PETSc

A high-performance library of scalable data structures and solver routines for parallel scientific applications modeled by partial differential equations.

Developed at Argonne National Laboratory, PETSc provides the numerical backbone for large-scale simulations on everything from local clusters to Exascale supercomputers. It offers robust abstractions for vectors, matrices, and solvers (including Newton-based methods) while supporting MPI-based parallelism and modern GPU backends like CUDA, HIP, and SYCL. Researchers use PETSc to handle complex physics in seismology, fluid dynamics, and electromagnetics by leveraging its built-in SNES (Scalable Nonlinear Equations Solvers) and TS (Time-Stepping) libraries. The toolkit integrates seamlessly with external solvers like HYPRE and MUMPS, ensuring flexibility for diverse computational workloads.

https://petsc.org/