serif::discretization::functional_space Namespace Reference

Classes
struct	DiscreteFunctionalSpace
	Compile-time descriptor for a discrete functional space. The difference between a FunctionalSpace and a discrete functional space is that a discrete functional space carries some additional information which is needed to actually construct a finite element space (e.g. polynomial order, and rank). Once you have a discrete functional space you have, for MFEM at least, enough information to fully define a finite element space. More...
struct	Rank
	Compile-time descriptor for the rank of a functional space. More...
struct	SpaceDescriptor
	Compile-time descriptor for a functional space. This struct is used to describe the family, continuity, trace, and mapping of a functional space at compile time. More...

Enumerations
enum class	Family { l2 , h1 , hdiv , hcurl }
	Compile-time descriptor for the family, continuity, trace, and mapping of a functional space. More...
enum class	Continuity { discontinuous , continuous , normal_continuous , tangential_continuous }
	Compile-time descriptor for the continuity of a functional space. This enum is parallel to the Family enum. More...
enum class	Trace { none , value , normal , tangential }
	Compile-time descriptor for the trace of a functional space. This enum is parallel to the Family enum. More...
enum class	Mapping { identity , contravariant_piola , covariant_piola }
	Compile-time descriptor for the mapping of a functional space. This tells the DomainMapper which piola transformations to use when moving between reference and physical spaces. More...

Variables
static auto	Family2StringMap = meta::enum_to_enum_string_map<Family>()
	Mapping from Family enum values to their string representations.
static auto	String2FamilyMap = meta::enum_to_string_enum_map<Family>()
	Mapping from string representations to Family enum values.
static auto	Continuity2StringMap = meta::enum_to_enum_string_map<Continuity>()
	Mapping from Continuity enum values to their string representations.
static auto	String2ContinuityMap = meta::enum_to_string_enum_map<Continuity>()
	Mapping from string representations to Continuity enum values.
static auto	Trace2StringMap = meta::enum_to_enum_string_map<Trace>()
	Mapping from Trace enum values to their string representations.
static auto	String2TraceMap = meta::enum_to_string_enum_map<Trace>()
	Mapping from string representations to Trace enum values.
static auto	Mapping2StringMap = meta::enum_to_enum_string_map<Mapping>()
	Mapping from Mapping enum values to their string representations.
static auto	String2MappingMap = meta::enum_to_string_enum_map<Mapping>()
	Mapping from string representations to Mapping enum values.
static constexpr SpaceDescriptor	L2
	Compile-time descriptor for an L2 functional space. This is a convenience descriptor that allows you to easily create an L2 functional space descriptor without having to specify all the parameters. The specifications are.
static constexpr SpaceDescriptor	H1
	Compile-time descriptor for an H1 functional space. This is a convenience descriptor that allows you to easily create an H1 functional space descriptor without having to specify all the parameters. The specifications are.
static constexpr SpaceDescriptor	Hdiv
	Compile-time descriptor for an H(div) functional space. This is a convenience descriptor that allows you to easily create an H(div) functional space descriptor without having to specify all the parameters. The specifications are.
static constexpr SpaceDescriptor	Hcurl
	Compile-time descriptor for an H(curl) functional space. This is a convenience descriptor that allows you to easily create an H(curl) functional space descriptor without having to specify all the parameters. The specifications are.

Enumeration Type Documentation

Continuity

enum class serif::discretization::functional_space::Continuity

strong

Compile-time descriptor for the continuity of a functional space. This enum is parallel to the Family enum.

Todo

There may be a better way to store these relations that forces them to be parallel rather than just relying on the programmer to keep them in sync.

Enumerator
discontinuous	Discontinuous functions, typically used for L2 spaces.
continuous	C0 continuous functions, typically used for H1 spaces.
normal_continuous	Functions with normal continuity, typically used for H(div) spaces.
tangential_continuous	Functions with tangential continuity, typically used for H(curl) spaces.

Family

enum class serif::discretization::functional_space::Family

strong

Compile-time descriptor for the family, continuity, trace, and mapping of a functional space.

Note

These are almost all of the functional spaces that MFEM supports, if in the future MFEM adds some other space and you wish to extend SERiF to support it (or you introduce some non MFEM backend with another space) then one early place you will need to modify is this enum.

We do not support mfem::ceed::ParAlgebraicCoarseSpace

Enumerator
l2	L2 space, typically used for discontinuous functions.
h1	H1 space, typically used for continuous functions.
hdiv	H(div) space, typically used for vector fields with normal continuity.
hcurl	H(curl) space, typically used for vector fields with tangential continuity.

Mapping

enum class serif::discretization::functional_space::Mapping

strong

Compile-time descriptor for the mapping of a functional space. This tells the DomainMapper which piola transformations to use when moving between reference and physical spaces.

Enumerator
identity	Identity mapping, typically used for L2 and H1 spaces.
contravariant_piola	Contravariant Piola mapping, preserving the normal trace, typically used for H(div) spaces. ( \( \frac{1}{\text{det(J)}}J\hat{\phi}(F^{-1}(x)) \) transforming some vector field \(\phi(x)\) for some transformation \( F \) with Jacobian \( J \))
covariant_piola	Covariant Piola mapping, preserving the tangential trace, typically used for H(curl) spaces. ( \( J^{-T}\hat{\phi}(F^{-1}(x)) \) transforming some vector field \(\phi(x)\) for some transformation \( F \) with Jacobian \( J \))

Trace

enum class serif::discretization::functional_space::Trace

strong

Compile-time descriptor for the trace of a functional space. This enum is parallel to the Family enum.

Enumerator
none	No trace, typically used for L2 spaces.
value	Value trace, typically used for H1 spaces.
normal	Normal trace, typically used for H(div) spaces.
tangential	Tangential trace, typically used for H(curl) spaces.

Variable Documentation

Continuity2StringMap

auto serif::discretization::functional_space::Continuity2StringMap = meta::enum_to_enum_string_map<Continuity>()

inlinestatic

Mapping from Continuity enum values to their string representations.

Family2StringMap

auto serif::discretization::functional_space::Family2StringMap = meta::enum_to_enum_string_map<Family>()

inlinestatic

Mapping from Family enum values to their string representations.

H1

SpaceDescriptor serif::discretization::functional_space::H1

inlinestaticconstexpr

Initial value:

{
        .family = Family::h1,
        .continuity = Continuity::continuous,
        .trace = Trace::value,
        .mapping = Mapping::identity
    }

Compile-time descriptor for an H1 functional space. This is a convenience descriptor that allows you to easily create an H1 functional space descriptor without having to specify all the parameters. The specifications are.

• family = Family::h1
• continuity = Continuity::continuous
• trace = Trace::value
• mapping = Mapping::identity

Hcurl

SpaceDescriptor serif::discretization::functional_space::Hcurl

inlinestaticconstexpr

Initial value:

{
        .family = Family::hcurl,
        .continuity = Continuity::tangential_continuous,
        .trace = Trace::tangential,
        .mapping = Mapping::covariant_piola
    }

Compile-time descriptor for an H(curl) functional space. This is a convenience descriptor that allows you to easily create an H(curl) functional space descriptor without having to specify all the parameters. The specifications are.

• family = Family::hcurl
• continuity = Continuity::tangential_continuous
• trace = Trace::tangential
• mapping = Mapping::covariant_piola

Hdiv

SpaceDescriptor serif::discretization::functional_space::Hdiv

inlinestaticconstexpr

Initial value:

{
        .family = Family::hdiv,
        .continuity = Continuity::normal_continuous,
        .trace = Trace::normal,
        .mapping = Mapping::contravariant_piola
    }

Compile-time descriptor for an H(div) functional space. This is a convenience descriptor that allows you to easily create an H(div) functional space descriptor without having to specify all the parameters. The specifications are.

• family = Family::hdiv
• continuity = Continuity::normal_continuous
• trace = Trace::normal
• mapping = Mapping::contravariant_piola

L2

SpaceDescriptor serif::discretization::functional_space::L2

inlinestaticconstexpr

Initial value:

{
        .family = Family::l2,
        .continuity = Continuity::discontinuous,
        .trace = Trace::none,
        .mapping = Mapping::identity
    }

Compile-time descriptor for an L2 functional space. This is a convenience descriptor that allows you to easily create an L2 functional space descriptor without having to specify all the parameters. The specifications are.

• family = Family::l2
• continuity = Continuity::discontinuous
• trace = Trace::none
• mapping = Mapping::identity

Mapping2StringMap

auto serif::discretization::functional_space::Mapping2StringMap = meta::enum_to_enum_string_map<Mapping>()

inlinestatic

Mapping from Mapping enum values to their string representations.

String2ContinuityMap

auto serif::discretization::functional_space::String2ContinuityMap = meta::enum_to_string_enum_map<Continuity>()

inlinestatic

Mapping from string representations to Continuity enum values.

String2FamilyMap

auto serif::discretization::functional_space::String2FamilyMap = meta::enum_to_string_enum_map<Family>()

inlinestatic

Mapping from string representations to Family enum values.

String2MappingMap

auto serif::discretization::functional_space::String2MappingMap = meta::enum_to_string_enum_map<Mapping>()

inlinestatic

Mapping from string representations to Mapping enum values.

String2TraceMap

auto serif::discretization::functional_space::String2TraceMap = meta::enum_to_string_enum_map<Trace>()

inlinestatic

Mapping from string representations to Trace enum values.

Trace2StringMap

auto serif::discretization::functional_space::Trace2StringMap = meta::enum_to_enum_string_map<Trace>()

inlinestatic

Mapping from Trace enum values to their string representations.