void BoundaryLFIntegrator::AssembleRHSElementVect(
const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
int dof = el.GetDof();
shape.SetSize(dof); // vector of size dof
elvect.SetSize(dof);
elvect = 0.0;
const IntegrationRule *ir = IntRule;
if (ir == NULL)
{
int intorder = oa * el.GetOrder() + ob; // <----------
ir = &IntRules.Get(el.GetGeomType(), intorder);
}
for (int i = 0; i < ir->GetNPoints(); i++)
{
const IntegrationPoint &ip = ir->IntPoint(i);
Tr.SetIntPoint (&ip);
double val = Tr.Weight() * Q.Eval(Tr, ip);
el.CalcShape(ip, shape);
add(elvect, ip.weight * val, shape, elvect);
}
}
void BoundaryNormalLFIntegrator::AssembleRHSElementVect(
const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
int dim = el.GetDim()+1;
int dof = el.GetDof();
Vector nor(dim), Qvec;
shape.SetSize(dof);
elvect.SetSize(dof);
elvect = 0.0;
const IntegrationRule *ir = IntRule;
if (ir == NULL)
{
int intorder = oa * el.GetOrder() + ob; // <----------
ir = &IntRules.Get(el.GetGeomType(), intorder);
}
for (int i = 0; i < ir->GetNPoints(); i++)
{
const IntegrationPoint &ip = ir->IntPoint(i);
Tr.SetIntPoint(&ip);
CalcOrtho(Tr.Jacobian(), nor);
Q.Eval(Qvec, Tr, ip);
el.CalcShape(ip, shape);
elvect.Add(ip.weight*(Qvec*nor), shape);
}
}
void VectorFEBoundaryTangentLFIntegrator::AssembleRHSElementVect(
const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
int dof = el.GetDof();
DenseMatrix vshape(dof, 2);
Vector f_loc(3);
Vector f_hat(2);
elvect.SetSize(dof);
elvect = 0.0;
const IntegrationRule *ir = IntRule;
if (ir == NULL)
{
int intorder = 2*el.GetOrder(); // <----------
ir = &IntRules.Get(el.GetGeomType(), intorder);
}
for (int i = 0; i < ir->GetNPoints(); i++)
{
const IntegrationPoint &ip = ir->IntPoint(i);
Tr.SetIntPoint(&ip);
f.Eval(f_loc, Tr, ip);
Tr.Jacobian().MultTranspose(f_loc, f_hat);
el.CalcVShape(ip, vshape);
Swap<double>(f_hat(0), f_hat(1));
f_hat(0) = -f_hat(0);
f_hat *= ip.weight;
vshape.AddMult(f_hat, elvect);
}
}
void VectorBoundaryFluxLFIntegrator::AssembleRHSElementVect(
const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
int dim = el.GetDim()+1;
int dof = el.GetDof();
shape.SetSize (dof);
nor.SetSize (dim);
elvect.SetSize (dim*dof);
const IntegrationRule *ir = IntRule;
if (ir == NULL)
ir = &IntRules.Get(el.GetGeomType(), el.GetOrder() + 1);
elvect = 0.0;
for (int i = 0; i < ir->GetNPoints(); i++)
{
const IntegrationPoint &ip = ir->IntPoint(i);
Tr.SetIntPoint (&ip);
CalcOrtho(Tr.Jacobian(), nor);
el.CalcShape (ip, shape);
nor *= Sign * ip.weight * F -> Eval (Tr, ip);
for (int j = 0; j < dof; j++)
for (int k = 0; k < dim; k++)
elvect(dof*k+j) += nor(k) * shape(j);
}
}
void VectorFEDomainLFIntegrator::AssembleRHSElementVect(
const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
int dof = el.GetDof();
int dim = el.GetDim();
vshape.SetSize(dof,dim);
vec.SetSize(dim);
elvect.SetSize(dof);
elvect = 0.0;
const IntegrationRule *ir = IntRule;
if (ir == NULL)
{
// int intorder = 2*el.GetOrder() - 1; // ok for O(h^{k+1}) conv. in L2
int intorder = 2*el.GetOrder();
ir = &IntRules.Get(el.GetGeomType(), intorder);
}
for (int i = 0; i < ir->GetNPoints(); i++)
{
const IntegrationPoint &ip = ir->IntPoint(i);
Tr.SetIntPoint (&ip);
el.CalcVShape(Tr, vshape);
QF.Eval (vec, Tr, ip);
vec *= ip.weight * Tr.Weight();
vshape.AddMult (vec, elvect);
}
}
void VectorBoundaryLFIntegrator::AssembleRHSElementVect(
const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
int vdim = Q.GetVDim();
int dof = el.GetDof();
shape.SetSize(dof);
vec.SetSize(vdim);
elvect.SetSize(dof * vdim);
elvect = 0.0;
const IntegrationRule *ir = IntRule;
if (ir == NULL)
{
int intorder = el.GetOrder() + 1;
ir = &IntRules.Get(el.GetGeomType(), intorder);
}
for (int i = 0; i < ir->GetNPoints(); i++)
{
const IntegrationPoint &ip = ir->IntPoint(i);
Q.Eval(vec, Tr, ip);
Tr.SetIntPoint (&ip);
vec *= Tr.Weight() * ip.weight;
el.CalcShape(ip, shape);
for (int k = 0; k < vdim; k++)
for (int s = 0; s < dof; s++)
elvect(dof*k+s) += vec(k) * shape(s);
}
}
void BoundaryFlowIntegrator::AssembleRHSElementVect(
const FiniteElement &el, FaceElementTransformations &Tr, Vector &elvect)
{
int dim, ndof, order;
double un, w, vu_data[3], nor_data[3];
dim = el.GetDim();
ndof = el.GetDof();
Vector vu(vu_data, dim), nor(nor_data, dim);
const IntegrationRule *ir = IntRule;
if (ir == NULL)
{
// Assuming order(u)==order(mesh)
order = Tr.Elem1->OrderW() + 2*el.GetOrder();
if (el.Space() == FunctionSpace::Pk)
order++;
ir = &IntRules.Get(Tr.FaceGeom, order);
}
shape.SetSize(ndof);
elvect.SetSize(ndof);
elvect = 0.0;
for (int p = 0; p < ir->GetNPoints(); p++)
{
const IntegrationPoint &ip = ir->IntPoint(p);
IntegrationPoint eip;
Tr.Loc1.Transform(ip, eip);
el.CalcShape(eip, shape);
Tr.Face->SetIntPoint(&ip);
u->Eval(vu, *Tr.Elem1, eip);
if (dim == 1)
nor(0) = 2*eip.x - 1.0;
else
CalcOrtho(Tr.Face->Jacobian(), nor);
un = vu * nor;
w = 0.5*alpha*un - beta*fabs(un);
w *= ip.weight*f->Eval(*Tr.Elem1, eip);
elvect.Add(w, shape);
}
}
void BoundaryTangentialLFIntegrator::AssembleRHSElementVect(
const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
{
int dim = el.GetDim()+1;
int dof = el.GetDof();
Vector tangent(dim), Qvec;
shape.SetSize(dof);
elvect.SetSize(dof);
elvect = 0.0;
if (dim != 2)
mfem_error("These methods make sense only in 2D problems.");
const IntegrationRule *ir = IntRule;
if (ir == NULL)
{
int intorder = oa * el.GetOrder() + ob; // <----------
ir = &IntRules.Get(el.GetGeomType(), intorder);
}
for (int i = 0; i < ir->GetNPoints(); i++)
{
const IntegrationPoint &ip = ir->IntPoint(i);
Tr.SetIntPoint(&ip);
const DenseMatrix &Jac = Tr.Jacobian();
tangent(0) = Jac(0,0);
tangent(1) = Jac(1,0);
Q.Eval(Qvec, Tr, ip);
el.CalcShape(ip, shape);
add(elvect, ip.weight*(Qvec*tangent), shape, elvect);
}
}
void DGDirichletLFIntegrator::AssembleRHSElementVect(
const FiniteElement &el, FaceElementTransformations &Tr, Vector &elvect)
{
int dim, ndof;
bool kappa_is_nonzero = (kappa != 0.);
double w;
dim = el.GetDim();
ndof = el.GetDof();
nor.SetSize(dim);
nh.SetSize(dim);
ni.SetSize(dim);
adjJ.SetSize(dim);
if (MQ)
mq.SetSize(dim);
shape.SetSize(ndof);
dshape.SetSize(ndof, dim);
dshape_dn.SetSize(ndof);
elvect.SetSize(ndof);
elvect = 0.0;
const IntegrationRule *ir = IntRule;
if (ir == NULL)
{
// a simple choice for the integration order; is this OK?
int order = 2*el.GetOrder();
ir = &IntRules.Get(Tr.FaceGeom, order);
}
for (int p = 0; p < ir->GetNPoints(); p++)
{
const IntegrationPoint &ip = ir->IntPoint(p);
IntegrationPoint eip;
Tr.Loc1.Transform(ip, eip);
Tr.Face->SetIntPoint(&ip);
if (dim == 1)
nor(0) = 2*eip.x - 1.0;
else
CalcOrtho(Tr.Face->Jacobian(), nor);
el.CalcShape(eip, shape);
el.CalcDShape(eip, dshape);
Tr.Elem1->SetIntPoint(&eip);
// compute uD through the face transformation
w = ip.weight * uD->Eval(*Tr.Face, ip) / Tr.Elem1->Weight();
if (!MQ)
{
if (Q)
w *= Q->Eval(*Tr.Elem1, eip);
ni.Set(w, nor);
}
else
{
nh.Set(w, nor);
MQ->Eval(mq, *Tr.Elem1, eip);
mq.MultTranspose(nh, ni);
}
CalcAdjugate(Tr.Elem1->Jacobian(), adjJ);
adjJ.Mult(ni, nh);
dshape.Mult(nh, dshape_dn);
elvect.Add(sigma, dshape_dn);
if (kappa_is_nonzero)
elvect.Add(kappa*(ni*nor), shape);
}
}