PDESolvern

PDESolvern is an open-source software library for solving partial differential equations (PDEs). Designed for use in physics, engineering, and applied mathematics, it provides a modular framework intended for rapid development, testing, and deployment of numerical solvers across a range of problem classes.

The library supports multiple discretization schemes including finite difference, finite element, and spectral methods, and it can handle elliptic, parabolic, and hyperbolic PDEs. It includes support for common boundary conditions (Dirichlet, Neumann, Robin) and source terms. Users can define complex geometries through built-in mesh generators or import meshes from standard formats.

In terms of performance and scalability, PDESolvern uses a C++ core with Python bindings for scripting. It features a modular solver stack with direct and iterative linear solvers (LU, CG, GMRES, BiCGSTAB) and preconditioning options. Time integration supports explicit and implicit schemes, including adaptive stepping. The package supports parallel execution via MPI for distributed memory and OpenMP for shared memory systems.

The API emphasizes readability and extensibility. Users define problems via a domain, equation specification, and boundary conditions, then assemble the system and call the solver. An example workflow includes assembling the system matrix, applying BCs, solving for the unknown field, and performing basic post-processing such as field visualization or export to formats like VTK or HDF5.

PDESolvern is released under a permissive license and maintains documentation, tutorials, and example problems. As an actively developed project, it emphasizes interoperability with other numerical tools and ongoing contributions from an open-source community.