Class xlifepp::FeSpace

class FeSpace : public xlifepp::Space

Inheritence diagram for xlifepp::FeSpace:

Collaboration diagram for xlifepp::FeSpace:

defines general data of a finite element space.

FeSpace class is not directly exposed to end users

Public Functions

FeSpace(const GeomDomain &gd, const Interpolation &in, const string_t &na, bool opt = true, bool withLocateData = true)

constructor from GeomDomain and Interpolation(s)

void addToBcDof(BCDof*, FeDof&, number_t, std::list<GeoNumPair>&, number_t, const Point&, const Point&, GeomElement*, int rev = 1)

tool for buildBCRTSpace()

tools for FeSpace:: buildBCRTSpace() add to the BC dof located on side s of element gelt, the parts of shape basis related to one vertex of an edge bcd: BcDof fed: FeDof s: side number elts: list of elements (counterclockwise) connected to the vertex (vnum) of side s X: middle point of side s gelt: related geometric element rev: reverse order vertex not on the boundary

void addToBcDofBoundary(BCDof*, FeDof&, number_t, std::list<GeoNumPair>&, number_t, const Point&, const Point&, GeomElement*, int rev = 1)

tool for buildBCRTSpace()

tools for FeSpace:: buildBCRTSpace() add to the BC dof located on side s of element gelt, the parts of shape basis related to one vertex of an edge elts is the list of elements (counterclockwise) connected to the vertex (vnum) of side s and X is the middle point of side s vertex on the boundary

void buildBCRTSpace()

special construction of BuffaChristiansen-RT space

buildBCRTSpace: special construction of BuffaChristiansen-RT space from F.P.

Andriulli, K.f Cools, H. Bagci, F. Olyslager, A. Buffa, S. Christiansen and E. Michielssen A Multiplicative Calderon Preconditioner for the Electric Field Integral Equation IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 56, NO. 8, AUGUST 2008 and XLiFE++ documentation

virtual void builddofid2rank() const

construct the map dofid2rank from dofs list

construct the map dofid2rank from dofs list, ranks start from 1

void buildElements()

construct the list of elements

void buildFeDofs()

construct the list of FeDofs

buildFeDofs: create FeDofs of FeSpace defined by a mesh domain and an interpolation algorithm: for Discontinuous Galerkin interpolation (_L2 space comforming), all local dofs are global dofs for “continuous” approximation with sharable dofs the algorithm travels the list of elements on each element, local dofs are indexed along a DofKey object wich uniquely determines a global dof: vertex dof: V + global mesh vertex number side dof: S + ascending global mesh numbers of side vertices + local dof number side of side dof: E + “ascending” global mesh numbers of side vertices + local dof number internal or not sharable dof: not indexed thus, a global dof is created from a local dof if it is not already indexed or if it is a non sharable dof

NOTE: algorithm of this new version is more general than the previous one it works by using a loop on ref dofs of ref elements while the old one using a loop on vertices, edges, faces and non sharable dofs Now all the dof informations are provided by refdof and not by refdof and refelement that leads to a more general and compact algorithm, probably more efficient !

virtual void buildgelt2elt() const

construct the map gelt2elt from elements list

buildgelt2elt: construct the map gelt2elt from elements list

dimen_t dimElements() const

return the dimension of FE elements

inline virtual number_t dimSpace() const

return the space dimension

inline virtual const Dof &dof(number_t n) const

return n-th FeDof as Dof (n=1,…)

inline virtual number_t dofId(number_t n) const

return the DoF id of n-th space DoF (n=1,…)

inline virtual const std::map<number_t, number_t> &dofid2rank() const

return the map dof to rank, built on fly

virtual std::vector<number_t> dofIds() const

return the DoF ids on space

virtual std::vector<number_t> dofsOn(const GeomDomain&, int_t ord = -1, dimen_t dim = 0, ProjectionType = _noProjection) const

return the set of dof numbers of dofs “located” on a domain: when a plain domain, return all the dofs when a side domain, return only dofs with support in the side domain when a side of side domain, return only dofs with support in the side of side domain

filter dofs along some characteristics (see Refdof class): order_: order of a derivative D.o.F or a moment D.o.F (0) supportDim_: dimension of the D.o.F geometric support (0 point, 1 segment, …) projectionType_: type of projection (_noProjection , _givenProjection, _dotnProjection, _crossnProjection)

order = -1 means all dofs

NOTE: this function is useful when the restriction of FeSpace on a side does not define a FeSubSpace for instance, this is the case for Raviart, Nedelec space where the trace on a side domain is not a finite element space

virtual const Element &element(GeomElement *gelt) const

access to element associated to a geomelement

inline virtual const Element &element(number_t k) const

access to k-th (k>=0) element (pointer) for FESpace and FESubspace only

virtual const Element *element_p(GeomElement *gelt) const

access to element associated to a geomelement

return element linked to a given geom element used gelt2elt map; has to be already built

inline virtual const Element *element_p(number_t k) const

access to k-th (k>=0) element (pointer) for FESpace and FESubspace only

inline virtual const std::vector<number_t> &elementDofs(number_t k) const

access to dofs ranks (local numbering) of k-th (>=0) element for FESpace and FESubspace only

inline virtual std::vector<number_t> elementParentDofs(number_t k) const

access to dofs ranks (parent numbering, same as local) of k-th (>=0) element for FESpace and FESubspace only

virtual bool extensionRequired() const

true if space has no trace space

true if trace space cannot be defined from trace of FE on side, case of edge FE

inline virtual const FeDof &fedof(number_t n) const

return n-th FeDof (n=1,…)

inline virtual const std::vector<FeDof> &feDofs() const

return dofs vector

inline virtual FeSpace *feSpace()

access to child fespace object

inline virtual const FeSpace *feSpace() const

access to child fespace object (const)

Graph graphOfDofs()

return the set of dof numbers of dofs “located” on a domain

create dof connection graph

virtual bool include(const Space*) const

return true if space is included in current space

template<typename T, typename K>
T &interpolate(const Vector<K>&, const Point&, T&, DiffOpType = _id, bool useNearest = false) const

compute interpolation value at P

inline virtual const Interpolation *interpolation() const

return pointer to interpolation

virtual bool isFE() const

true if FE space or FeSubspace

virtual bool isSpectral() const

true if spectral space

virtual Dof &locateDof(const Point&) const

locate Lagrange dof nearest a given point

locate Lagrange dof nearest of a given point

const Element *locateElement(const Point &P, bool useNearest = false, bool errorOnOutDom = true, real_t tol = theLocateToleranceFactor) const

locate element of the Fespace containing P

number_t maxDegree() const

max degree of polynomials involved by shape functions

max degree of polynomials involved by shape functions if not polynomial return a default degree 5

inline virtual number_t nbDofs() const

number of dofs (a dof may be a vector dof)

inline virtual number_t nbOfElements() const

number of elements for FESpace and FESubspace only

virtual number_t numElement(GeomElement *gelt) const

access to element number associated to a geomelement

access to element number associated to a geomelement if not found return the size of gelt2elt (number of elements)

virtual void print(std::ostream&) const

print utility

inline virtual const std::set<RefElement*> &refElements() const

access to set of pointer to RefElement (refElts) involved in FESpace

virtual std::pair<number_t, number_t> renumberDofs()

renumber dofs with bandwith minimisation

inline virtual Space *rootSpace()

access to root space pointer

inline virtual const Space *rootSpace() const

access to root space pointer (const)

inline virtual void shiftDofs(number_t n)

shift dofs numbering from n (special utility for SpSpace)

virtual StrucType strucType() const

return structure type of basis function (scalar or vector)

virtual ValueType valueType() const

return value type of basis function (real or complex)

Public Members

mutable std::map<number_t, number_t> dofid2rank_

map dof iD -> rank in dofs vector

std::vector<FeDof> dofs

list of global degrees of freedom

std::vector<Element> elements

list of finite elements

mutable std::map<GeomElement*, number_t> gelt2elt

map GeomElement -> element number (useful to interpolation tools)

std::set<RefElement*> refElts

set of pointer to RefElement involved in FeSpace (usually one)

Public Static Attributes

static number_t lastEltIndex = 0

to manage a unique index for elements

for unique elements numbering