PETSc in a nutshell

See 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).

  • Multiple sparse and dense matrix storage formats,

  • Limited memory variable metric representations,

  • block and nested representations,

  • Easy, efficient matrix assembly and interface.

• 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

  • Performing sensitivity analysis with the TS ODE Solvers.

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

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

Model/Discretization Interfaces to Solvers

• Simple structured grids, DMDA.

• Staggered grids, DMSTAG: Staggered, Structured Grid, DMSTAG.

• Unstructured grids, DMPlex: Unstructured Grids, DMPLEX.

• Networks/graphs, for example the power grid, river networks, the nervous system, Networks, DMNETWORK.

• Quad or octree grids, DMFOREST.

• Particles, DMSWARM.

See also

For full feature list see:

• Vector table

• Matrix table

• Linear solvers table

• Nonlinear solvers table

• ODE integrators table

• Optimizers table

• Model/discretization interfaces to solvers table

Utilities for Simulations/Solvers

Runtime

• control of the simulation via runtime options

• visualization of the solvers and simulation via viewers,

• monitoring of solution progress,

• profiling of the performance,

• robust error handling.