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===================
PETSc in a nutshell
===================
See :any:`handson` to immediately jump in and run PETSc code.
PETSc/TAO is a tool for writing, analyzing, and optimizing large-scale numerical simulations.
.. image:: /images/manual/library_structure.svg
:alt: PETSc Structure Diagram
:align: center
Algebraic objects
=================
* :any:`Vectors <ch_vectors>` - containers for simulation solutions, right-hand sides of linear systems, etc (``Vec``).
* :any:`Matrices <ch_matrices>` - contain Jacobians and operators that define linear systems (``Mat``).
* :any:`Multiple sparse and dense matrix storage formats<doc_matrix>`,
* :any:`Limited memory variable metric representations<sec_matlmvm>`,
* :any:`block<sec_block_matrices>` and :any:`nested<sec_matnest>` representations,
* :any:`Easy, efficient matrix assembly and interface <sec_matcreate>`.
* Indices - used to access portions of vectors and matrix, for example {1,2,4} or 1:10 (``IS``).
Solvers
=======
* :any:`Linear solvers<ch_ksp>` based on preconditioners (``PC``) and Krylov subspace methods (``KSP``).
* :any:`Nonlinear solvers <ch_snes>` (``SNES``).
* :any:`Time integrators <ch_ts>`, (ODE/PDE), explicit, implicit, IMEX, (``TS``)
* Local and global error estimators
* :any:`section_sa`.
* :any:`Optimization <ch_tao>` with equality and inequality constraints, first and second order (Newton) methods (``Tao``).
* Eigenvalue/Eigenvectors and related algorithms in the package `SLEPc <https://slepc.upv.es>`__.
Model/Discretization Interfaces to Solvers
==========================================
* Simple structured grids, ``DMDA``.
* Staggered grids, :any:`ch_stag`, ``DMSTAG``.
* Unstructured grids, :any:`ch_unstructured`, ``DMPLEX``.
* Networks/graphs, for example the power grid, river networks, the nervous system, :any:`ch_network`, ``DMNETWORK``.
* Quad or octree grids, ``DMFOREST``.
* Particles, ``DMSWARM``.
.. seealso::
For full feature list see:
- :ref:`Vector table <doc_vector>`
- :ref:`Matrix table <doc_matrix>`
- :ref:`Linear solvers table <doc_linsolve>`
- :ref:`Nonlinear solvers table <doc_nonlinsolve>`
- :ref:`ODE integrators table <integrator_table>`
- :ref:`Optimizers table <doc_taosolve>`
- :ref:`Model/discretization interfaces to solvers table <dm_table>`
Utilities for Simulations/Solvers
=================================
Runtime
* control of the simulation via :any:`runtime options <sec_options>`
* visualization of the solvers and simulation via :any:`viewers <sec_viewers>`,
* :any:`monitoring <sec_kspmonitor>` of solution progress,
* :any:`profiling <ch_profiling>` of the performance,
* robust :any:`error handling <sec_errors>`.
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