Lines Matching refs:vector

30 …f_0$ represents all terms in {eq}`residual` which multiply the (possibly vector-valued) test funct…
51 …ous ($H^1$) elements, where we use the notions **T-vector**, **L-vector**, **E-vector** and **Q-ve…
75 - True degrees of freedom/unknowns, **T-vector**:
78   > - this is a non-overlapping vector decomposition
81   > ```{image} ../../img/T-vector.svg
84 - Local (w.r.t. processors) degrees of freedom/unknowns, **L-vector**:
87 …> - this is an overlapping vector decomposition with overlaps only across different processors---t…
90   > ```{image} ../../img/L-vector.svg
93 - Per element decomposition, **E-vector**:
98   > ```{image} ../../img/E-vector.svg
103   > - the **L-vector** is enhanced with the hanging/dependent DoFs
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…
108   > ```{image} ../../img/L-vector-AMR.svg
115 - Quadrature point vector, **Q-vector**:
117 …> - this is similar to **E-vector** where instead of DoFs, the vector represents values at quadrat…
121   > - **X-vector**, or **primal X-vector**, and **X'-vector**, or **dual X-vector**
123   > - for example, the mass matrix operator maps a **T-vector** to a **T'-vector**
124   > - the solutions vector is a **T-vector**, and the RHS vector is a **T'-vector**
125 …arallel prolongation operator, one can map the solution **T-vector** to a solution **L-vector**, e…
132 …in TA indicates that the data format represents an operator from a **T-vector** to a **T'-vector**.
144 …note that the element prolongation operator is the mapping from an **L-vector** to an **E-vector**.
149   > - the stored data can be viewed as a **Q-vector**.
154 … of the coefficient, e.g. constant, piecewise-constant, or given as a **Q-vector** (Q-coefficient).
159 For example, one can compute and store a global matrix on **T-vector** level.
160 Alternatively, one can compute and store only the subdomain (**L-vector**) or element (**E-vector**…
167 …and an operator *apply* (evaluation) phase that computes the action of $\bm{A}$ on an input vector.
175 …he **T-vector** over MPI ranks (a non-overlapping decomposition, as is typically used for sparse m…
181 Our API is thus focused on the **L-vector** level, where the logical devices, which in the library …
191 …ementations and coordinates their action to the original operator on **L-vector** level (i.e. inde…
197 Flow of data through vector types inside libCEED Operators, through backend implementations of $\bm…
212 - **L-**, **E-** and **Q-vector** are represented as variables of type {ref}`CeedVector`.
257 The second argument is an expected vector length.
258 … the caller must ensure that the number of quadrature points `Q` is divisible by the vector length.
321 …m P$ so that the **L-vector** can be processed uniformly and applying the constraints via $\bm{\ma…
326 … matching field name, basis ($\bm{B}$), element restriction ($\bm{\mathcal{E}}$), and **L-vector**.
327 The flag `CEED_VECTOR_ACTIVE` indicates that the vector corresponding to that field will be provide…
328 Otherwise the input/output will be read from/written to the specified **L-vector**.
352 …perator `op_mass` and its {c:func}`CeedOperatorApply()` to the input **L-vector** `U` with output …