PETSc

PETSc (Portable, Extensible Toolkit for Scientific Computation) is a suite of data structures and routines for the scalable solution of scientific applications modeled by partial differential equations. It provides parallel linear and nonlinear solvers, time integrators, and miscellaneous components for discretization, mesh management, and preconditioning. PETSc is designed for high-performance computing on distributed-memory architectures using the Message Passing Interface (MPI). It aims to enable robust, scalable, and portable software for large-scale scientific computations.

The core library exposes a small set of abstract objects and modular components. Vec and Mat represent global vectors and sparse matrices; KSP provides Krylov subspace linear solvers with a hierarchy of preconditioners (PC); SNES handles nonlinear solvers; TS offers time-stepping schemes; DM (data management) manages problem-specific grids and fields (e.g., DMDA, DMPLEX). The toolkit supports interfaces to Fortran, C++, and scripting languages such as Python (petsc4py). Users can extend PETSc with external libraries (e.g., HYPRE, MUMPS, METIS/ParMETIS, and SLEPc for eigenproblems).

PETSc emphasizes portability and performance, with support for various architectures, GPUs, and accelerators through backends and plugins. It includes extensive documentation, tutorials, and a large suite of example programs to aid development. The BSD-style license makes it freely available for academic and commercial work. In practice, PETSc is widely used for solving linear and nonlinear systems arising from PDE discretizations, time-dependent simulations, optimization problems, and multiphysics applications, often in conjunction with higher-level frameworks and research codes.