# PETSc in a nutshell#

See Hands-On Tutorials, by Mathematical Problem to immediately jump in and run PETSc code.

PETSc/TAO is a tool for writing, analyzing, and optimizing large-scale numerical simulations.

## Algebraic objects#

• Vectors - containers for simulation solutions, right hand sides of linear systems, etc (Vec).

• Matrices - contain Jacobians and operators that define linear systems (Mat).

• Indices - used to access portions of vectors and matrix, for example {1,2,4} or 1:10 (IS).

## Solvers#

• Linear solvers based on preconditioners (PC) and Krylov subspace methods (KSP).

• Nonlinear solvers (SNES).

• Time integrators, (ODE/PDE), explicit, implicit, IMEX, (TS)

• Local and global error estimators

• Optimization with equality and inequality constraints, first and second order (Newton) methods (Tao).

• Eigenvalue/Eigenvectors and related algorithms in the package SLEPc.