std::string TCASTable::toPVS(int prec) const {
std::string s = "(# ";
s += "TAU := (: "+Fm1(TAU[0]);
for (int i=1; i < 7; i++) {
s += ", "+Fm1(TAU[i]);
}
s += " :), TCOA := (: "+Fm1(TCOA[0]);
for (int i=1; i < 7; i++) {
s += ", "+Fm1(TCOA[i]);
}
s += " :), DMOD := (: "+FmPrecision(DMOD[0],prec);
for (int i=1; i < 7; i++) {
s += ", "+FmPrecision(DMOD[i],prec);
}
s += " :), ZTHR := (: "+FmPrecision(ZTHR[0],prec);
for (int i=1; i < 7; i++) {
s += ", "+FmPrecision(ZTHR[i],prec);
}
s += " :), HMD := (: "+FmPrecision(HMD[0],prec);
for (int i=1; i < 7; i++) {
s += ", "+FmPrecision(HMD[i],prec);
}
s += " :), HMDFilter := ";
s += (HMDFilter ? "TRUE" : "FALSE");
return s + " #)";
}
Float operator() (
Fun &F ,
const FloatVector &a ,
const FloatVector &b ,
const SizeVector &n ,
const SizeVector &p ,
Float &e )
{ Float r;
typedef IntegrateLast<
Fun ,
SizeVector ,
FloatVector ,
Float > IntegrateOne;
IntegrateOne Fm1(&F, m-1, a, b, n, p);
RombergMul<
IntegrateOne,
SizeVector ,
FloatVector ,
m-1 > RombergMulM1;
Fm1.ClearEsum();
Fm1.ClearEcount();
r = RombergMulM1(Fm1, a, b, n, p, e);
size_t i, j;
Float prod = 1;
size_t pow2 = 1;
for(i = 0; i < m-1; i++)
{ prod *= (b[i] - a[i]);
for(j = 0; j < (n[i] - 1); j++)
pow2 *= 2;
}
assert( Fm1.GetEcount() == (pow2+1) );
e = e + Fm1.GetEsum() * prod / Fm1.GetEcount();
return r;
}
//---------------------------------------------------------
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;
}
std::string WCVTable::toPVS(int prec) const {
return "(# DTHR := "+FmPrecision(DTHR,prec)+", ZTHR := "+FmPrecision(ZTHR,prec)+
", TTHR := "+Fm1(TTHR)+", TCOA := "+Fm1(TCOA)+" #)";
}
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
}
