sphinx/source/libCEEDapi.md

10 …ents are used, the resulting sparse matrix representation of the global operator is computationall…
11 libCEED provides an interface for matrix-free operator description that enables efficient evaluatio…
51 This is illustrated below for the simple case of symmetric linear operator on third order ($Q_3$) s…
62 (fig-operator-decomp)=
123   > - for example, the mass matrix operator maps a **T-vector** to a **T'-vector**
125 …> - using the parallel prolongation operator, one can map the solution **T-vector** to a solution …
132 …> - the T in TA indicates that the data format represents an operator from a **T-vector** to a **T…
137 …> - the parallel prolongation operator, $\bm{P}$, (and its transpose) should use optimized matrix-…
138   > - note that $\bm{P}$ is the operator mapping T-vectors to L-vectors.
144 …> - note that the element prolongation operator is the mapping from an **L-vector** to an **E-vect…
158 Since the global operator $\bm{A}$ is just a series of variational restrictions with $\bm{B}$, $\bm…
166 …ry transfers (with respect to the polynomial order) and near-optimal FLOPs for operator evaluation.
167 It consists of an operator *setup* phase, that evaluates and stores $\bm{D}$ and an operator *apply…
168 When desired, the setup phase may be done as a side-effect of evaluating a different operator, such…
173 …ee transition operators, $\bm{P}$, $\bm{\mathcal{E}}$ and $\bm{B}$, the operator evaluation is dec…
177 …E}}$, $\bm{B}$ and $\bm{D}$ clearly separate the MPI parallelism in the operator ($\bm{P}$) from t…
191 … *backend* implementations and coordinates their action to the original operator on **L-vector** l…
194 (fig-operator-schematic)=
217 - the overall operator $\bm{\mathcal{E}}^T \bm{B}^T \bm{D} \bm{B} \bm{\mathcal{E}}$ is represented …
219 … simple 1D mass matrix (cf. [tests/t500-operator.c](https://github.com/CEED/libCEED/blob/main/test…
221 ```{literalinclude} ../../../tests/t500-operator.c
226 …up operator, combining the quadrature weights with the Jacobian information for the mesh transform…
229 (fig-operator-schematic-mass)=
232 …$\bm{D}$, and input/output vectors corresponding to the libCEED operators in the t500-operator test
237 ```{literalinclude} ../../../tests/t500-operator.c
250 ```{literalinclude} ../../../tests/t500-operator.c
270 …D_EVAL_INTERP` for both input and output fields indicates that the mass operator only contains ter…
292 ```{literalinclude} ../../../tests/t500-operator.c
304 ```{literalinclude} ../../../tests/t500-operator.c
310 ```{literalinclude} ../../../tests/t500-operator.c
325 As with {ref}`CeedQFunction`s, operator fields are added
327 …tes that the vector corresponding to that field will be provided to the operator when {c:func}`Cee…
331 This is accomplished by the operator `op_setup` and its application to `X`, the nodes of the mesh (…
334 ```{literalinclude} ../../../tests/t500-operator.c
340 ```{literalinclude} ../../../tests/t500-operator.c
346 ```{literalinclude} ../../../tests/t500-operator.c
352 The action of the operator is then represented by operator `op_mass` and its {c:func}`CeedOperatorA…
354 ```{literalinclude} ../../../tests/t500-operator.c
360 ```{literalinclude} ../../../tests/t500-operator.c
366 ```{literalinclude} ../../../tests/t500-operator.c