//---------------------------------------------------------
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;
}
// GAUSS-LOBATTO QUADRATURE ALONG EDGE
void SetEdgeDataGL_Unst(const mesh& Mesh,
int NumQuadPoints,
int NumBasisOrder,
edge_data_Unst* EdgeData)
{
// Quick error check
if (NumQuadPoints<2 || NumQuadPoints>6 || NumBasisOrder<1 || NumBasisOrder>5)
{
printf(" \n");
printf(" Error in SetEdgeData_Unst.cpp \n");
printf(" NumQuadPoints must be 2,3,4,5, or 6.\n");
printf(" NumBasisOrder must be 1,2,3,4, or 5.\n");
printf(" NumQuadPoints = %i\n",NumQuadPoints);
printf(" NumBasisOrder = %i\n",NumBasisOrder);
printf("\n");
exit(1);
}
// ---------------------------------
// Set quadrature weights and points
// ---------------------------------
switch( NumQuadPoints )
{
case 2:
EdgeData->GL_wgts1d->set(1, 1.0 );
EdgeData->GL_wgts1d->set(2, 1.0 );
EdgeData->GL_xpts1d->set(1, 1.0 );
EdgeData->GL_xpts1d->set(2, -1.0 );
break;
case 3:
EdgeData->GL_wgts1d->set(1, onethird );
EdgeData->GL_wgts1d->set(2, 4.0*onethird );
EdgeData->GL_wgts1d->set(3, onethird );
EdgeData->GL_xpts1d->set(1, 1.0 );
EdgeData->GL_xpts1d->set(2, 0.0 );
EdgeData->GL_xpts1d->set(3, -1.0 );
break;
case 4:
EdgeData->GL_wgts1d->set(1, 0.5*onethird );
EdgeData->GL_wgts1d->set(2, 2.5*onethird );
EdgeData->GL_wgts1d->set(3, 2.5*onethird );
EdgeData->GL_wgts1d->set(4, 0.5*onethird );
EdgeData->GL_xpts1d->set(1, 1.0 );
EdgeData->GL_xpts1d->set(2, osq5 );
EdgeData->GL_xpts1d->set(3, -osq5 );
EdgeData->GL_xpts1d->set(4, -1.0 );
break;
case 5:
EdgeData->GL_wgts1d->set(1, 0.1 );
EdgeData->GL_wgts1d->set(2, 49.0/90.0 );
EdgeData->GL_wgts1d->set(3, 32.0/45.0 );
EdgeData->GL_wgts1d->set(4, 49.0/90.0 );
EdgeData->GL_wgts1d->set(5, 0.1 );
EdgeData->GL_xpts1d->set(1, 1.0 );
EdgeData->GL_xpts1d->set(2, sq3*osq7 );
EdgeData->GL_xpts1d->set(3, 0.0 );
EdgeData->GL_xpts1d->set(4, -sq3*osq7 );
EdgeData->GL_xpts1d->set(5, -1.0 );
break;
case 6:
EdgeData->GL_wgts1d->set(1, 0.2*onethird );
EdgeData->GL_wgts1d->set(2, (1.4 - 0.1*sq7)*onethird );
EdgeData->GL_wgts1d->set(3, (1.4 + 0.1*sq7)*onethird );
EdgeData->GL_wgts1d->set(4, (1.4 + 0.1*sq7)*onethird );
EdgeData->GL_wgts1d->set(5, (1.4 - 0.1*sq7)*onethird );
EdgeData->GL_wgts1d->set(6, 0.2*onethird );
EdgeData->GL_xpts1d->set(1, 1.0 );
EdgeData->GL_xpts1d->set(2, (1/21.0)*sqrt(147.0+42.0*sq7) );
EdgeData->GL_xpts1d->set(3, (1/21.0)*sqrt(147.0-42.0*sq7) );
EdgeData->GL_xpts1d->set(4, -(1/21.0)*sqrt(147.0-42.0*sq7) );
EdgeData->GL_xpts1d->set(5, -(1/21.0)*sqrt(147.0+42.0*sq7) );
EdgeData->GL_xpts1d->set(6, -1.0 );
break;
}
// ---------------------------------
// Legendre basis functions on the
// left and right of each edge
// ---------------------------------
const int NumEdges = Mesh.get_NumEdges();
const int NumBasisComps = (NumBasisOrder*(NumBasisOrder+1))/2;
dTensor1 xp1(3);
dTensor1 yp1(3);
dTensor1 xp2(3);
dTensor1 yp2(3);
dTensor1 xy1(2);
dTensor1 xy2(2);
dTensor1 mu1(NumBasisComps);
dTensor1 mu2(NumBasisComps);
for (int i=1; i<=NumEdges; i++)
{
// Get edge information
const double x1 = Mesh.get_edge(i,1);
const double y1 = Mesh.get_edge(i,2);
const double x2 = Mesh.get_edge(i,3);
const double y2 = Mesh.get_edge(i,4);
const int e1 = Mesh.get_eelem(i,1);
const int e2 = Mesh.get_eelem(i,2);
// Get element information about
// the two elements that meet at
// the current edge
const double Area1 = Mesh.get_area_prim(e1);
const double Area2 = Mesh.get_area_prim(e2);
for (int k=1; k<=3; k++)
{
xp1.set(k, Mesh.get_node(Mesh.get_tnode(e1,k),1) );
yp1.set(k, Mesh.get_node(Mesh.get_tnode(e1,k),2) );
xp2.set(k, Mesh.get_node(Mesh.get_tnode(e2,k),1) );
yp2.set(k, Mesh.get_node(Mesh.get_tnode(e2,k),2) );
}
const double xc1 = (xp1.get(1) + xp1.get(2) + xp1.get(3))/3.0;
const double yc1 = (yp1.get(1) + yp1.get(2) + yp1.get(3))/3.0;
const double xc2 = (xp2.get(1) + xp2.get(2) + xp2.get(3))/3.0;
const double yc2 = (yp2.get(1) + yp2.get(2) + yp2.get(3))/3.0;
// quadrature points on the edge
for (int m=1; m<=NumQuadPoints; m++)
{
// Take integration point s (in [-1,1])
// and map to physical domain
const double s = EdgeData->GL_xpts1d->get(m);
const double x = x1 + 0.5*(s+1.0)*(x2-x1);
const double y = y1 + 0.5*(s+1.0)*(y2-y1);
// Take physical point (x,y)
// and map into the coordinates
// of the two triangles that are
// adjacent to the current edge
xy1.set(1, ((yp1.get(3)-yp1.get(1))*(x-xc1)
+ (xp1.get(1)-xp1.get(3))*(y-yc1))/(2.0*Area1) );
xy1.set(2, ((yp1.get(1)-yp1.get(2))*(x-xc1)
+ (xp1.get(2)-xp1.get(1))*(y-yc1))/(2.0*Area1) );
xy2.set(1, ((yp2.get(3)-yp2.get(1))*(x-xc2)
+ (xp2.get(1)-xp2.get(3))*(y-yc2))/(2.0*Area2) );
xy2.set(2, ((yp2.get(1)-yp2.get(2))*(x-xc2)
+ (xp2.get(2)-xp2.get(1))*(y-yc2))/(2.0*Area2) );
// Evaluate monomials at locations xy1
double xi = xy1.get(1);
double xi2 = xi*xi;
double xi3 = xi*xi2;
double xi4 = xi*xi3;
double eta = xy1.get(2);
double eta2 = eta*eta;
double eta3 = eta*eta2;
double eta4 = eta*eta3;
switch( NumBasisOrder )
{
case 5: // fifth order
mu1.set(15, eta4 );
mu1.set(14, xi4 );
mu1.set(13, xi2*eta2 );
mu1.set(12, eta3*xi );
mu1.set(11, xi3*eta );
case 4: // fourth order
mu1.set(10, eta3 );
mu1.set(9, xi3 );
mu1.set(8, xi*eta2 );
mu1.set(7, eta*xi2 );
case 3: // third order
mu1.set(6, eta2 );
mu1.set(5, xi2 );
mu1.set(4, xi*eta );
case 2: // second order
mu1.set(3, eta );
mu1.set(2, xi );
case 1: // first order
mu1.set(1, 1.0 );
break;
}
// Evaluate monomials at locations xy2
xi = xy2.get(1);
xi2 = xi*xi;
xi3 = xi*xi2;
xi4 = xi*xi3;
eta = xy2.get(2);
eta2 = eta*eta;
eta3 = eta*eta2;
eta4 = eta*eta3;
switch( NumBasisOrder )
{
case 5: // fifth order
mu2.set(15, eta4 );
mu2.set(14, xi4 );
mu2.set(13, xi2*eta2 );
mu2.set(12, eta3*xi );
mu2.set(11, xi3*eta );
case 4: // fourth order
mu2.set(10, eta3 );
mu2.set(9, xi3 );
mu2.set(8, xi*eta2 );
mu2.set(7, eta*xi2 );
case 3: // third order
mu2.set(6, eta2 );
mu2.set(5, xi2 );
mu2.set(4, xi*eta );
case 2: // second order
mu2.set(3, eta );
mu2.set(2, xi );
case 1: // first order
mu2.set(1, 1.0 );
break;
}
// Finally, convert monomials to Legendre Polys
// on the two adjacent triangle
for (int k=1; k<=NumBasisComps; k++)
{
double tmp1 = 0.0;
double tmp2 = 0.0;
for (int j=1; j<=k; j++)
{
tmp1 = tmp1 + Mmat[k-1][j-1]*mu1.get(j);
tmp2 = tmp2 + Mmat[k-1][j-1]*mu2.get(j);
}
EdgeData->GL_phi_left->set(i,m,k, tmp1 );
EdgeData->GL_phi_right->set(i,m,k, tmp2 );
}
}
}
}
