sphinx/source/libCEEDapi.md

51 …us ($H^1$) elements, where we use the notions **T-vector**, **L-vector**, **E-vector** and **Q-vec…
56 - Element restriction $\bm{\mathcal{E}}$
60 …t and trial space differ, they get their own versions of $\bm{P}$, $\bm{\mathcal{E}}$ and $\bm{B}$.
68 …adaptive mesh refinement (AMR), the restrictions $\bm{P}$ and $\bm{\mathcal{E}}$ will involve not …
93 - Per element decomposition, **E-vector**:
98   > ```{image} ../../img/E-vector.svg
105 …> - this way, an **E-vector** can be derived from an **L-vector** without any communications and w…
106 …> - in other words, an entry in an **E-vector** is obtained by copying an entry from the correspon…
117 …> - this is similar to **E-vector** where instead of DoFs, the vector represents values at quadrat…
122   > - here X can be any of the T, L, E, or Q categories
144 …> - note that the element prolongation operator is the mapping from an **L-vector** to an **E-vect…
158 …$ is just a series of variational restrictions with $\bm{B}$, $\bm{\mathcal{E}}$ and $\bm{P}$, sta…
160 …r**) or element (**E-vector**) matrices and perform the action of $\bm{A}$ using matvecs with $\bm…
163 …D}$ (or portions of it) and evaluate the actions of $\bm{P}$, $\bm{\mathcal{E}}$ and $\bm{B}$ on-t…
173 … $\bm{P}$, $\bm{\mathcal{E}}$ and $\bm{B}$, the operator evaluation is decoupled  on their ranges,…
177 …cal{E}}$, $\bm{B}$ and $\bm{D}$ clearly separate the MPI parallelism in the operator ($\bm{P}$) fr…
178 …r algebra for $\bm{P}$, sparse (on-device) linear algebra for $\bm{\mathcal{E}}$, dense/structured…
191 …ser essentially describes in the *frontend* the operators $\bm{\bm{\mathcal{E}}}$, $\bm{B}$, and $…
197 …ide libCEED Operators, through backend implementations of $\bm{\bm{\mathcal{E}}}$, $\bm{B}$, and $…
212 - **L-**, **E-** and **Q-vector** are represented as variables of type {ref}`CeedVector`.
213   (A backend may choose to operate incrementally without forming explicit **E-** or **Q-vectors**.)
214 - $\bm{\mathcal{E}}$ is represented as variable of type {ref}`CeedElemRestriction`.
217 - the overall operator $\bm{\mathcal{E}}^T \bm{B}^T \bm{D} \bm{B} \bm{\mathcal{E}}$ is represented …
232 Specific combination of $\bm{\bm{\mathcal{E}}}$, $\bm{B}$, $\bm{D}$, and input/output vectors corre…
301 The $\bm{\mathcal{E}}$ operators for the mesh nodes, `elem_restr_x`, and the unknown field, `elem_r…
319 … store **E-vectors** (inter-element continuity has been subsumed by the parallel restriction $\bm{…
320 We plan to support other structured representations of $\bm{\mathcal{E}}$ which will be added accor…
321 …rocessed uniformly and applying the constraints via $\bm{\mathcal{E}}$ so that the **E-vector** is…
324 These operations, $\bm{\mathcal{E}}$, $\bm{B}$, and $\bm{D}$, are combined with a {ref}`CeedOperato…
326 separately with a matching field name, basis ($\bm{B}$), element restriction ($\bm{\mathcal{E}}$), …