1# PETSc in a nutshell 2 3See {any}`handson` to immediately jump in and run PETSc code. 4 5PETSc/TAO is a tool for writing, analyzing, and optimizing large-scale numerical simulations. 6 7```{image} /images/manual/library_structure.svg 8:align: center 9:alt: PETSc Structure Diagram 10``` 11 12## Algebraic objects 13 14- {any}`Vectors <ch_vectors>` - containers for simulation solutions, right-hand sides of linear systems, etc (`Vec`). 15 16- {any}`Matrices <ch_matrices>` - contain Jacobians and operators that define linear systems (`Mat`). 17 18 - {any}`Multiple sparse and dense matrix storage formats<doc_matrix>`, 19 - {any}`Limited memory variable metric representations<sec_matlmvm>`, 20 - {any}`block<sec_block_matrices>` and {any}`nested<sec_matnest>` representations, 21 - {any}`Easy, efficient matrix assembly and interface <sec_matcreate>`. 22 23- Indices - used to access portions of vectors and matrix, for example {1,2,4} or 1:10 (`IS`). 24 25## Solvers 26 27- {any}`Linear solvers<ch_ksp>` based on preconditioners (`PC`) and Krylov subspace methods (`KSP`). 28 29- {any}`Nonlinear solvers <ch_snes>` (`SNES`). 30 31- {any}`Time integrators <ch_ts>`, (ODE/PDE), explicit, implicit, IMEX, (`TS`) 32 33 - Local and global error estimators 34 - {any}`section_sa`. 35 36- {any}`Optimization <ch_tao>` with equality and inequality constraints, first and second order (Newton) methods (`Tao`). 37 38- {any}`PetscRegressor <ch_regressor>` for regression and classification problems (`PetscRegressor`). 39 40- Eigenvalue/Eigenvectors and related algorithms in the package [SLEPc](https://slepc.upv.es). 41 42## Model/Discretization Interfaces to Solvers 43 44- Simple structured grids, `DMDA`. 45- Staggered grids, {any}`ch_stag`, `DMSTAG`. 46- Unstructured grids, {any}`ch_unstructured`, `DMPLEX`. 47- Networks/graphs, for example the power grid, river networks, the nervous system, {any}`ch_network`, `DMNETWORK`. 48- Quad or octree grids, `DMFOREST`. 49- Particles, `DMSWARM`. 50 51:::{seealso} 52For full feature list see: 53 54- {ref}`Vector table <doc_vector>` 55- {ref}`Matrix table <doc_matrix>` 56- {ref}`Linear solvers table <doc_linsolve>` 57- {ref}`Nonlinear solvers table <doc_nonlinsolve>` 58- {ref}`ODE integrators table <integrator_table>` 59- {ref}`Optimizers table <doc_taosolve>` 60- {ref}`Model/discretization interfaces to solvers table <dm_table>` 61::: 62 63## Utilities for Simulations/Solvers 64 65Runtime 66 67- control of the simulation via {any}`runtime options <sec_options>` 68- visualization of the solvers and simulation via {any}`viewers <sec_viewers>`, 69- {any}`monitoring <sec_kspmonitor>` of solution progress, 70- {any}`profiling <ch_profiling>` of the performance, 71- robust {any}`error handling <sec_errors>`. 72
