CeedBasis¶

A CeedBasis defines the discrete finite element basis and associated quadrature rule.

Discrete element bases and quadrature¶

typedef struct CeedBasis_private *CeedBasis¶: Handle for object describing discrete finite element evaluations.

const CeedBasis CEED_BASIS_NONE = &ceed_basis_none¶: Argument for CeedOperatorSetField indicating that the field does not require a CeedBasis.

const CeedBasis CEED_BASIS_COLLOCATED = &ceed_basis_none¶: This feature will be removed. Use CEED_BASIS_NONE.

int CeedBasisCreateTensorH1(Ceed ceed, CeedInt dim, CeedInt num_comp, CeedInt P_1d, CeedInt Q_1d, const CeedScalar *interp_1d, const CeedScalar *grad_1d, const CeedScalar *q_ref_1d, const CeedScalar *q_weight_1d, CeedBasis *basis)¶

Create a tensor-product basis for H^1 discretizations.

User Functions

Parameters

ceed – [in] Ceed object where the CeedBasis will be created
dim – [in] Topological dimension
num_comp – [in] Number of field components (1 for scalar fields)
P_1d – [in] Number of nodes in one dimension
Q_1d – [in] Number of quadrature points in one dimension
interp_1d – [in] Row-major (Q_1d * P_1d) matrix expressing the values of nodal basis functions at quadrature points
grad_1d – [in] Row-major (Q_1d * P_1d) matrix expressing derivatives of nodal basis functions at quadrature points
q_ref_1d – [in] Array of length Q_1d holding the locations of quadrature points on the 1D reference element [-1, 1]
q_weight_1d – [in] Array of length Q_1d holding the quadrature weights on the reference element
basis – [out] Address of the variable where the newly created CeedBasis will be stored.

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisCreateTensorH1Lagrange(Ceed ceed, CeedInt dim, CeedInt num_comp, CeedInt P, CeedInt Q, CeedQuadMode quad_mode, CeedBasis *basis)¶

Create a tensor-product Lagrange basis.

User Functions

Parameters

ceed – [in] Ceed object where the CeedBasis will be created
dim – [in] Topological dimension of element
num_comp – [in] Number of field components (1 for scalar fields)
P – [in] Number of Gauss-Lobatto nodes in one dimension. The polynomial degree of the resulting Q_k element is k=P-1.
Q – [in] Number of quadrature points in one dimension.
quad_mode – [in] Distribution of the Q quadrature points (affects order of accuracy for the quadrature)
basis – [out] Address of the variable where the newly created CeedBasis will be stored.

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisCreateH1(Ceed ceed, CeedElemTopology topo, CeedInt num_comp, CeedInt num_nodes, CeedInt num_qpts, const CeedScalar *interp, const CeedScalar *grad, const CeedScalar *q_ref, const CeedScalar *q_weight, CeedBasis *basis)¶

Create a non tensor-product basis for H^1 discretizations.

User Functions

Parameters

ceed – [in] Ceed object where the CeedBasis will be created
topo – [in] Topology of element, e.g. hypercube, simplex, ect
num_comp – [in] Number of field components (1 for scalar fields)
num_nodes – [in] Total number of nodes
num_qpts – [in] Total number of quadrature points
interp – [in] Row-major (num_qpts * num_nodes) matrix expressing the values of nodal basis functions at quadrature points
grad – [in] Row-major (dim * num_qpts * num_nodes) matrix expressing derivatives of nodal basis functions at quadrature points
q_ref – [in] Array of length num_qpts * dim holding the locations of quadrature points on the reference element
q_weight – [in] Array of length num_qpts holding the quadrature weights on the reference element
basis – [out] Address of the variable where the newly created CeedBasis will be stored.

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisCreateHdiv(Ceed ceed, CeedElemTopology topo, CeedInt num_comp, CeedInt num_nodes, CeedInt num_qpts, const CeedScalar *interp, const CeedScalar *div, const CeedScalar *q_ref, const CeedScalar *q_weight, CeedBasis *basis)¶

Create a non tensor-product basis for \(H(\mathrm{div})\) discretizations.

User Functions

Parameters

ceed – [in] Ceed object where the CeedBasis will be created
topo – [in] Topology of element (CEED_TOPOLOGY_QUAD, CEED_TOPOLOGY_PRISM, etc.), dimension of which is used in some array sizes below
num_comp – [in] Number of components (usually 1 for vectors in H(div) bases)
num_nodes – [in] Total number of nodes (dofs per element)
num_qpts – [in] Total number of quadrature points
interp – [in] Row-major (dim * num_qpts * num_nodes) matrix expressing the values of basis functions at quadrature points
div – [in] Row-major (num_qpts * num_nodes) matrix expressing divergence of basis functions at quadrature points
q_ref – [in] Array of length num_qpts * dim holding the locations of quadrature points on the reference element
q_weight – [in] Array of length num_qpts holding the quadrature weights on the reference element
basis – [out] Address of the variable where the newly created CeedBasis will be stored.

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisCreateHcurl(Ceed ceed, CeedElemTopology topo, CeedInt num_comp, CeedInt num_nodes, CeedInt num_qpts, const CeedScalar *interp, const CeedScalar *curl, const CeedScalar *q_ref, const CeedScalar *q_weight, CeedBasis *basis)¶

Create a non tensor-product basis for \(H(\mathrm{curl})\) discretizations.

User Functions

Parameters

ceed – [in] Ceed object where the CeedBasis will be created
topo – [in] Topology of element (CEED_TOPOLOGY_QUAD, CEED_TOPOLOGY_PRISM, etc.), dimension of which is used in some array sizes below
num_comp – [in] Number of components (usually 1 for vectors in H(curl) bases)
num_nodes – [in] Total number of nodes (dofs per element)
num_qpts – [in] Total number of quadrature points
interp – [in] Row-major (dim * num_qpts * num_nodes) matrix expressing the values of basis functions at quadrature points
curl – [in] Row-major (curl_comp * num_qpts * num_nodes, curl_comp = 1 if dim < 3 else dim) matrix expressing curl of basis functions at quadrature points
q_ref – [in] Array of length num_qpts * dim holding the locations of quadrature points on the reference element
q_weight – [in] Array of length num_qpts holding the quadrature weights on the reference element
basis – [out] Address of the variable where the newly created CeedBasis will be stored.

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisCreateProjection(CeedBasis basis_from, CeedBasis basis_to, CeedBasis *basis_project)¶

Create a CeedBasis for projection from the nodes of basis_from to the nodes of basis_to.

Only CEED_EVAL_INTERP will be valid for the new basis, basis_project. For H^1 spaces, CEED_EVAL_GRAD will also be valid. The interpolation is given by interp_project = interp_to^+ * interp_from, where the pseudoinverse interp_to^+ is given by QR factorization. The gradient (for the H^1 case) is given by grad_project = interp_to^+ * grad_from.

Note: basis_from and basis_to must have compatible quadrature spaces.

Note: basis_project will have the same number of components as basis_from, regardless of the number of components that basis_to has. If basis_from has 3 components and basis_to has 5 components, then basis_project will have 3 components.

User Functions

Parameters

basis_from – [in] CeedBasis to prolong from
basis_to – [in] CeedBasis to prolong to
basis_project – [out] Address of the variable where the newly created CeedBasis will be stored.

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisReferenceCopy(CeedBasis basis, CeedBasis *basis_copy)¶

Copy the pointer to a CeedBasis.

Note: If the value of basis_copy passed into this function is non-NULL, then it is assumed that basis_copy is a pointer to a CeedBasis. This CeedBasis will be destroyed if basis_copy is the only reference to this CeedBasis.

User Functions

Parameters

basis – [in] CeedBasis to copy reference to
basis_copy – [inout] Variable to store copied reference

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisView(CeedBasis basis, FILE *stream)¶

View a CeedBasis.

User Functions

Parameters

basis – [in] CeedBasis to view
stream – [in] Stream to view to, e.g., stdout

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisApply(CeedBasis basis, CeedInt num_elem, CeedTransposeMode t_mode, CeedEvalMode eval_mode, CeedVector u, CeedVector v)¶

Apply basis evaluation from nodes to quadrature points or vice versa.

User Functions

Parameters

basis – [in] CeedBasis to evaluate
num_elem – [in] The number of elements to apply the basis evaluation to; the backend will specify the ordering in CeedElemRestrictionCreateBlocked()
t_mode – [in] CEED_NOTRANSPOSE to evaluate from nodes to quadrature points; CEED_TRANSPOSE to apply the transpose, mapping from quadrature points to nodes
eval_mode – [in] CEED_EVAL_NONE to use values directly, CEED_EVAL_INTERP to use interpolated values, CEED_EVAL_GRAD to use gradients, CEED_EVAL_DIV to use divergence, CEED_EVAL_CURL to use curl, CEED_EVAL_WEIGHT to use quadrature weights.
u – [in] Input CeedVector
v – [out] Output CeedVector

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisApplyAtPoints(CeedBasis basis, CeedInt num_points, CeedTransposeMode t_mode, CeedEvalMode eval_mode, CeedVector x_ref, CeedVector u, CeedVector v)¶

Apply basis evaluation from nodes to arbitrary points.

User Functions

Parameters

basis – [in] CeedBasis to evaluate
num_points – [in] The number of points to apply the basis evaluation to
t_mode – [in] CEED_NOTRANSPOSE to evaluate from nodes to points; CEED_TRANSPOSE to apply the transpose, mapping from points to nodes
eval_mode – [in] CEED_EVAL_INTERP to use interpolated values, CEED_EVAL_GRAD to use gradients
x_ref – [in] CeedVector holding reference coordinates of each point
u – [in] Input CeedVector, of length num_nodes * num_comp for CEED_NOTRANSPOSE
v – [out] Output CeedVector, of length num_points * num_q_comp for CEED_NOTRANSPOSE with CEED_EVAL_INTERP

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetCeed(CeedBasis basis, Ceed *ceed)¶

Get Ceed associated with a CeedBasis.

Advanced Functions

Parameters

basis – [in] CeedBasis
ceed – [out] Variable to store Ceed

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetDimension(CeedBasis basis, CeedInt *dim)¶

Get dimension for given CeedBasis.

Advanced Functions

Parameters

basis – [in] CeedBasis
dim – [out] Variable to store dimension of basis

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetTopology(CeedBasis basis, CeedElemTopology *topo)¶

Get topology for given CeedBasis.

Advanced Functions

Parameters

basis – [in] CeedBasis
topo – [out] Variable to store topology of basis

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetNumComponents(CeedBasis basis, CeedInt *num_comp)¶

Get number of components for given CeedBasis.

Advanced Functions

Parameters

basis – [in] CeedBasis
num_comp – [out] Variable to store number of components of basis

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetNumNodes(CeedBasis basis, CeedInt *P)¶

Get total number of nodes (in dim dimensions) of a CeedBasis.

Utility Functions

Parameters

basis – [in] CeedBasis
P – [out] Variable to store number of nodes

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetNumNodes1D(CeedBasis basis, CeedInt *P_1d)¶

Get total number of nodes (in 1 dimension) of a CeedBasis.

Advanced Functions

Parameters

basis – [in] CeedBasis
P_1d – [out] Variable to store number of nodes

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetNumQuadraturePoints(CeedBasis basis, CeedInt *Q)¶

Get total number of quadrature points (in dim dimensions) of a CeedBasis.

Utility Functions

Parameters

basis – [in] CeedBasis
Q – [out] Variable to store number of quadrature points

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetNumQuadraturePoints1D(CeedBasis basis, CeedInt *Q_1d)¶

Get total number of quadrature points (in 1 dimension) of a CeedBasis.

Advanced Functions

Parameters

basis – [in] CeedBasis
Q_1d – [out] Variable to store number of quadrature points

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetQRef(CeedBasis basis, const CeedScalar **q_ref)¶

Get reference coordinates of quadrature points (in dim dimensions) of a CeedBasis.

Advanced Functions

Parameters

basis – [in] CeedBasis
q_ref – [out] Variable to store reference coordinates of quadrature points

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetQWeights(CeedBasis basis, const CeedScalar **q_weight)¶

Get quadrature weights of quadrature points (in dim dimensions) of a CeedBasis.

Advanced Functions

Parameters

basis – [in] CeedBasis
q_weight – [out] Variable to store quadrature weights

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetInterp(CeedBasis basis, const CeedScalar **interp)¶

Get interpolation matrix of a CeedBasis.

Advanced Functions

Parameters

basis – [in] CeedBasis
interp – [out] Variable to store interpolation matrix

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetInterp1D(CeedBasis basis, const CeedScalar **interp_1d)¶

Get 1D interpolation matrix of a tensor product CeedBasis.

Backend Developer Functions

Parameters

basis – [in] CeedBasis
interp_1d – [out] Variable to store interpolation matrix

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetGrad(CeedBasis basis, const CeedScalar **grad)¶

Get gradient matrix of a CeedBasis.

Advanced Functions

Parameters

basis – [in] CeedBasis
grad – [out] Variable to store gradient matrix

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetGrad1D(CeedBasis basis, const CeedScalar **grad_1d)¶

Get 1D gradient matrix of a tensor product CeedBasis.

Advanced Functions

Parameters

basis – [in] CeedBasis
grad_1d – [out] Variable to store gradient matrix

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetDiv(CeedBasis basis, const CeedScalar **div)¶

Get divergence matrix of a CeedBasis.

Advanced Functions

Parameters

basis – [in] CeedBasis
div – [out] Variable to store divergence matrix

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisGetCurl(CeedBasis basis, const CeedScalar **curl)¶

Get curl matrix of a CeedBasis.

Advanced Functions

Parameters

basis – [in] CeedBasis
curl – [out] Variable to store curl matrix

Returns

An error code: 0 - success, otherwise - failure

int CeedBasisDestroy(CeedBasis *basis)¶

Destroy a CeedBasis.

User Functions

Parameters

basis – [inout] CeedBasis to destroy

Returns

An error code: 0 - success, otherwise - failure

int CeedGaussQuadrature(CeedInt Q, CeedScalar *q_ref_1d, CeedScalar *q_weight_1d)¶

Construct a Gauss-Legendre quadrature.

Utility Functions

Parameters

Q – [in] Number of quadrature points (integrates polynomials of degree 2*Q-1 exactly)
q_ref_1d – [out] Array of length Q to hold the abscissa on [-1, 1]
q_weight_1d – [out] Array of length Q to hold the weights

Returns

An error code: 0 - success, otherwise - failure

int CeedLobattoQuadrature(CeedInt Q, CeedScalar *q_ref_1d, CeedScalar *q_weight_1d)¶

Construct a Gauss-Legendre-Lobatto quadrature.

Utility Functions

Parameters

Q – [in] Number of quadrature points (integrates polynomials of degree 2*Q-3 exactly)
q_ref_1d – [out] Array of length Q to hold the abscissa on [-1, 1]
q_weight_1d – [out] Array of length Q to hold the weights

Returns

An error code: 0 - success, otherwise - failure

Typedefs and Enumerations¶

enum CeedTransposeMode¶

Denotes whether a linear transformation or its transpose should be applied.

Values:

enumerator CEED_NOTRANSPOSE¶: Apply the linear transformation.

enumerator CEED_TRANSPOSE¶: Apply the transpose.

enum CeedEvalMode¶

Basis evaluation mode.

Values:

enumerator CEED_EVAL_NONE¶: Perform no evaluation (either because there is no data or it is already at quadrature points)

enumerator CEED_EVAL_INTERP¶: Interpolate from nodes to quadrature points.

enumerator CEED_EVAL_GRAD¶: Evaluate gradients at quadrature points from input in the basis.

enumerator CEED_EVAL_DIV¶: Evaluate divergence at quadrature points from input in the basis.

enumerator CEED_EVAL_CURL¶: Evaluate curl at quadrature points from input in the basis.

enumerator CEED_EVAL_WEIGHT¶: Using no input, evaluate quadrature weights on the reference element.

enum CeedQuadMode¶

Type of quadrature; also used for location of nodes.

Values:

enumerator CEED_GAUSS¶: Gauss-Legendre quadrature.

enumerator CEED_GAUSS_LOBATTO¶: Gauss-Legendre-Lobatto quadrature.

enum CeedElemTopology¶

Type of basis shape to create non-tensor element basis.

Dimension can be extracted with bitwise AND (CeedElemTopology & 2**(dim + 2)) == TRUE

Values:

enumerator CEED_TOPOLOGY_LINE¶: Line.

enumerator CEED_TOPOLOGY_TRIANGLE¶: Triangle - 2D shape.

enumerator CEED_TOPOLOGY_QUAD¶: Quadralateral - 2D shape.

enumerator CEED_TOPOLOGY_TET¶: Tetrahedron - 3D shape.

enumerator CEED_TOPOLOGY_PYRAMID¶: Pyramid - 3D shape.

enumerator CEED_TOPOLOGY_PRISM¶: Prism - 3D shape.

enumerator CEED_TOPOLOGY_HEX¶: Hexehedron - 3D shape.