inline void TPZQuadraticQuad::GradX(const TPZFMatrix<REAL> &nodes,TPZVec<T> &loc, TPZFMatrix<T> &gradx){
gradx.Resize(3,2);
gradx.Zero();
int nrow = nodes.Rows();
int ncol = nodes.Cols();
#ifdef PZDEBUG
if(nrow != 3 || ncol != 8){
std::cout << "Objects of incompatible lengths, gradient cannot be computed." << std::endl;
std::cout << "nodes matrix must be 3x8." << std::endl;
DebugStop();
}
#endif
TPZFNMatrix<3,T> phi(NNodes,1);
TPZFNMatrix<6,T> dphi(2,NNodes);
TShape(loc,phi,dphi);
for(int i = 0; i < NNodes; i++)
{
for(int j = 0; j < 3; j++)
{
gradx(j,0) += nodes.GetVal(j,i)*dphi(0,i);
gradx(j,1) += nodes.GetVal(j,i)*dphi(1,i);
}
}
}
void TPBrCellMarx::ExtractMatrix(TPZManVector<REAL> &input, TPZFMatrix<REAL> &output)
{
output.Resize(input.NElements(), 1);
int i;
for (i=0; i<input.NElements(); i++) {
output(i,0) = input[i];
}
}
void SolExataU(const TPZVec<REAL> &pt, TPZVec<STATE> &solU, TPZFMatrix<STATE> &GradU){
double x = pt[0];
GradU.Resize(2, 1);
solU[0]= 4.*x - 4.*x*x;
GradU(0,0) = 4.-8.*x;
GradU(1,0) = 0.;
}
void SolSuave(const TPZVec<REAL> &loc, TPZVec<STATE> &u, TPZFMatrix<STATE> &du){
const REAL x = loc[0];
const REAL y = loc[1];
const REAL sol = /*x*(1.-x)*y*(1.-y);*/sin(M_PI*x)*sin(M_PI*y);
u[0] = sol;
du.Resize(2, 1);
du(0,0) = /*(1. - x)*(1. - y)*y - x*(1. - y)*y;*/M_PI*cos(M_PI*x)*sin(M_PI*y);
du(1,0) = /*(1. - x)*x*(1. - y) - (1. - x)*x*y;*/M_PI*cos(M_PI*y)*sin(M_PI*x);
}
void TPBrCellMarx::ExtractMatrix(TPZManVector<TFad<TPBrCellMarx::NUMVARS,REAL> > &input, TPZFMatrix<REAL> &output)
{
output.Resize(NUMVARS, NUMVARS);
int i,j;
for (i=0; i<NUMVARS; i++) {
for (j=0; j<NUMVARS; j++) {
output(i,j) = input[i].d(j);
}
}
}
void SolExataP(const TPZVec<REAL> &pt, TPZVec<STATE> &solP, TPZFMatrix<STATE> &GradP){
REAL x = pt[0];
REAL y = pt[1];
GradP.Resize(2, 1);
solP[0]= sin(M_PI*x)*sin(M_PI*y);
GradP(0,0) = M_PI*cos(M_PI*x)*sin(M_PI*y);
GradP(1,0) = M_PI*cos(M_PI*y)*sin(M_PI*x);
}
void TPZGeoTriangle::Jacobian(TPZFMatrix<REAL> & coord, TPZVec<REAL> ¶m,TPZFMatrix<REAL> &jacobian,TPZFMatrix<REAL> &axes,REAL &detjac,TPZFMatrix<REAL> &jacinv) {
int spacedim = coord.Rows();
jacobian.Resize(2,2);
axes.Resize(2,3);
jacinv.Resize(2,2);
TPZFNMatrix<3> phi(3,1);
TPZFNMatrix<6> dphi(2,3),axest(3,2);
jacobian.Zero();
Shape(param,phi,dphi);
TPZFNMatrix<6> VecMatrix(3,2,0.);
for(int i = 0; i < 3; i++) {
for(int j = 0; j < spacedim; j++) {
VecMatrix(j,0) += coord(j,i)*dphi(0,i);
VecMatrix(j,1) += coord(j,i)*dphi(1,i);
}
}
VecMatrix.GramSchmidt(axest,jacobian);
axest.Transpose(&axes);
detjac = jacobian(0,0)*jacobian(1,1)-jacobian(1,0)*jacobian(0,1);
if(IsZero(detjac))
{
std::stringstream sout;
sout << "Singular Jacobian " << detjac;
LOGPZ_ERROR(logger, sout.str())
detjac = ZeroTolerance();
}
if(detjac)
{
jacinv(0,0) = jacobian(1,1)/detjac;
jacinv(1,1) = jacobian(0,0)/detjac;
jacinv(0,1) = -jacobian(0,1)/detjac;
jacinv(1,0) = -jacobian(1,0)/detjac;
}
else
{
jacinv.Zero();
}
}
void EstadoAd(const TPZVec<REAL> &loc, TPZVec<STATE> &u, TPZFMatrix<STATE> &du){
const REAL x = loc[0];
const REAL y = loc[1];
u.Resize(1, 0.);
du.Resize(3, 1.);
du(0,0)=du(1,0)=du(2,0)=0.;
//const REAL alpha=0.001;
const REAL sol = 10.*x*y*(1-x)*(1-y);
u[0] = sol;
}
void OOPParMatrix::BuildMe(int size, TPZMatrix<REAL> * matrix, TPZFMatrix<REAL> & vU)
{
matrix->Resize(size, size);
int i, j;
vU.Resize(size, 1);
for(i = 0; i < size; i++)
{
double value;
for(j=0; j < size; j++)
{
value = rand()/1e8;
matrix->Put(i, j, value);
}
vU.Put(i, 0,value * 1.4);
}
}
void TPZErrorIndicator::Sort(TPZFMatrix &error, TPZFMatrix &perm) {
int i,j,k;
int imin = 0;
int imax = error.Rows();
perm.Resize(imax,error.Cols());
for (i=0;i<imax;i++)
for (j=0;j<error.Cols();j++) perm(i,j) = i;
for(i=imin; i<imax; i++) {
for(j=i+1; j<imax; j++) {
for (k=0;k<error.Cols();k++){
if(error((int)perm(i,k)) < error((int)perm(j,k))) {
int kp = (int) perm(i,k);
perm(i,k) = perm(j,k);
perm(j,k) = kp;
}
}
}
}
}
bool TPZPrism::MapToSide(int side, TPZVec<T> &InternalPar, TPZVec<T> &SidePar, TPZFMatrix<T> &JacToSide) {
double zero = 1.E-5;
T qsi = InternalPar[0];
T eta = InternalPar[1];
T zeta = InternalPar[2];
bool regularmap = true;
switch(side)
{
case 0:
case 1:
case 2:
case 3:
case 4:
case 5:
{
SidePar.Resize(0); JacToSide.Resize(0,0);
break;
}
case 6://1D
SidePar.Resize(1);
JacToSide.Resize(1,3);
if(fabs((T)(eta-1.)) < zero)
{
SidePar[0] = 0.;
JacToSide(0,0) = 1.;
JacToSide(0,1) = 1.;
JacToSide(0,2) = 0.;
regularmap = false;
}
else
{
SidePar[0] = 2.*qsi/(1.-eta) - 1.;
JacToSide(0,0) = 2./(1.-eta); JacToSide(0,1) = 2.*qsi/((1.-eta)*(1.-eta)); JacToSide(0,2) = 0.;
}
break;
case 7://1D
SidePar.Resize(1); JacToSide.Resize(1,3);
if(fabs((T)(qsi+eta)) < zero)
{
SidePar[0] = 0.;
JacToSide(0,0) = 1.;
JacToSide(0,1) = 1.;
JacToSide(0,2) = 0.;
regularmap = false;
}
else
{
SidePar[0] = 1. - 2.*qsi/(qsi + eta);
JacToSide(0,0) = -2.*eta/((qsi+eta)*(qsi+eta)); JacToSide(0,1) = 2.*qsi/((qsi+eta)*(qsi+eta)); JacToSide(0,2) = 0.;
}
break;
case 8://1D
SidePar.Resize(1); JacToSide.Resize(1,3);
if(fabs((T)(qsi-1.)) < zero)
{
SidePar[0] = 0.;
JacToSide(0,0) = 1.; JacToSide(0,1) = 1.; JacToSide(0,2) = 0.;
regularmap = false;
}
else
{
SidePar[0] = 1. - 2.*eta/(1.-qsi);
JacToSide(0,0) = -2.*eta/((1.-qsi)*(1.-qsi)); JacToSide(0,1) = -2./(1.-qsi); JacToSide(0,2) = 0.;
}
break;
case 9://1D
SidePar.Resize(1); JacToSide.Resize(1,3);
SidePar[0] = zeta;
JacToSide(0,0) = 0.; JacToSide(0,1) = 0.; JacToSide(0,2) = 1.;
break;
case 10://1D
SidePar.Resize(1); JacToSide.Resize(1,3);
SidePar[0] = zeta;
JacToSide(0,0) = 0.; JacToSide(0,1) = 0.; JacToSide(0,2) = 1.;
break;
case 11://1D
SidePar.Resize(1); JacToSide.Resize(1,3);
SidePar[0] = zeta;
JacToSide(0,0) = 0.; JacToSide(0,1) = 0.; JacToSide(0,2) = 1.;
break;
case 12://1D
SidePar.Resize(1); JacToSide.Resize(1,3);
if(fabs((T)(eta-1.)) < zero)
{
SidePar[0] = 0.;
JacToSide(0,0) = 1.; JacToSide(0,1) = 1.; JacToSide(0,2) = 0.;
regularmap = false;
}
else
{
SidePar[0] = 2.*qsi/(1.-eta) - 1.;
JacToSide(0,0) = 2./(1.-eta); JacToSide(0,1) = 2.*qsi/((1.-eta)*(1.-eta)); JacToSide(0,2) = 0.;
}
break;
case 13://1D
SidePar.Resize(1); JacToSide.Resize(1,3);
if(fabs((T)(qsi+eta)) < zero)
{
SidePar[0] = 0.;
JacToSide(0,0) = 1.; JacToSide(0,1) = 1.; JacToSide(0,2) = 0.;
regularmap = false;
}
else
{
SidePar[0] = 1. - 2.*qsi/(qsi + eta);
JacToSide(0,0) = -2.*eta/((qsi+eta)*(qsi+eta)); JacToSide(0,1) = 2.*qsi/((qsi+eta)*(qsi+eta)); JacToSide(0,2) = 0.;
}
break;
case 14://1D
SidePar.Resize(1); JacToSide.Resize(1,3);
if(fabs((T)(qsi-1.)) < zero)
{
SidePar[0] = 0.;
JacToSide(0,0) = 1.; JacToSide(0,1) = 1.; JacToSide(0,2) = 0.;
regularmap = false;
}
else
{
SidePar[0] = 1. - 2.*eta/(1.-qsi);
JacToSide(0,0) = -2.*eta/((1.-qsi)*(1.-qsi)); JacToSide(0,1) = -2./(1.-qsi); JacToSide(0,2) = 0.;
}
break;
case 15://2D - triangle
SidePar.Resize(2); JacToSide.Resize(2,3);
SidePar[0] = qsi; SidePar[1] = eta;
JacToSide(0,0) = 1.; JacToSide(0,1) = 0.; JacToSide(0,2) = 0.;
JacToSide(1,0) = 0.; JacToSide(1,1) = 1.; JacToSide(1,2) = 0.;
break;
case 16://2D - quadrilateral
SidePar.Resize(2); JacToSide.Resize(2,3);
if(fabs((T)(eta-1.)) < zero)
{
SidePar[0] = 0.; SidePar[1] = zeta;
JacToSide(0,0) = 1.; JacToSide(0,1) = 1.; JacToSide(0,2) = 0.;
JacToSide(1,0) = 0.; JacToSide(1,1) = 0.; JacToSide(1,2) = 1.;
regularmap = false;
}
else
{
SidePar[0] = 2.*qsi/(1.-eta) - 1.; SidePar[1] = zeta;
JacToSide(0,0) = 2./(1.-eta); JacToSide(0,1) = 2.*qsi/((1.-eta)*(1.-eta)); JacToSide(0,2) = 0.;
JacToSide(1,0) = 0.; JacToSide(1,1) = 0.; JacToSide(0,2) = 1.;
}
break;
case 17://2D - quadrilateral
SidePar.Resize(2); JacToSide.Resize(2,3);
if(fabs((T)(qsi+eta)) < zero)
{
SidePar[0] = 0.; SidePar[1] = zeta;
JacToSide(0,0) = 1.; JacToSide(0,1) = 1.; JacToSide(0,2) = 0.;
JacToSide(1,0) = 0.; JacToSide(1,1) = 0.; JacToSide(1,2) = 1.;
regularmap = false;
}
else
{
SidePar[0] = 1. - 2.*qsi/(qsi + eta); SidePar[1] = zeta;
JacToSide(0,0) = -2.*eta/((qsi+eta)*(qsi+eta)); JacToSide(0,1) = 2.*qsi/((qsi+eta)*(qsi+eta)); JacToSide(0,2) = 0.;
JacToSide(1,0) = 0.; JacToSide(1,1) = 0.; JacToSide(0,2) = 1.;
}
break;
case 18://2D - quadrilateral
SidePar.Resize(2); JacToSide.Resize(2,3);
if(fabs((T)(qsi-1.)) < zero)
{
SidePar[0] = 0.; SidePar[1] = zeta;
JacToSide(0,0) = 1.; JacToSide(0,1) = 1.; JacToSide(0,2) = 0.;
JacToSide(1,0) = 0.; JacToSide(1,1) = 0.; JacToSide(1,2) = 1.;
regularmap = false;
}
else
{
SidePar[0] = 1. - 2.*eta/(1.-qsi); SidePar[1] = zeta;
JacToSide(0,0) = -2.*eta/((1.-qsi)*(1.-qsi)); JacToSide(0,1) = -2./(1.-qsi); JacToSide(0,2) = 0.;
JacToSide(1,0) = 0.; JacToSide(1,1) = 0.; JacToSide(0,2) = 1.;
}
break;
case 19://2D - triangle
SidePar.Resize(2); JacToSide.Resize(2,3);
SidePar[0] = qsi; SidePar[1] = eta;
JacToSide(0,0) = 1.; JacToSide(0,1) = 0.; JacToSide(0,2) = 0.;
JacToSide(1,0) = 0.; JacToSide(1,1) = 1.; JacToSide(1,2) = 0.;
break;
case 20:
SidePar = InternalPar;
JacToSide.Resize(3, 3);
JacToSide.Identity();
break;
}
if(side > 20)
{
cout << "Cant compute MapToSide method in TPZGeoPrism class!\nParameter (SIDE) must be between 6 and 19!\nMethod Aborted!\n";
DebugStop();
}
return regularmap;
}
bool TPZPoint::MapToSide(int side, TPZVec<T> &InternalPar, TPZVec<T> &SidePar, TPZFMatrix<T> &JacToSide) {
SidePar.Resize(0); JacToSide.Resize(0,0);
return true;
}
void TPZGeoTriangle::VecHdiv(TPZFMatrix<REAL> & coord, TPZFMatrix<REAL> & fNormalVec,TPZVec<int> &fVectorSide) {
if(coord.Rows()!=3)
{
cout<< "Erro na dimens�o das linhas de coord"<< endl;
}
if(coord.Cols()!=3)
{
cout<< "Erro na dimens�o das colunas de coord"<< endl;
}
TPZVec<REAL> p1(3), p2(3), p3(3),result(3);
for(int j=0; j<3; j++)
{
p1[j]=coord(j,0);
p2[j]=coord(j,1);
p3[j]=coord(j,2);
}
fNormalVec.Resize(14, 3);
fVectorSide.Resize(14);
int count=0;
//primeira face
for(int j=0; j<3; j++) //v0
{
fNormalVec(0,j) = coord(j,0)- coord(j,2);
}
fVectorSide[count]=0;
count++;
for(int j=0; j<3; j++) //v1
{
fNormalVec(1,j) = coord(j,1)- coord(j,2);
}
fVectorSide[count]=1;
count++;
//v2
ComputeNormal(p1,p2,p3,result);
fNormalVec(2,0) = -result[0];
fNormalVec(2,1) = -result[1];
fNormalVec(2,2) = -result[2];
fVectorSide[count]=3;
count++;
//segunda face
for(int j=0; j<3; j++) //v3
{
fNormalVec(3,j) = coord(j,1)- coord(j,0);
}
fVectorSide[count]=1;
count++;
for(int j=0; j<3; j++) //v4
{
fNormalVec(4,j) = coord(j,2)- coord(j,0);
}
fVectorSide[count]=2;
count++;
//v5
ComputeNormal(p2,p3,p1,result);
fNormalVec(5,0) = -result[0];
fNormalVec(5,1) = -result[1];
fNormalVec(5,2) = -result[2];
fVectorSide[count]=4;
count++;
//terceira face
for(int j=0; j<3; j++) //v6
{
fNormalVec(6,j) = coord(j,2)- coord(j,1);
}
fVectorSide[count]=2;
count++;
for(int j=0; j<3; j++) //v7
{
fNormalVec(7,j) = coord(j,0)- coord(j,1);
}
fVectorSide[count]=0;
count++;
//v8
ComputeNormal(p3,p1,p2,result);
fNormalVec(8,0) = -result[0];
fNormalVec(8,1) = -result[1];
fNormalVec(8,2) = -result[2];
fVectorSide[count]=5;
count++;
// internos tangentes
for(int j=0; j<3; j++) //v9
{
fNormalVec(9,j) = coord(j,1)- coord(j,0);
}
fVectorSide[count]=3;
count++;
for(int j=0; j<3; j++) //v10
{
fNormalVec(10,j) = coord(j,2)- coord(j,1);
}
fVectorSide[count]=4;
count++;
for(int j=0; j<3; j++) //v11
{
fNormalVec(11,j) = coord(j,0)- coord(j,2);
}
fVectorSide[count]=5;
count++;
//internos meio
TPZVec<REAL> midle(3,0.);
midle[0]=(1./3.)*(coord(0,2)+coord(0,0)+coord(0,1));
midle[1]=(1./3.)*(coord(1,2)+coord(1,0)+coord(1,1));
midle[2]=(1./3.)*(coord(2,2)+coord(2,0)+coord(2,1));
TPZFMatrix<REAL> jacobian;
TPZFMatrix<REAL> axes;
REAL detjac;
TPZFMatrix<REAL> jacinv;
Jacobian(coord,midle,jacobian,axes,detjac,jacinv);
fNormalVec(12,0)=axes(0,0);
fNormalVec(12,1)=axes(0,1);
fNormalVec(12,2)=axes(0,2);
fNormalVec(13,0)=axes(1,0);
fNormalVec(13,1)=axes(1,1);
fNormalVec(13,2)=axes(1,2);
fVectorSide[count]=6;
fVectorSide[count+1]=6;
//normaliza��o
for(int k=0; k<14; k++)
{
REAL temp=0.;
temp=sqrt( fNormalVec(k,0)*fNormalVec(k,0) + fNormalVec(k,1)*fNormalVec(k,1) + fNormalVec(k,2)*fNormalVec(k,2));
fNormalVec(k,0) *=1./temp;
fNormalVec(k,1) *=1./temp;
}
// produto normal == 1
for(int kk=0; kk<3; kk++)
{
REAL temp1=0.;
REAL temp2=0.;
temp1 = fNormalVec(kk*3,0)*fNormalVec(kk*3+2,0) + fNormalVec(kk*3,1)*fNormalVec(kk*3+2,1);
temp2 = fNormalVec(kk*3+1,0)*fNormalVec(kk*3+2,0) + fNormalVec(kk*3+1,1)*fNormalVec(kk*3+2,1);
fNormalVec(kk*3,0) *=1./temp1;
fNormalVec(kk*3,1) *=1./temp1;
fNormalVec(kk*3+1,0) *=1./temp2;
fNormalVec(kk*3+1,1) *=1./temp2;
}
#ifdef LOG4CXX
{
std::stringstream sout;
fNormalVec.Print("fNormalVec", sout);
LOGPZ_DEBUG(logger,sout.str())
}
#endif
}
bool TPZGeoTriangle::MapToSide(int side, TPZVec<REAL> &InternalPar, TPZVec<REAL> &SidePar, TPZFMatrix<REAL> &JacToSide) {
double zero = 1.E-5;
REAL qsi = InternalPar[0];
REAL eta = InternalPar[1];
SidePar.Resize(1);
JacToSide.Resize(1,2);
if((qsi + eta - 1.) > 1.e-5 || qsi < -1.e-5 || eta < -1.e-5)
{
cout << "Point (qsi,eta) = (" << qsi << "," << eta << ") is out of TPZGeoTriangle Master Element Range!\n";
cout << "See TPZGeoTriangle::MapToSide() method!\n";
DebugStop();
}
if(qsi < 0.) qsi = 0.;
if(eta < 0.) eta = 0.;
if(qsi+eta > 1.)
{
REAL qsieta = 1.-qsi-eta;
qsi += qsieta/2.;
eta += qsieta/2.;
}
bool regularmap = true;
switch(side)
{
case 3:
if(fabs(eta - 1.) < zero)
{
SidePar[0] = 0.;
JacToSide(0,0) = 0.;
JacToSide(0,1) = 0.;
regularmap = false;
}
else
{
SidePar[0] = 2.*qsi/(1.-eta) - 1.;
JacToSide(0,0) = 2./(1.-eta);
JacToSide(0,1) = 2.*qsi/((1.-eta)*(1.-eta));
}
break;
case 4:
if(qsi+eta < zero)
{
SidePar[0] = 0.;
JacToSide(0,0) = 0.;
JacToSide(0,1) = 0.;
regularmap = false;
}
else
{
SidePar[0] = 1. - 2.*qsi/(qsi + eta);
JacToSide(0,0) = -2.*eta/((qsi+eta)*(qsi+eta));
JacToSide(0,1) = 2.*qsi/((qsi+eta)*(qsi+eta));
}
break;
case 5:
if(fabs(qsi - 1.) < zero)
{
SidePar[0] = 0.;
JacToSide(0,0) = 0.;
JacToSide(0,1) = 0.;
regularmap = false;
}
else
{
SidePar[0] = 1. - 2.*eta/(1.-qsi);
JacToSide(0,0) = -2.*eta/((1.-qsi)*(1.-qsi));
JacToSide(0,1) = -2./(1.-qsi);
}
break;
}
if(side < 3 || side > 5)
{
cout << "Cant compute MapToSide method in TPZGeoTriangle class!\nParameter (SIDE) must be 3, 4 or 5!\nMethod Aborted!\n";
DebugStop();
}
return regularmap;
}
/**
* Calcula os valores das funcoes de forma e suas derivadas
* @point ponto onde calcular as funcoes de forma
* @phi valores das funcoes de forma
* @dphi valores das derivadas das funcoes de forma
*/
void TElemento0d::Shape(std::vector<double> &point, std::vector<double> &phi, TPZFMatrix &dphi)
{
phi.resize(1);
phi[0] = 1.;
dphi.Resize(0,1);
}
void TElemento0d::Jacobian(std::vector< double >& point, TPZFMatrix& jacobian, TPZFMatrix& jacinv, double &detjac, TMalha& malha)
{
jacobian.Resize(0,0);
jacinv.Resize(0,0);
detjac = 1;
}
