PETSc in a nutshell

PETSc/TAO is a tool for writing, analyzing, and optimizing properties of 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 (see MatType).

  • 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).

See also

For full feature list and prerequisites see:

• Vector table

• Matrix table

• Linear solver table

• Nonlinear solver table

• Tao solver table

DM: Interfacing Solvers to Models/Discretizations

• DMDA - for simulations computed on simple structured grids

• DMSTAG: Staggered, Structured Grids in PETSc - for simulations computed on staggered grids, (DMSTAG)

• DMPlex: Unstructured Grids in PETSc - for simulation computed on unstructured meshes, (DMPLEX)

• Networks - for simulations on networks or graphs, for example the power grid, river networks, the nervous system, (DMNETWORK)

• DMP4EST - for simulations on collections of quad or octree meshes

• DMSWARM - for simulations on particles

Utilities for the Simulation/Solver Process

Runtime

• control of the simulation, Runtime Options

• visualization of the solvers and simulation, Viewers: Looking at PETSc Objects,

• monitoring of solution progress,

• Profiling of the performance,

• robust Error Handling.