void ConvectionDiffusionFE<TDomain>::
add_def_A_elem(LocalVector& d, const LocalVector& u, GridObject* elem, const MathVector<dim> vCornerCoords[])
{
// request geometry
const TFEGeom& geo = GeomProvider<TFEGeom>::get(m_lfeID, m_quadOrder);
number integrand, shape_u;
MathMatrix<dim,dim> D;
MathVector<dim> v, Dgrad_u, grad_u;
// loop integration points
for(size_t ip = 0; ip < geo.num_ip(); ++ip)
{
// get current u and grad_u
VecSet(grad_u, 0.0);
shape_u = 0.0;
for(size_t j = 0; j < geo.num_sh(); ++j)
{
VecScaleAppend(grad_u, u(_C_,j), geo.global_grad(ip, j));
shape_u += u(_C_,j) * geo.shape(ip, j);
}
// Diffusion
if(m_imDiffusion.data_given())
MatVecMult(Dgrad_u, m_imDiffusion[ip], grad_u);
else
VecSet(Dgrad_u, 0.0);
// Convection
if(m_imVelocity.data_given())
VecScaleAppend(Dgrad_u, -1*shape_u, m_imVelocity[ip]);
// Convection
if(m_imFlux.data_given())
VecScaleAppend(Dgrad_u, 1.0, m_imFlux[ip]);
// loop test spaces
for(size_t i = 0; i < geo.num_sh(); ++i)
{
// compute integrand
integrand = VecDot(Dgrad_u, geo.global_grad(ip, i));
// add Reaction Rate
if(m_imReactionRate.data_given())
integrand += m_imReactionRate[ip] * shape_u * geo.shape(ip, i);
// add Reaction
if(m_imReaction.data_given())
integrand += m_imReaction[ip] * geo.shape(ip, i);
// multiply by integration weight
integrand *= geo.weight(ip);
// add to local defect
d(_C_, i) += integrand;
}
}
}
void ConvectionDiffusionFE<TDomain>::
lin_def_diffusion(const LocalVector& u,
std::vector<std::vector<MathMatrix<dim,dim> > > vvvLinDef[],
const size_t nip)
{
// request geometry
const TFEGeom& geo = GeomProvider<TFEGeom>::get(m_lfeID, m_quadOrder);
MathVector<dim> grad_u;
// loop integration points
for(size_t ip = 0; ip < geo.num_ip(); ++ip)
{
// get current u and grad_u
VecSet(grad_u, 0.0);
for(size_t j = 0; j < geo.num_sh(); ++j)
VecScaleAppend(grad_u, u(_C_,j), geo.global_grad(ip, j));
// loop test spaces
for(size_t i = 0; i < geo.num_sh(); ++i)
{
for(size_t k = 0; k < (size_t)dim; ++k)
for(size_t j = 0; j < (size_t)dim; ++j)
(vvvLinDef[ip][_C_][i])(k,j) = grad_u[j] * geo.global_grad(ip, i)[k]
* geo.weight(ip);
}
}
}
void ConvectionDiffusionFE<TDomain>::
add_jac_A_elem(LocalMatrix& J, const LocalVector& u, GridObject* elem, const MathVector<dim> vCornerCoords[])
{
// request geometry
const TFEGeom& geo = GeomProvider<TFEGeom>::get(m_lfeID, m_quadOrder);
MathVector<dim> v, Dgrad;
// loop integration points
for(size_t ip = 0; ip < geo.num_ip(); ++ip)
{
// loop trial space
for(size_t j = 0; j < geo.num_sh(); ++j)
{
// Diffusion
if(m_imDiffusion.data_given())
MatVecMult(Dgrad, m_imDiffusion[ip], geo.global_grad(ip, j));
else
VecSet(Dgrad, 0.0);
// Convection
if(m_imVelocity.data_given())
VecScaleAppend(Dgrad, -1*geo.shape(ip,j), m_imVelocity[ip]);
// no explicit dependency on m_imFlux
// loop test space
for(size_t i = 0; i < geo.num_sh(); ++i)
{
// compute integrand
number integrand = VecDot(Dgrad, geo.global_grad(ip, i));
// Reaction
if(m_imReactionRate.data_given())
integrand += m_imReactionRate[ip] * geo.shape(ip, j) * geo.shape(ip, i);
// no explicit dependency on m_imReaction
// multiply by weight
integrand *= geo.weight(ip);
// add to local matrix
J(_C_, i, _C_, j) += integrand;
}
}
}
}
void ConvectionDiffusionFVCR<TDomain>::
lin_def_diffusion(const LocalVector& u,
std::vector<std::vector<MathMatrix<dim,dim> > > vvvLinDef[],
const size_t nip)
{
// get finite volume geometry
static const TFVGeom& geo = GeomProvider<TFVGeom>::get();
// get conv shapes
// const IConvectionShapes<dim>& convShape = get_updated_conv_shapes(geo);
// reset the values for the linearized defect
for(size_t ip = 0; ip < nip; ++ip)
for(size_t c = 0; c < vvvLinDef[ip].size(); ++c)
for(size_t sh = 0; sh < vvvLinDef[ip][c].size(); ++sh)
vvvLinDef[ip][c][sh] = 0.0;
// loop Sub Control Volume Faces (SCVF)
for(size_t ip = 0; ip < geo.num_scvf(); ++ip)
{
// get current SCVF
const typename TFVGeom::SCVF& scvf = geo.scvf(ip);
// compute gradient at ip
MathVector<dim> grad_u; VecSet(grad_u, 0.0);
for(size_t sh = 0; sh < scvf.num_sh(); ++sh)
VecScaleAppend(grad_u, u(_C_,sh), scvf.global_grad(sh));
// compute the lin defect at this ip
MathMatrix<dim,dim> linDefect;
// part coming from -\nabla u * \vec{n}
for(size_t k=0; k < (size_t)dim; ++k)
for(size_t j = 0; j < (size_t)dim; ++j)
linDefect(j,k) = (scvf.normal())[j] * grad_u[k];
// add contribution from convection shapes
// if(convShape.non_zero_deriv_diffusion())
// for(size_t sh = 0; sh < scvf.num_sh(); ++sh)
// MatAdd(linDefect, convShape.D_diffusion(ip, sh), u(_C_, sh));
// add contributions
vvvLinDef[ip][_C_][scvf.from()] -= linDefect;
vvvLinDef[ip][_C_][scvf.to() ] += linDefect;
}
}
void ConvectionDiffusionFVCR<TDomain>::
ex_grad(MathVector<dim> vValue[],
const MathVector<dim> vGlobIP[],
number time, int si,
const LocalVector& u,
GridObject* elem,
const MathVector<dim> vCornerCoords[],
const MathVector<TFVGeom::dim> vLocIP[],
const size_t nip,
bool bDeriv,
std::vector<std::vector<MathVector<dim> > > vvvDeriv[])
{
// Get finite volume geometry
static const TFVGeom& geo = GeomProvider<TFVGeom>::get();
// reference element
typedef typename reference_element_traits<TElem>::reference_element_type
ref_elem_type;
// reference dimension
static const int refDim = ref_elem_type::dim;
// number of shape functions
static const size_t numSH = ref_elem_type::numCorners;
// CRFV SCVF ip
if(vLocIP == geo.scvf_local_ips())
{
// Loop Sub Control Volume Faces (SCVF)
for(size_t ip = 0; ip < geo.num_scvf(); ++ip)
{
// Get current SCVF
const typename TFVGeom::SCVF& scvf = geo.scvf(ip);
VecSet(vValue[ip], 0.0);
for(size_t sh = 0; sh < scvf.num_sh(); ++sh)
VecScaleAppend(vValue[ip], u(_C_, sh), scvf.global_grad(sh));
if(bDeriv)
for(size_t sh = 0; sh < scvf.num_sh(); ++sh)
vvvDeriv[ip][_C_][sh] = scvf.global_grad(sh);
}
}
// general case
else
{
// get trial space
LagrangeP1<ref_elem_type>& rTrialSpace = Provider<LagrangeP1<ref_elem_type> >::get();
// storage for shape function at ip
MathVector<refDim> vLocGrad[numSH];
MathVector<refDim> locGrad;
// Reference Mapping
MathMatrix<dim, refDim> JTInv;
ReferenceMapping<ref_elem_type, dim> mapping(vCornerCoords);
// loop ips
for(size_t ip = 0; ip < nip; ++ip)
{
// evaluate at shapes at ip
rTrialSpace.grads(vLocGrad, vLocIP[ip]);
// compute grad at ip
VecSet(locGrad, 0.0);
for(size_t sh = 0; sh < numSH; ++sh)
VecScaleAppend(locGrad, u(_C_, sh), vLocGrad[sh]);
// compute global grad
mapping.jacobian_transposed_inverse(JTInv, vLocIP[ip]);
MatVecMult(vValue[ip], JTInv, locGrad);
// compute derivative w.r.t. to unknowns iff needed
if(bDeriv)
for(size_t sh = 0; sh < numSH; ++sh)
MatVecMult(vvvDeriv[ip][_C_][sh], JTInv, vLocGrad[sh]);
}
}
};
void ConvectionDiffusionFVCR<TDomain>::
add_def_A_elem(LocalVector& d, const LocalVector& u, GridObject* elem, const MathVector<dim> vCornerCoords[])
{
// get finite volume geometry
static const TFVGeom& geo = GeomProvider<TFVGeom>::get();
// get conv shapes
// const IConvectionShapes<dim>& convShape = get_updated_conv_shapes(geo);
if(m_imDiffusion.data_given() || m_imVelocity.data_given())
{
// loop Sub Control Volume Faces (SCVF)
for(size_t ip = 0; ip < geo.num_scvf(); ++ip)
{
// get current SCVF
const typename TFVGeom::SCVF& scvf = geo.scvf(ip);
/////////////////////////////////////////////////////
// Diffusive Term
/////////////////////////////////////////////////////
if(m_imDiffusion.data_given())
{
// to compute D \nabla c
MathVector<dim> Dgrad_c, grad_c;
// compute gradient and shape at ip
VecSet(grad_c, 0.0);
for(size_t sh = 0; sh < scvf.num_sh(); ++sh)
VecScaleAppend(grad_c, u(_C_,sh), scvf.global_grad(sh));
// scale by diffusion tensor
MatVecMult(Dgrad_c, m_imDiffusion[ip], grad_c);
// Compute flux
const number diff_flux = VecDot(Dgrad_c, scvf.normal());
// Add to local defect
d(_C_, scvf.from()) -= diff_flux;
d(_C_, scvf.to() ) += diff_flux;
}
/////////////////////////////////////////////////////
// Convective Term
/////////////////////////////////////////////////////
/* if(m_imVelocity.data_given())
{
// sum up convective flux using convection shapes
number conv_flux = 0.0;
for(size_t sh = 0; sh < convShape.num_sh(); ++sh)
conv_flux += u(_C_, sh) * convShape(ip, sh);
// add to local defect
d(_C_, scvf.from()) += conv_flux;
d(_C_, scvf.to() ) -= conv_flux;
}*/
}
}
// reaction rate
if(m_imReactionRate.data_given())
{
// loop Sub Control Volumes (SCV)
for(size_t ip = 0; ip < geo.num_scv(); ++ip)
{
// get current SCV
const typename TFVGeom::SCV& scv = geo.scv(ip);
// get associated node
const int co = scv.node_id();
// Add to local defect
d(_C_, co) += u(_C_, co) * m_imReactionRate[ip] * scv.volume();
}
}
// reaction rate
if(m_imReaction.data_given())
{
// loop Sub Control Volumes (SCV)
for(size_t ip = 0; ip < geo.num_scv(); ++ip)
{
// get current SCV
const typename TFVGeom::SCV& scv = geo.scv(ip);
// get associated node
const int co = scv.node_id();
// Add to local defect
d(_C_, co) += m_imReaction[ip] * scv.volume();
}
}
// handle constrained dofs, compute defect of interpolation equation
if(TFVGeom::usesHangingNodes){
for (size_t i=0;i<geo.num_constrained_dofs();i++){
const typename TFVGeom::CONSTRAINED_DOF& cd = geo.constrained_dof(i);
const size_t index = cd.index();
number defect = u(_C_,index);
for (size_t j=0;j<cd.num_constraining_dofs();j++)
defect -= cd.constraining_dofs_weight(j) * u(_C_,cd.constraining_dofs_index(j));
d(_C_,index) = defect;
}
}
}
void ConvectionDiffusionFE<TDomain>::
compute_err_est_A_elem(const LocalVector& u, GridObject* elem, const MathVector<dim> vCornerCoords[], const number& scale)
{
typedef typename reference_element_traits<TElem>::reference_element_type ref_elem_type;
err_est_type* err_est_data = dynamic_cast<err_est_type*>(this->m_spErrEstData.get());
if (err_est_data->surface_view().get() == NULL) {UG_THROW("Error estimator has NULL surface view.");}
MultiGrid* pErrEstGrid = (MultiGrid*) (err_est_data->surface_view()->subset_handler()->multi_grid());
// request geometry
static const TFEGeom& geo = GeomProvider<TFEGeom>::get();
// SIDE TERMS //
// get the sides of the element
// We have to cast elem to a pointer of type SideAndElemErrEstData::elem_type
// for the SideAndElemErrEstData::operator() to work properly.
// This cannot generally be achieved by casting to TElem*, since this method is also registered for
// lower-dimensional types TElem, and must therefore be compilable, even if it is never EVER to be executed.
// The way we achieve this here, is by calling associated_elements_sorted() which has an implementation for
// all possible types. Whatever comes out of it is of course complete nonsense if (and only if)
// SideAndElemErrEstData::elem_type != TElem. To be on the safe side, we throw an error if the number of
// entries in the list is not as it should be.
typename MultiGrid::traits<typename SideAndElemErrEstData<TDomain>::side_type>::secure_container side_list;
pErrEstGrid->associated_elements_sorted(side_list, (TElem*) elem);
if (side_list.size() != (size_t) ref_elem_type::numSides)
UG_THROW ("Mismatch of numbers of sides in 'ConvectionDiffusionFE::compute_err_est_elem'");
// some help variables
MathVector<dim> fluxDensity, gradC, normal;
// FIXME: The computation of the gradient has to be reworked.
// In the case of P1 shape functions, it is valid. For Q1 shape functions, however,
// the gradient is not constant (but bilinear) on the element - and along the sides.
// We cannot use the FVGeom here. Instead, we need to calculate the gradient in each IP!
// calculate grad u as average (over scvf)
VecSet(gradC, 0.0);
for(size_t ii = 0; ii < geo.num_ip(); ++ii)
{
for (size_t j=0; j<m_shapeValues.num_sh(); j++)
VecScaleAppend(gradC, u(_C_,j), geo.global_grad(ii, j));
}
VecScale(gradC, gradC, (1.0/geo.num_ip()));
// calculate flux through the sides
size_t passedIPs = 0;
for (size_t side=0; side < (size_t) ref_elem_type::numSides; side++)
{
// normal on side
SideNormal<ref_elem_type,dim>(normal, side, vCornerCoords);
VecNormalize(normal, normal);
try
{
for (size_t sip = 0; sip < err_est_data->num_side_ips(side_list[side]); sip++)
{
size_t ip = passedIPs + sip;
VecSet(fluxDensity, 0.0);
// diffusion //
if (m_imDiffusion.data_given())
MatVecScaleMultAppend(fluxDensity, -1.0, m_imDiffusion[ip], gradC);
// convection //
if (m_imVelocity.data_given())
{
number val = 0.0;
for (size_t sh = 0; sh < m_shapeValues.num_sh(); sh++)
val += u(_C_,sh) * m_shapeValues.shapeAtSideIP(sh,sip);
VecScaleAppend(fluxDensity, val, m_imVelocity[ip]);
}
// general flux //
if (m_imFlux.data_given())
VecAppend(fluxDensity, m_imFlux[ip]);
(*err_est_data)(side_list[side],sip) += scale * VecDot(fluxDensity, normal);
}
passedIPs += err_est_data->num_side_ips(side_list[side]);
}
UG_CATCH_THROW("Values for the error estimator could not be assembled at every IP." << std::endl
<< "Maybe wrong type of ErrEstData object? This implementation needs: SideAndElemErrEstData.");
}
// VOLUME TERMS //
typename MultiGrid::traits<typename SideAndElemErrEstData<TDomain>::elem_type>::secure_container elem_list;
pErrEstGrid->associated_elements_sorted(elem_list, (TElem*) elem);
if (elem_list.size() != 1)
UG_THROW ("Mismatch of numbers of sides in 'ConvectionDiffusionFE::compute_err_est_elem'");
try
{
for (size_t ip = 0; ip < err_est_data->num_elem_ips(elem->reference_object_id()); ip++)
{
number total = 0.0;
// diffusion // TODO ONLY FOR (PIECEWISE) CONSTANT DIFFUSION TENSOR SO FAR!
// div(D*grad(c))
// nothing to do, as c is piecewise linear and div(D*grad(c)) disappears
// if D is diagonal and c bilinear, this should also vanish (confirm this!)
// convection // TODO ONLY FOR (PIECEWISE) CONSTANT OR DIVERGENCE-FREE
// VELOCITY FIELDS SO FAR!
// div(v*c) = div(v)*c + v*grad(c) -- gradC has been calculated above
if (m_imVelocity.data_given())
total += VecDot(m_imVelocity[ip], gradC);
// general flux // TODO ONLY FOR DIVERGENCE-FREE FLUX FIELD SO FAR!
// nothing to do
// reaction //
if (m_imReactionRate.data_given())
{
number val = 0.0;
for (size_t sh = 0; sh < geo.num_sh(); sh++)
val += u(_C_,sh) * m_shapeValues.shapeAtElemIP(sh,ip);
total += m_imReactionRate[ip] * val;
}
if (m_imReaction.data_given())
{
total += m_imReaction[ip];
}
(*err_est_data)(elem_list[0],ip) += scale * total;
}
}
UG_CATCH_THROW("Values for the error estimator could not be assembled at every IP." << std::endl
<< "Maybe wrong type of ErrEstData object? This implementation needs: SideAndElemErrEstData.");
}
void ConvectionDiffusionFE<TDomain>::
ex_grad(MathVector<dim> vValue[],
const MathVector<dim> vGlobIP[],
number time, int si,
const LocalVector& u,
GridObject* elem,
const MathVector<dim> vCornerCoords[],
const MathVector<TFEGeom::dim> vLocIP[],
const size_t nip,
bool bDeriv,
std::vector<std::vector<MathVector<dim> > > vvvDeriv[])
{
// request geometry
const TFEGeom& geo = GeomProvider<TFEGeom>::get(m_lfeID, m_quadOrder);
// reference element
typedef typename reference_element_traits<TElem>::reference_element_type
ref_elem_type;
// reference dimension
static const int refDim = reference_element_traits<TElem>::dim;
// reference object id
static const ReferenceObjectID roid = ref_elem_type::REFERENCE_OBJECT_ID;
// FE
if(vLocIP == geo.local_ips())
{
// Loop ip
for(size_t ip = 0; ip < geo.num_ip(); ++ip)
{
VecSet(vValue[ip], 0.0);
for(size_t sh = 0; sh < geo.num_sh(); ++sh)
VecScaleAppend(vValue[ip], u(_C_, sh), geo.global_grad(ip, sh));
if(bDeriv)
for(size_t sh = 0; sh < geo.num_sh(); ++sh)
vvvDeriv[ip][_C_][sh] = geo.global_grad(ip, sh);
}
}
// general case
else
{
// request for trial space
try{
const LocalShapeFunctionSet<refDim>& rTrialSpace
= LocalFiniteElementProvider::get<refDim>(roid, m_lfeID);
// number of shape functions
const size_t numSH = rTrialSpace.num_sh();
// storage for shape function at ip
std::vector<MathVector<refDim> > vLocGrad(numSH);
MathVector<refDim> locGrad;
// Reference Mapping
MathMatrix<dim, refDim> JTInv;
ReferenceMapping<ref_elem_type, dim> mapping(vCornerCoords);
// loop ips
for(size_t ip = 0; ip < nip; ++ip)
{
// evaluate at shapes at ip
rTrialSpace.grads(vLocGrad, vLocIP[ip]);
// compute grad at ip
VecSet(locGrad, 0.0);
for(size_t sh = 0; sh < numSH; ++sh)
VecScaleAppend(locGrad, u(_C_, sh), vLocGrad[sh]);
// compute global grad
mapping.jacobian_transposed_inverse(JTInv, vLocIP[ip]);
MatVecMult(vValue[ip], JTInv, locGrad);
// compute derivative w.r.t. to unknowns iff needed
if(bDeriv)
for(size_t sh = 0; sh < numSH; ++sh)
MatVecMult(vvvDeriv[ip][_C_][sh], JTInv, vLocGrad[sh]);
}
}
UG_CATCH_THROW("ConvectionDiffusion::ex_grad: trial space missing.");
}
};
void GradientDataExport<dim>::eval_and_deriv(MathVector<dim> vValue[],
const MathVector<dim> vGlobIP[],
number time, int si,
GridObject* elem,
const MathVector<dim> vCornerCoords[],
const MathVector<refDim> vLocIP[],
const size_t nip,
LocalVector* u,
bool bDeriv,
int s,
std::vector<std::vector<MathVector<dim> > > vvvDeriv[],
const MathMatrix<refDim, dim>* vJT) const
{
// abbreviation for component
static const int _C_ = 0;
// reference object id
const ReferenceObjectID roid = elem->reference_object_id();
// local finite element id
const LFEID& lfeID = this->function_group().local_finite_element_id(_C_);
// access local vector by map
u->access_by_map(this->map());
// request for trial space
try{
const LocalShapeFunctionSet<refDim>& rTrialSpace
= LocalFiniteElementProvider::get<refDim>(roid, lfeID);
// Reference Mapping
MathMatrix<dim, refDim> JTInv;
std::vector<MathMatrix<refDim, dim> > vJTtmp;
if(!vJT){
DimReferenceMapping<refDim, dim>& map
= ReferenceMappingProvider::get<refDim, dim>(roid, vCornerCoords);
vJTtmp.resize(nip);
map.jacobian_transposed(&vJTtmp[0], vLocIP, nip);
vJT = &vJTtmp[0];
}
// storage for shape function at ip
std::vector<MathVector<refDim> > vLocGrad;
MathVector<refDim> locGrad;
// loop ips
for(size_t ip = 0; ip < nip; ++ip)
{
// evaluate at shapes at ip
rTrialSpace.grads(vLocGrad, vLocIP[ip]);
// compute grad at ip
VecSet(locGrad, 0.0);
for(size_t sh = 0; sh < vLocGrad.size(); ++sh)
VecScaleAppend(locGrad, (*u)(_C_, sh), vLocGrad[sh]);
Inverse(JTInv, vJT[ip]);
MatVecMult(vValue[ip], JTInv, locGrad);
// store derivative
if(bDeriv)
for(size_t sh = 0; sh < vLocGrad.size(); ++sh)
MatVecMult(vvvDeriv[ip][_C_][sh], JTInv, vLocGrad[sh]);
}
}
UG_CATCH_THROW("GradientDataExport: Trial space missing, Reference Object: "
<<roid<<", Trial Space: "<<lfeID<<", refDim="<<refDim);
}