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12 structures that can be understood by the linear algebraic and solver components of PETSc (`Vec`, `M…
15 … `DMNetwork` mesh descriptions, much of its operation is general enough to be utilized for other t…
22 Specific entries (or collections of entries) in a `Vec` (or a simple array) can be associated with …
24 Other iterable set examples can be as simple as the points of a finite difference grid, or cells of…
27 So given the tuple for a mesh point, its data can be accessed by `array[offset + d]`, where `d` in …
31 The mesh points for a `PetscSection` must be contiguously numbered and are defined to be in some ra…
33 … must be contiguously numbered, the indexes into the array (defined by each `(ndof, offset)` tuple…
34 In other words, there may be elements in the array that are not associated with any mesh points, th…
40 If `ndof` is not set for a mesh point, it is assumed to be 0.
44 This concatenation can be done in a different order by setting a permutation, which is described in…
46 Alternatively, the offset for each mesh point can be set manually by `PetscSectionSetOffset()`, tho…
55 2. Specify the number of dofs per point with `PetscSectionSetDof()`. Any values not set will be zer…
78 …dof for each point on each field with `PetscSectionSetFieldDof()`. Any values not set will be zero.
79 4. Set the **total** number of dof for each point with `PetscSectionSetDof()`. Thus value must be g…
80    `PetscSectionSetFieldDof()` at that point. Again, values not set will be zero.
85 A `PetscSection` with one field and and offsets set in `PetscSectionSetUp()` may be thought of as d…
89 In other words, will the array be laid out in a point-major or field-major fashion.
119 …SectionGetStorageSize()` to determine the total number of entries that can be stored in an array o…
128 The memory locations in the associated array are found using an **offset** which can be obtained wi…
151 `PetscSection` can also be applied to distributed problems as well.
157 For each shared mesh point, appoint one process to be the owner of that mesh point.
166 The `globalSection` can be used to create global vectors, just as the local section is used to crea…
168 To perform the global-to-local and local-to-global communication, we define `sectionSF` to be the `…
173 The `localSection`, `globalSection`, `pointSF`, and `sectionSF` on a `DM` can be obtained via `DMGe…
174 Additionally, communication from global to local vectors and vice versa can be done via `DMGlobalTo…
179 In addition to describing parallel data, the `localSection`/`globalSection` pair can be used to des…
183 Constraints should be indicated in the `localSection`.
185 This must be done before `PetscSectionCreateGlobalSection()` is called to create the `globalSection…
187 … to have constraints set in a `localSection`, but have the `globalSection` be generated to include…
195 …etUp()` is called, the data laid out in the associated array is assumed to be in the same order of…
198 It may be desired to have a different the ordering of data in the array than the order of grid poin…
201 This can be accomplished by either changing the indexes of the grid points themselves, or by inform…
207 This must be called before `PetscSectionSetUp()` and will only affect the calculation of the offset…
216 A description of those features will be left to {any}`ch_unstructured`.
221 [^petscsection-footnote]: A `PetscSection` can be thought of as a generalization of `PetscLayout`, …