===================
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>`.
