Lines Matching refs:bm

18 \langle v, u \rangle = \int_\Omega v u d \bm{x},
21 where $\bm{x} \in \mathbb{R}^d \supset \Omega$.
26 \langle  \bm v,  \bm f(u) \rangle = \int_\Omega  \bm v \cdot  \bm f_0 (u, \nabla u) + \nabla \bm v …
29 for all $\bm v$ in the corresponding homogeneous space $V_0$, where $\bm f_0$ and $\bm f_1$ contain…
30 …bm f_0$ represents all terms in {eq}`residual` which multiply the (possibly vector-valued) test fu…
31 For an n-component problems in $d$ dimensions, $\bm f_0 \in \mathbb{R}^n$ and $\bm f_1 \in \mathbb{…
34 …bm v \!:\! \bm f_1$ represents contraction over both fields and spatial dimensions while a single …
39 …tory), we store the term $\bm f_0$ directly into `v`, and the term $\bm f_1$ directly into `dv` (w…
40 If equation {eq}`residual` only presents a term of the type $\bm f_0$, the {ref}`CeedQFunction` wil…
41 If equation {eq}`residual` also presents a term of the type $\bm f_1$, then the {ref}`CeedQFunction…
55 - Subdomain restriction $\bm{P}$
56 - Element restriction $\bm{\mathcal{E}}$
57 - Basis (Dofs-to-Qpts) evaluator $\bm{B}$
58 - Operator at quadrature points $\bm{D}$
60 …t and trial space differ, they get their own versions of $\bm{P}$, $\bm{\mathcal{E}}$ and $\bm{B}$.
68 Note that in the case of adaptive mesh refinement (AMR), the restrictions $\bm{P}$ and $\bm{\mathca…
69 … subdomains ($\bm P_1$, $\bm P_2$, etc.), and it may be convenient to split $\bm{D}$ as the produc…
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.
158 …bm{A}$ is just a series of variational restrictions with $\bm{B}$, $\bm{\mathcal{E}}$ and $\bm{P}$…
160 …E-vector**) matrices and perform the action of $\bm{A}$ using matvecs with $\bm{P}$ or $\bm{P}$ an…
163 …e we compute and store only $\bm{D}$ (or portions of it) and evaluate the actions of $\bm{P}$, $\b…
164 … quadrature points on *quad* and *hex* elements to perform the action of $\bm{B}$ without storing …
167 …phase, that evaluates and stores $\bm{D}$ and an operator *apply* (evaluation) phase that computes…
169 …y phases are different depending on the physics being expressed and the representation of $\bm{D}$.
173 …tors, $\bm{P}$, $\bm{\mathcal{E}}$ and $\bm{B}$, the operator evaluation is decoupled  on their ra…
175 Thus, a natural mapping of $\bm{A}$ on a parallel computer is to split the **T-vector** over MPI ra…
177 …bm{P}$, $\bm{\mathcal{E}}$, $\bm{B}$ and $\bm{D}$ clearly separate the MPI parallelism in the oper…
178 …bm{P}$, sparse (on-device) linear algebra for $\bm{\mathcal{E}}$, dense/structured linear algebra …
186 The communications among the devices, e.g. required for applying the action of $\bm{P}$, are curren…
191 …essentially describes in the *frontend* the operators $\bm{\bm{\mathcal{E}}}$, $\bm{B}$, and $\bm{…
197 …libCEED Operators, through backend implementations of $\bm{\bm{\mathcal{E}}}$, $\bm{B}$, and $\bm{…
214 - $\bm{\mathcal{E}}$ is represented as variable of type {ref}`CeedElemRestriction`.
215 - $\bm{B}$ is represented as variable of type {ref}`CeedBasis`.
216 - the action of $\bm{D}$ is represented as variable of type {ref}`CeedQFunction`.
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…
247 …nd stores $\bm{D}$, in this case a scalar value in each quadrature point, while `mass` uses these …
288 The $\bm{B}$ operators for the mesh nodes, `basis_x`, and the unknown field, `basis_u`, are defined…
301 The $\bm{\mathcal{E}}$ operators for the mesh nodes, `elem_restr_x`, and the unknown field, `elem_r…
319 …ontinuity has been subsumed by the parallel restriction $\bm{P}$), the element restriction $\bm{\m…
320 We plan to support other structured representations of $\bm{\mathcal{E}}$ which will be added accor…
321 …g the node constraints via $\bm P$ so that the **L-vector** can be processed uniformly and applyin…
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 ($\bm{\mathcal{E}}$), …
330 With partial assembly, we first perform a setup stage where $\bm{D}$ is evaluated and stored.