Definition file for Intrepid2 utilities. More...

#include "Intrepid2_Utils.hpp"

Functions
KOKKOS_INLINE_FUNCTION ordinal_type	Intrepid2::getFieldRank (const EFunctionSpace spaceType)
	Returns the rank of fields in a function space of the specified type. More...

KOKKOS_INLINE_FUNCTION ordinal_type	Intrepid2::getOperatorRank (const EFunctionSpace spaceType, const EOperator operatorType, const ordinal_type spaceDim)
	Returns rank of an operator. More...

KOKKOS_INLINE_FUNCTION ordinal_type	Intrepid2::getOperatorOrder (const EOperator operatorType)
	Returns order of an operator. More...

KOKKOS_INLINE_FUNCTION ordinal_type	Intrepid2::getDkEnumeration (const ordinal_type xMult, const ordinal_type yMult, const ordinal_type zMult)

KOKKOS_INLINE_FUNCTION ordinal_type	Intrepid2::getDkCardinality (const EOperator operatorType, const ordinal_type spaceDim)
	Returns cardinality of Dk, i.e., the number of all derivatives of order k. More...

Detailed Description

Definition file for Intrepid2 utilities.

Author: Created by P. Bochev and D. Ridzal and Kyungjoo Kim.

Definition in file Intrepid2_UtilsDef.hpp.

Function Documentation

◆ getDkCardinality()

KOKKOS_INLINE_FUNCTION ordinal_type Intrepid2::getDkCardinality	(	const EOperator	operatorType,
		const ordinal_type	spaceDim
	)

Returns cardinality of Dk, i.e., the number of all derivatives of order k.

The set of all partial derivatives of order k is isomorphic to the set of all multisets of cardinality k with elements taken from the sets {x}, {x,y}, and {x,y,z} in 1D, 2D, and 3D respectively. For example, the partial derivative $\displaystyle D\{1,2,1\}f = \frac{d^4 f}{dx dy^2 dz}$ maps to the multiset $\{x, y, z\}$ with multiplicities $\{1,2,1\}$ . The number of all such multisets is given by the binomial coefficient

$\begin{pmatrix} spaceDim + k - 1 \\ spaceDim - 1 \end{pmatrix}$

Therefore:

in 1D: cardinality = 1
in 2D: cardinality = k + 1
in 3D: cardinality = (k + 1)*(k + 2)/2

Parameters

operatorType	[in] - k-th derivative operator Dk
spaceDim	[in] - space dimension

Returns: the number of all partial derivatives of order k

Definition at line 410 of file Intrepid2_BasisDef.hpp.

References Intrepid2::getDkCardinality().

Referenced by Intrepid2::getDkCardinality().

◆ getDkEnumeration()

KOKKOS_INLINE_FUNCTION ordinal_type Intrepid2::getDkEnumeration	(	const ordinal_type	xMult,
		const ordinal_type	yMult,
		const ordinal_type	zMult
	)

Definition at line 230 of file Intrepid2_UtilsDef.hpp.

◆ getFieldRank()

KOKKOS_INLINE_FUNCTION ordinal_type Intrepid2::getFieldRank ( const EFunctionSpace spaceType )

Returns the rank of fields in a function space of the specified type.

Field rank is defined as the number of indices needed to specify function value and equals 0, 1,or 2 for scalars, vectors and tensors, respectively. The scalar field spaces in Intrepid are FUNCTION_SPACE_HGRAD and FUNCTION_SPACE_HVOL. The vector field spaces are FUNCTION_SPACE_HCURL, FUNCTION_SPACE_HDIV and FUNCTION_SPACE_VECTOR_HGRAD. FUNCTION_SPACE_TENSOR_HGRAD contains rank-2 tensors.

Parameters

spaceType [in] - function space type

Returns: rank of the fields in the specified function space

Definition at line 67 of file Intrepid2_BasisDef.hpp.

References Intrepid2::getFieldRank().

Referenced by Intrepid2::getFieldRank(), and Intrepid2::getOperatorRank().

◆ getOperatorOrder()

KOKKOS_INLINE_FUNCTION ordinal_type Intrepid2::getOperatorOrder ( const EOperator operatorType )

Returns order of an operator.

Parameters

operatorType [in] - type of the operator whose order we want to know

Returns: result ranges from 0 (for OPERATOR_VALUE) to 10 (OPERATOR_D10)

Definition at line 194 of file Intrepid2_BasisDef.hpp.

References Intrepid2::getOperatorOrder().

Referenced by Intrepid2::getOperatorOrder().

◆ getOperatorRank()

KOKKOS_INLINE_FUNCTION ordinal_type Intrepid2::getOperatorRank	(	const EFunctionSpace	spaceType,
		const EOperator	operatorType,
		const ordinal_type	spaceDim
	)

Returns rank of an operator.

When an operator acts on a field of a certain rank, the result can be a field with the same or a different rank. Operator rank is defined the difference between the ranks of the output field and the input field:

Rank(OPERATOR) = Rank(OPERATOR(FIELD)) - Rank(FIELD)

Therefore, operator rank allows us to figure out the rank of the result:

Rank(OPERATOR(FIELD)) = Rank(FIELD) + Rank(OPERATOR)

and provides means to size properly arrays for output results. The following table summarizes operator ranks (~ denotes undefined, below slash means 3D). By default, in 1D any operator other than VALUE has rank 1, i.e., GRAD, CURL and DIV reduce to d/dx and Dk are the higher-order derivatives d^k/dx^k. Only scalar functions are allowed in 1D.

|========|======|============================|=========|==========|==========|==========|
| field  | rank |  FUNCTION_SPACE_[type]     |  VALUE  | GRAD, Dk |   CURL   |    DIV   |
|--------|------|----------------------------|---------|----------|----------|----------|
| scalar |   0  |  HGRAD, HVOL               |    0    |     1    | 3-dim/~  |     ~    |
| vector |   1  |  HCURL, HDIV, VECTOR_HGRAD |    0    |     1    | dim - 3  |    -1    |
| tensor |   2  |  TENSOR_HGRAD              |    0    |     1    | dim - 3  |    -1    |
|--------|------|----------------------------|---------|----------|----------|----------|
|   1D   |   0  |  HGRAD, HVOL only          |    0    |     1    |     1    |     1    |
|=======================================================================================|

Parameters

spaceType	[in] - function space type
operatorType	[in] - the operator acting on the specified function space
spaceDim	[in] - spatial dimension

Returns: rank of the operator as defined in the table

Definition at line 96 of file Intrepid2_BasisDef.hpp.

References Intrepid2::getFieldRank(), and Intrepid2::getOperatorRank().

Referenced by Intrepid2::getOperatorRank().

Functions

Detailed Description

Function Documentation

◆ getDkCardinality()

◆ getDkEnumeration()

◆ getFieldRank()

◆ getOperatorOrder()

◆ getOperatorRank()