder);
// build Gauss node data for all element faces
NGauss = (Nint+1); GaussFaceMesh2D(NGauss);
#if (1)
//-------------------------------------
// check all node sets
//-------------------------------------
Output_Mesh();
//OutputNodes(false); // volume nodes
//OutputNodes(true); // face nodes
//OutputNodes_cub(); // cubature
//OutputNodes_gauss(); // quadrature
//umLOG(1, "\n*** Exiting after CUb, Gauss\n\n");
//return;
#endif
// recover memory from registry
NDG_garbage_collect();
// prepare data...
PreCalcBdryData();
// dual splitting scheme coefficients
g0 = 1.0; a0 = 1.0; a1 = 0.0; b0 = 1.0; b1 = 0.0;
CurvedINSPressureSetUp2D(); // Build pressure matrix and boundary forcing (IPDG)
NDG_garbage_collect(); // recover memory from registry
CurvedINSViscousSetUp2D(); // Build viscous matrix and boundary forcing (IPDG)
NDG_garbage_collect(); // recover memory from registry
(this->*ExactSolutionBC) // Form inhomogeneous boundary term for rhs data
(Fx, Fy, nx,ny, mapI, mapO, mapW, mapC, 0.0, nu,
refbcUx, refbcUy, refbcPR, refbcdUndt);
// storage for history of fields and nonlinear terms
Uxold=Ux; NUx=0.0; Uyold=Uy; NUy=0.0; dpdn=0.0;
time_work += timer.read() - ti0; // add cost of NDG setup
// start time stepping
time = 0.0;
for (tstep=1; tstep<=Nsteps; ++tstep)
{
tw1=timer.read(); // time NDG work
// update dual splitting scheme coefficients after
// first time step, then recalculate operators
if (2 == tstep)
{
// release and recreate Cholesky solvers
reset_solvers();
g0 = 1.5; a0 = 2.0; a1 = -0.5; b0 = 2.0; b1 = -1.0;
// Rebuild pressure and viscous matrixes for new g0
CurvedINSPressureSetUp2D();
CurvedINSViscousSetUp2D();
NDG_garbage_collect();
umMSG(1, "2nd sparse setup completed\n");
//umERROR("Testing", "Exiting early");
}
TimeScaleBCData(); // apply temporal scaling factors to bc data
INSAdvection2D(); // compute nonlinear terms NUx, NUy
//CurvedINSAdvection2D; // curved version
INSPressure2D(); // compute pressure PR and intermediate UxTT, UyTT
//CurvedINSPressure2D; // curved version
CurvedINSViscous2D(); // compute viscous solves and update velocity
time_work += timer.read() - tw1; // accumulate cost of NDG work
time = tstep*dt; // increment time
Report(); // report results
// if (tstep>100) break;
}
time_total = timer.read()-ti0; // stop timing
FinalReport(); // final report
}
//---------------------------------------------------------
DMat& NDG2D::ConformingHrefine2D(IMat& edgerefineflag, const DMat& Qin)
//---------------------------------------------------------
{
#if (0)
OutputNodes(false); // volume nodes
//OutputNodes(true); // face nodes
#endif
// function newQ = ConformingHrefine2D(edgerefineflag, Q)
// Purpose: apply edge splits as requested by edgerefineflag
IVec v1("v1"), v2("v2"), v3("v3"), tvi;
DVec x1("x1"), x2("x2"), x3("x3"), y1("y1"), y2("y2"), y3("y3");
DVec a1("a1"), a2("a2"), a3("a3");
// count vertices
assert (VX.size() == Nv);
// find vertex triplets for elements to be refined
v1 = EToV(All,1); v2 = EToV(All,2); v3 = EToV(All,3);
x1 = VX(v1); x2 = VX(v2); x3 = VX(v3);
y1 = VY(v1); y2 = VY(v2); y3 = VY(v3);
// find angles at each element vertex (in radians)
VertexAngles(x1,x2,x3,y1,y2,y3, a1,a2,a3);
// absolute value of angle size
a1.set_abs(); a2.set_abs(); a3.set_abs();
int k=0,k1=0,f1=0,k2=0,f2=0, e1=0,e2=0,e3=0, b1=0,b2=0,b3=0, ref=0;
IVec m1,m2,m3; DVec mx1, my1, mx2, my2, mx3, my3;
// create new vertices at edge centers of marked elements
// (use unique numbering derived from unique edge number))
m1 = max(IVec(Nv*(v1-1)+v2+1), IVec(Nv*(v2-1)+v1+1)); mx1=0.5*(x1+x2); my1=0.5*(y1+y2);
m2 = max(IVec(Nv*(v2-1)+v3+1), IVec(Nv*(v3-1)+v2+1)); mx2=0.5*(x2+x3); my2=0.5*(y2+y3);
m3 = max(IVec(Nv*(v1-1)+v3+1), IVec(Nv*(v3-1)+v1+1)); mx3=0.5*(x3+x1); my3=0.5*(y3+y1);
// ensure that both elements sharing an edge are split
for (k1=1; k1<=K; ++k1) {
for (f1=1; f1<=Nfaces; ++f1) {
if (edgerefineflag(k1,f1)) {
k2 = EToE(k1,f1);
f2 = EToF(k1,f1);
edgerefineflag(k2,f2) = 1;
}
}
}
// store old data
IMat oldEToV = EToV; DVec oldVX = VX, oldVY = VY;
// count the number of elements in the refined mesh
int newK = countrefinefaces(edgerefineflag);
EToV.resize(newK, Nfaces, true, 0);
IMat newBCType(newK,3, "newBCType");
// kold = [];
IVec kold(newK, "kold"); Index1D KI,KIo;
int sk=1, skstart=0, skend=0;
for (k=1; k<=K; ++k)
{
skstart = sk;
e1 = edgerefineflag(k,1); b1 = BCType(k,1);
e2 = edgerefineflag(k,2); b2 = BCType(k,2);
e3 = edgerefineflag(k,3); b3 = BCType(k,3);
ref = e1 + 2*e2 + 4*e3;
switch (ref) {
case 0:
EToV(sk, All) = IVec(v1(k),v2(k),v3(k)); newBCType(sk,All) = IVec(b1, b2, b3); ++sk;
break;
case 1:
EToV(sk, All) = IVec(v1(k),m1(k),v3(k)); newBCType(sk,All) = IVec(b1, 0, b3); ++sk;
EToV(sk, All) = IVec(m1(k),v2(k),v3(k)); newBCType(sk,All) = IVec(b1, b2, 0); ++sk;
break;
case 2:
EToV(sk, All) = IVec(v2(k),m2(k),v1(k)); newBCType(sk,All) = IVec(b2, 0, b1); ++sk;
EToV(sk, All) = IVec(m2(k),v3(k),v1(k)); newBCType(sk,All) = IVec(b2, b3, 0); ++sk;
break;
case 4:
EToV(sk, All) = IVec(v3(k),m3(k),v2(k)); newBCType(sk,All) = IVec(b3, 0, b2); ++sk;
EToV(sk, All) = IVec(m3(k),v1(k),v2(k)); newBCType(sk,All) = IVec(b3, b1, 0); ++sk;
break;
case 3:
EToV(sk, All) = IVec(m1(k),v2(k),m2(k)); newBCType(sk,All) = IVec(b1, b2, 0); ++sk;
if (a1(k) > a3(k)) { // split largest angle
EToV(sk, All) = IVec(v1(k),m1(k),m2(k)); newBCType(sk,All) = IVec(b1, 0, 0); ++sk;
EToV(sk, All) = IVec(v1(k),m2(k),v3(k)); newBCType(sk,All) = IVec( 0, b2, b3); ++sk;
} else {
EToV(sk, All) = IVec(v3(k),m1(k),m2(k)); newBCType(sk,All) = IVec( 0, 0, b2); ++sk;
EToV(sk, All) = IVec(v3(k),v1(k),m1(k)); newBCType(sk,All) = IVec(b3, b1, 0); ++sk;
}
break;
case 5:
EToV(sk, All) = IVec(v1(k),m1(k),m3(k)); newBCType(sk,All) = IVec(b1, 0, b3); ++sk;
if (a2(k) > a3(k)) {
// split largest angle
EToV(sk, All) = IVec(v2(k),m3(k),m1(k)); newBCType(sk,All) = IVec( 0, 0, b1); ++sk;
EToV(sk, All) = IVec(v2(k),v3(k),m3(k)); newBCType(sk,All) = IVec(b2, b3, 0); ++sk;
} else {
EToV(sk, All) = IVec(v3(k),m3(k),m1(k)); newBCType(sk,All) = IVec(b3, 0, 0); ++sk;
EToV(sk, All) = IVec(v3(k),m1(k),v2(k)); newBCType(sk,All) = IVec( 0, b1, b2); ++sk;
}
break;
case 6:
EToV(sk, All) = IVec(v3(k),m3(k),m2(k)); newBCType(sk,All) = IVec(b3, 0, b2); ++sk;
if (a1(k) > a2(k)) {
// split largest angle
EToV(sk, All) = IVec(v1(k),m2(k),m3(k)); newBCType(sk,All) = IVec( 0, 0, b3); ++sk;
EToV(sk, All) = IVec(v1(k),v2(k),m2(k)); newBCType(sk,All) = IVec(b1, b2, 0); ++sk;
} else {
EToV(sk, All) = IVec(v2(k),m2(k),m3(k)); newBCType(sk,All) = IVec(b2, 0, 0); ++sk;
EToV(sk, All) = IVec(v2(k),m3(k),v1(k)); newBCType(sk,All) = IVec( 0 , b3, b1); ++sk;
}
break;
default:
// split all
EToV(sk, All) = IVec(m1(k),m2(k),m3(k)); newBCType(sk, All) = IVec( 0, 0, 0); ++sk;
EToV(sk, All) = IVec(v1(k),m1(k),m3(k)); newBCType(sk, All) = IVec(b1, 0, b3); ++sk;
EToV(sk, All) = IVec(v2(k),m2(k),m1(k)); newBCType(sk, All) = IVec(b2, 0, b1); ++sk;
EToV(sk, All) = IVec(v3(k),m3(k),m2(k)); newBCType(sk, All) = IVec(b3, 0, b2); ++sk;
break;
}
skend = sk;
// kold = [kold; k*ones(skend-skstart, 1)];
// element k is to be refined into (1:4) child elements.
// store parent element numbers in array "kold" to help
// with accessing parent vertex data during refinement.
KI.reset(skstart, skend-1); // ids of child elements
kold(KI) = k; // mark as children of element k
}
// Finished with edgerefineflag. Delete if OBJ_temp
if (edgerefineflag.get_mode() == OBJ_temp) {
delete (&edgerefineflag);
}
// renumber new nodes contiguously
// ids = unique([v1;v2;v3;m1;m2;m3]);
bool unique=true; IVec IDS, ids;
IDS = concat( concat(v1,v2,v3), concat(m1,m2,m3) );
ids = sort(IDS, unique);
Nv = ids.size();
int max_id = EToV.max_val();
umMSG(1, "max id in EToV is %d\n", max_id);
// M N nnz vals triplet
CSi newids(max_id,1, Nv, 1, 1 );
// newids = sparse(max(max(EToV)),1);
int i=0, j=1;
for (i=1; i<=Nv; ++i) {
// newids(ids)= (1:Nv);
newids.set1(ids(i),j, i); // load 1-based triplets
} // row col x
newids.compress(); // convert to csc form
// Matlab -----------------------------------------------
// v1 = newids(v1); v2 = newids(v2); v3 = newids(v3);
// m1 = newids(m1); m2 = newids(m2); m3 = newids(m3);
//-------------------------------------------------------
int KVi=v1.size(), KMi=m1.size();
// read from copies, overwrite originals
// 1. reload ids for new vertices
tvi = v1; for (i=1;i<=KVi;++i) {v1(i) = newids(tvi(i), 1);}
tvi = v2; for (i=1;i<=KVi;++i) {v2(i) = newids(tvi(i), 1);}
tvi = v3; for (i=1;i<=KVi;++i) {v3(i) = newids(tvi(i), 1);}
// 2. load ids for new (midpoint) vertices
tvi = m1; for (i=1;i<=KMi;++i) {m1(i) = newids(tvi(i), 1);}
tvi = m2; for (i=1;i<=KMi;++i) {m2(i) = newids(tvi(i), 1);}
tvi = m3; for (i=1;i<=KMi;++i) {m3(i) = newids(tvi(i), 1);}
VX.resize(Nv); VY.resize(Nv);
VX(v1) = x1; VX(v2) = x2; VX(v3) = x3;
VY(v1) = y1; VY(v2) = y2; VY(v3) = y3;
VX(m1) = mx1; VX(m2) = mx2; VX(m3) = mx3;
VY(m1) = my1; VY(m2) = my2; VY(m3) = my3;
if (newK != (sk-1)) {
umERROR("NDG2D::ConformingHrefine2D", "Inconsistent element count: expect %d, but sk = %d", newK, (sk-1));
} else {
K = newK; // sk-1;
}
// dumpIMat(EToV, "EToV (before)");
// EToV = newids(EToV);
for (j=1; j<=3; ++j) {
for (k=1; k<=K; ++k) {
EToV(k,j) = newids(EToV(k,j), 1);
}
}
#if (0)
dumpIMat(EToV, "EToV (after)");
// umERROR("Checking ids", "Nigel, check EToV");
#endif
BCType = newBCType;
Nv = VX.size();
// xold = x; yold = y;
StartUp2D();
#if (1)
OutputNodes(false); // volume nodes
//OutputNodes(true); // face nodes
//umERROR("Exiting early", "Check adapted {volume,face} nodes");
#endif
// allocate return object
int Nfields = Qin.num_cols();
DMat* tmpQ = new DMat(Np*K, Nfields, "newQ", OBJ_temp);
DMat& newQ = *tmpQ; // use a reference for syntax
// quick return, if no interpolation is required
if (Qin.size()<1) {
return newQ;
}
DVec rOUT(Np),sOUT(Np),xout,yout,xy1(2),xy2(2),xy3(2),tmp(2),rhs;
int ko=0,kv1=0,kv2=0,kv3=0,n=0; DMat A(2,2), interp;
DMat oldQ = const_cast<DMat&>(Qin);
for (k=1; k<=K; ++k)
{
ko = kold(k); xout = x(All,k); yout = y(All,k);
kv1=oldEToV(ko,1); kv2=oldEToV(ko,2); kv3=oldEToV(ko,3);
xy1.set(oldVX(kv1), oldVY(kv1));
xy2.set(oldVX(kv2), oldVY(kv2));
xy3.set(oldVX(kv3), oldVY(kv3));
A.set_col(1, xy2-xy1); A.set_col(2, xy3-xy1);
for (i=1; i<=Np; ++i) {
tmp.set(xout(i), yout(i));
rhs = 2.0*tmp - xy2 - xy3;
tmp = A|rhs;
rOUT(i) = tmp(1);
sOUT(i) = tmp(2);
}
KI.reset (Np*(k -1)+1, Np*k ); // nodes in new element k
KIo.reset(Np*(ko-1)+1, Np*ko); // nodes in old element ko
interp = Vandermonde2D(N, rOUT, sOUT)*invV;
for (n=1; n<=Nfields; ++n)
{
//newQ(:,k,n)= interp* Q(:,ko,n);
//DVec tm1 = interp*oldQ(KIo,n);
//dumpDVec(tm1, "tm1");
newQ(KI,n) = interp*oldQ(KIo,n);
}
}
return newQ;
}
//---------------------------------------------------------
DVec& NDG2D::PoissonIPDGbc2D
(DVec& ubc, //[in]
DVec& qbc //[in]
)
//---------------------------------------------------------
{
// function [OP] = PoissonIPDGbc2D()
// Purpose: Set up the discrete Poisson matrix directly
// using LDG. The operator is set up in the weak form
// build DG derivative matrices
int max_OP = (K*Np*Np*(1+Nfaces));
// initialize parameters
DVec faceR("faceR"), faceS("faceS");
DMat V1D("V1D"), Dx("Dx"),Dy("Dy"), Dn1("Dn1"), mmE_Fm1("mmE(:,Fm1)");
IVec Fm("Fm"), Fm1("Fm1"), fidM("fidM");
double lnx=0.0,lny=0.0,lsJ=0.0,hinv=0.0,gtau=0.0;
int i=0,k1=0,f1=0,id=0;
IVec i1_Nfp = Range(1,Nfp);
double N1N1 = double((N+1)*(N+1));
// build local face matrices
DMat massEdge[4]; // = zeros(Np,Np,Nfaces);
for (i=1; i<=Nfaces; ++i) {
massEdge[i].resize(Np,Np);
}
// face mass matrix 1
Fm = Fmask(All,1); faceR = r(Fm);
V1D = Vandermonde1D(N, faceR);
massEdge[1](Fm,Fm) = inv(V1D*trans(V1D));
// face mass matrix 2
Fm = Fmask(All,2); faceR = r(Fm);
V1D = Vandermonde1D(N, faceR);
massEdge[2](Fm,Fm) = inv(V1D*trans(V1D));
// face mass matrix 3
Fm = Fmask(All,3); faceS = s(Fm);
V1D = Vandermonde1D(N, faceS);
massEdge[3](Fm,Fm) = inv(V1D*trans(V1D));
// build DG right hand side
DVec* pBC = new DVec(Np*K, "bc", OBJ_temp);
DVec& bc = (*pBC); // reference, for syntax
////////////////////////////////////////////////////////////////
umMSG(1, "\n ==> {OP} assembly [bc]: ");
for (k1=1; k1<=K; ++k1)
{
if (! (k1%100)) { umMSG(1, "%d, ",k1); }
// rows1 = outer(Range((k1-1)*Np+1,k1*Np), Ones(NGauss));
// Build element-to-element parts of operator
for (f1=1; f1<=Nfaces; ++f1)
{
if (BCType(k1,f1))
{
////////////////////////added by Kevin ///////////////////////////////
Fm1 = Fmask(All,f1);
fidM = (k1-1)*Nfp*Nfaces + (f1-1)*Nfp + i1_Nfp;
id = 1+(f1-1)*Nfp + (k1-1)*Nfp*Nfaces;
lnx = nx(id); lny = ny(id);
lsJ = sJ(id); hinv = Fscale(id);
Dx = rx(1,k1)*Dr + sx(1,k1)*Ds;
Dy = ry(1,k1)*Dr + sy(1,k1)*Ds;
Dn1 = lnx*Dx + lny*Dy;
//mmE = lsJ*massEdge(:,:,f1);
//bc(All,k1) += (gtau*mmE(All,Fm1) - Dn1'*mmE(All,Fm1))*ubc(fidM);
mmE_Fm1 = massEdge[f1](All,Fm1); mmE_Fm1 *= lsJ;
gtau = 10*N1N1*hinv; // set penalty scaling
//bc(All,k1) += (gtau*mmE_Fm1 - trans(Dn1)*mmE_Fm1) * ubc(fidM);
switch(BCType(k1,f1)){
case BC_Dirichlet:
bc(Np*(k1-1)+Range(1,Np)) += (gtau*mmE_Fm1 - trans(Dn1)*mmE_Fm1)*ubc(fidM);
break;
case BC_Neuman:
bc(Np*(k1-1)+Range(1,Np)) += mmE_Fm1*qbc(fidM);
break;
default:
std::cout<<"warning: boundary condition is incorrect"<<std::endl;
}
}
}
}
return bc;
}
void NDG2D::PoissonIPDGbc2D(
CSd& spOP //[out] sparse operator
)
{
// function [OP] = PoissonIPDGbc2D()
// Purpose: Set up the discrete Poisson matrix directly
// using LDG. The operator is set up in the weak form
// build DG derivative matrices
int max_OP = (K*Np*Np*(1+Nfaces));
//initialize parameters
DVec faceR("faceR"), faceS("faceS");
IVec Fm("Fm"), Fm1("Fm1"), fidM("fidM");
DMat V1D("V1D"); int i=0;
// build local face matrices
DMat massEdge[4]; // = zeros(Np,Np,Nfaces);
for (i=1; i<=Nfaces; ++i) {
massEdge[i].resize(Np,Np);
}
// face mass matrix 1
Fm = Fmask(All,1); faceR = r(Fm);
V1D = Vandermonde1D(N, faceR);
massEdge[1](Fm,Fm) = inv(V1D*trans(V1D));
// face mass matrix 2
Fm = Fmask(All,2); faceR = r(Fm);
V1D = Vandermonde1D(N, faceR);
massEdge[2](Fm,Fm) = inv(V1D*trans(V1D));
// face mass matrix 3
Fm = Fmask(All,3); faceS = s(Fm);
V1D = Vandermonde1D(N, faceS);
massEdge[3](Fm,Fm) = inv(V1D*trans(V1D));
//continue initialize parameters
DMat Dx("Dx"),Dy("Dy"), Dn1("Dn1"), mmE_Fm1("mmE(:,Fm1)");
double lnx=0.0,lny=0.0,lsJ=0.0,hinv=0.0,gtau=0.0;
int k1=0,f1=0,id=0;
IVec i1_Nfp = Range(1,Nfp);
double N1N1 = double((N+1)*(N+1));
// "OP" triplets (i,j,x), extracted to {Ai,Aj,Ax}
IVec OPi(max_OP),OPj(max_OP), Ai,Aj; DVec OPx(max_OP), Ax;
IMat rows1, cols1; Index1D entries; DMat OP11(Np,Nfp, 0.0);
// global node numbering
entries.reset(1,Np*Nfp);
cols1 = outer(Ones(Np), Range(1,Nfp));
umMSG(1, "\n ==> {OP} assembly [bc]: ");
for (k1=1; k1<=K; ++k1)
{
if (! (k1%100)) { umMSG(1, "%d, ",k1); }
rows1 = outer(Range((k1-1)*Np+1,k1*Np), Ones(Nfp));
// Build element-to-element parts of operator
for (f1=1; f1<=Nfaces; ++f1)
{
if (BCType(k1,f1))
{
////////////////////////added by Kevin ///////////////////////////////
Fm1 = Fmask(All,f1);
fidM = (k1-1)*Nfp*Nfaces + (f1-1)*Nfp + i1_Nfp;
id = 1+(f1-1)*Nfp + (k1-1)*Nfp*Nfaces;
lnx = nx(id); lny = ny(id);
lsJ = sJ(id); hinv = Fscale(id);
Dx = rx(1,k1)*Dr + sx(1,k1)*Ds;
Dy = ry(1,k1)*Dr + sy(1,k1)*Ds;
Dn1 = lnx*Dx + lny*Dy;
//mmE = lsJ*massEdge(:,:,f1);
//bc(All,k1) += (gtau*mmE(All,Fm1) - Dn1'*mmE(All,Fm1))*ubc(fidM);
mmE_Fm1 = massEdge[f1](All,Fm1); mmE_Fm1 *= lsJ;
gtau = 10*N1N1*hinv; // set penalty scaling
//bc(All,k1) += (gtau*mmE_Fm1 - trans(Dn1)*mmE_Fm1) * ubc(fidM);
switch(BCType(k1,f1)){
case BC_Dirichlet:
OP11 = gtau*mmE_Fm1 - trans(Dn1)*mmE_Fm1;
break;
case BC_Neuman:
OP11 = mmE_Fm1;
break;
default:
std::cout<<"warning: boundary condition is incorrect"<<std::endl;
}
OPi(entries)=rows1; OPj(entries)=cols1; OPx(entries)=OP11;
entries += (Np*Nfp);
}
cols1 += Nfp;
}
}
umMSG(1, "\n ==> {OPbc} to sparse\n");
entries.reset(1, entries.hi()-(Np*Nfp));
// extract triplets from large buffers
Ai=OPi(entries); Aj=OPj(entries); Ax=OPx(entries);
// These arrays can be HUGE, so force deallocation
OPi.Free(); OPj.Free(); OPx.Free();
// return 0-based sparse result
Ai -= 1; Aj -= 1;
//-------------------------------------------------------
// This operator is not symmetric, and will NOT be
// factorised, only used to create reference RHS's:
//
// refrhsbcPR = spOP1 * bcPR;
// refrhsbcUx = spOP2 * bcUx;
// refrhsbcUy = spOP2 * bcUy;
//
// Load ALL elements (both upper and lower triangles):
//-------------------------------------------------------
spOP.load(Np*K, Nfp*Nfaces*K, Ai,Aj,Ax, sp_All,false, 1e-15,true);
Ai.Free(); Aj.Free(); Ax.Free();
umMSG(1, " ==> {OPbc} ready.\n");
#if (1)
// check on original estimates for nnx
umMSG(1, " ==> max_OP: %12d\n", max_OP);
umMSG(1, " ==> nnz_OP: %12d\n", entries.hi());
#endif
}
