Meshing / Triangular and tetrahedral meshing

• TetWild - Generate tetrahedral meshes for triangular surface meshes. (C++, GPL 3, GitHub (⭐696))

Multi-purpose toolkits

• PETSc - Parallel solution of scientific applications modeled by PDEs. (C, 2-clause BSD, GitLab)

Meshing / Triangular and tetrahedral meshing

• distmesh - Simple generator for unstructured triangular and tetrahedral meshes. (MATLAB, GPL 3)

Data formats / Mesh tools

• NetCDF - Software libraries and data formats for array-oriented scientific data. (C/C++/Fortran/Java/Python, custom open-source license, GitHub (⭐582))

• XDMF - eXtensible Data Model and Format for data from High Performance Computing codes. (C++, GitLab)

Data formats / Mesh tools

• HDF5 - Data model, library, and file format for storing and managing data. (C/Fortran, BSD, GitHub (⭐892))

Community / Mesh tools

• Gabriel Peyré on Bluesky - One post a day on computational mathematics.

Meshing / Triangular and tetrahedral meshing

• trimesh - Loading and using triangular meshes with an emphasis on watertight surfaces. (Python, MIT, GitHub (⭐3.5k))

Meshing / Triangular and tetrahedral meshing

• pygalmesh (⭐665) - Python interface for CGAL's 3D meshing capabilities. (Python, GPL 3, GitHub)

• dmsh (⭐222) - Simple generator for unstructured triangular meshes, inspired by distmesh. (Python, proprietary, GitHub)

Meshing / Mesh tools

• optimesh (⭐626) - Triangular mesh smoothing. (Python, proprietary, GitHub)

• meshplex (⭐108) - Fast tools for simplex meshes. (Python, proprietary, GitHub)

Other libraries and tools / Mesh tools

• quadpy (⭐785) - Numerical integration (quadrature, cubature) in Python. (Python, proprietary, GitHub)

• accupy (⭐107) - Accurate sums and dot products for Python. (Python, GPL 3, GitHub)

• orthopy (⭐189) - Compute orthogonal polynomials efficiently. (Python, proprietary, GitHub)

Visualization / Mesh tools

• morphologica (⭐310) - Header-only, modern OpenGL code to visualize numerical simulations at runtime. (C++, Apache 2.0, GitHub)

Basic linear algebra

• BLAS - Standard building blocks for performing basic vector and matrix operations. (Fortran, public domain, GitHub (⭐1.8k))

• LAPACK - Routines for solving systems of linear equations, linear least-squares, eigenvalue problems, etc. (Fortran, BSD, GitHub (⭐1.8k))

Visualization / Mesh tools

• F3D - Cross-platform, fast, and minimalist 3D viewer with scientific visualization tools. (C++, BSD, GitHub (⭐4.1k))

Community / Mesh tools

• Jack Dongarra's software list - List of freely available software for the solution of linear algebra problems.

• NA Digest - Collection of articles on topics related to numerical analysis and those who practice it.

Finite Elements

• MFEM - Free, lightweight, scalable C++ library for finite element methods. (C++, BSD-3-Clause, GitHub (⭐2.1k))

Other libraries and tools / Mesh tools

• HPDDM (⭐154) - High-performance unified framework for domain decomposition methods. (C++, LGPL 3, GitHub)

Meshing / Triangular and tetrahedral meshing

• Triangle - Two-dimensional quality mesh generator and Delaunay triangulator. (C, nonfree software)

• SeismicMesh (⭐140) - Parallel 2D/3D triangle/tetrahedral mesh generation with sliver removal. (Python and C++, GPL 3, GitHub)

Meshing / Quadrilateral and hexahedral meshing

• QuadriFlow - Scalable and robust quadrangulation from triangulation. (C++, BSD, GitHub (⭐804))

Meshing / Mesh tools

• meshio (⭐2.3k) - I/O for various mesh formats, file conversion. (Python, MIT, GitHub)

• MOAB - Representing and evaluating mesh data. (C++, mostly LGPL 3, Bitbucket)

• pmp-library - Polygon mesh processing library. (C++, MIT with Employer Disclaimer, GitHub (⭐1.4k))

• Mmg - Robust, open-source & multidisciplinary software for remeshing. (C, LGPL 3, GitHub (⭐451))

Other libraries and tools / Mesh tools

• PyDMD (⭐115) - Dynamic Mode Decomposition (DMD) in Python. (Python, MIT, GitHub)

Finite Elements

• FEniCS - Computing platform for solving PDEs in Python and C++. (C++/Python, LGPL 3, GitHub/Bitbucket)

• scikit-fem (⭐608) - Simple finite element assemblers. (Python, BSD/GPL, GitHub)

Visualization / Mesh tools

• TTK - Topological data analysis and visualization. (C++/Python, BSD, GitHub (⭐466))

Other libraries and tools / Mesh tools

• shenfun - High-performance Python library for the spectral Galerkin method. (Python, BSD-2, GitHub (⭐226))

Other libraries and tools / Mesh tools

• cvxpy - Modeling language for convex optimization problems. (Python, Apache 2.0, GitHub (⭐6.1k))

• PyGMO - Massively parallel optimization. (Python/C++, MPL 2, GitHub (⭐520))

Community / Mesh tools

• Discord: Numerical Software - Discord messaging server on numerical software.

Other libraries and tools / Mesh tools

• Dedalus - Solve partial differential equations with spectral methods. (Python, GPL 3, GitHub (⭐658))

Data formats / Mesh tools

• Zarr - Format for the storage of chunked, compressed, N-dimensional arrays. (Python, MIT, GitHub (⭐1.9k))

Other libraries and tools / Mesh tools

• pyGAM - Generalized Additive Models in Python. (Python, Apache 2.0, GitHub (⭐947))

Visualization / Mesh tools

• yt - Toolkit for analysis and visualization of volumetric data. (Python, BSD, GitHub (⭐540))

Meshing / Triangular and tetrahedral meshing

• pygmsh (⭐951) - Python interface for Gmsh. (Python, GPL 3, GitHub)

Visualization / Mesh tools

• vedo - Library for scientific analysis and visualization of 3D objects based on VTK. (Python, MIT, GitHub (⭐2.2k))

Other libraries and tools / Mesh tools

• preCICE - Coupling library for partitioned multi-physics simulations (FSI, CHT, and more). (C++, LGPL 3, GitHub)

Basic linear algebra

• blaze - High-performance C++ math library for dense and sparse arithmetic. (C++, BSD, Bitbucket)

Finite Elements

• libceed - Code for Efficient Extensible Discretizations. (C, 2-clause BSD, GitHub (⭐244))

Basic linear algebra

• Eigen - C++ template library for linear algebra. (C++, MPL 2, GitLab)

Meshing / Triangular and tetrahedral meshing

• fTetWild - Same as TetWild, but faster. (C++, MPL 2, GitHub (⭐542))

Other libraries and tools / Mesh tools

• SLEPc - Scalable Library for Eigenvalue Problem Computations. (C, 2-clause BSD, GitLab)

Visualization / Mesh tools

• PyVista - 3D plotting and mesh analysis through a streamlined interface for VTK. (Python, MIT, GitHub (⭐3.5k))

Finite Elements

• FreeFEM - High level multiphysics-multimesh finite element language. (C++, LGPL, GitHub)

Meshing / Triangular and tetrahedral meshing

• TriWild - Robust triangulation with curve constraints. (C++, MPL 2, GitHub (⭐259))

Visualization / Mesh tools

• ParaView - Multi-platform data analysis and visualization application based on VTK. (C++, BSD, GitLab)

• VTK - Process images and create 3D computer graphics. (C++, BSD, GitLab)

• Mayavi - 3D scientific data visualization and plotting in Python. (Python, BSD, GitHub (⭐1.4k))

• Polyscope - Viewer and user interface for 3D geometry processing. (C++, MIT, GitHub (⭐2.1k))

Other libraries and tools / Mesh tools

• NFFT - Nonequispaced fast Fourier transform. (C/MATLAB, GPL 2, GitHub (⭐184))

Community / Mesh tools

• Nick Higham's blog - Mostly on MATLAB, general computing advice.

Other libraries and tools / Mesh tools

• PyWavelets - Wavelet transforms in Python. (Python, MIT, GitHub (⭐2.3k))

Sparse linear solvers / Mesh tools

• hypre - Library of high-performance preconditioners and solvers. (C, Apache 2.0/MIT, GitHub (⭐819))

Other libraries and tools / Mesh tools

• pyMOR - Model Order Reduction with Python. (Python, 2-clause BSD, GitHub (⭐340))

Basic linear algebra

• OpenBLAS - Optimized BLAS library based on GotoBLAS2. (C and Assembly, BSD, GitHub (⭐7.3k))

• BLIS (⭐2.6k) - High-performance BLAS-like dense linear algebra libraries. (C, BSD, GitHub)

Finite Elements

• MOOSE - Multiphysics Object Oriented Simulation Environment. (C++, LGPL 2.1, GitHub (⭐2.2k))

Basic linear algebra

• Ginkgo - High-performance manycore linear algebra library, focus on sparse systems. (C++, BSD, GitHub (⭐557))

Other libraries and tools / Mesh tools

• Chebfun - Computing with functions to about 15-digit accuracy. (MATLAB, BSD, GitHub (⭐659))

Finite Elements

• SfePy - Simple Finite Elements in Python. (Python, BSD, GitHub (⭐824))

Community / Mesh tools

• Wolfgang Bangerth's video class - MATH 676: Finite element methods in scientific computing.

Community / Mesh tools

• John D. Cook's blog - Feats of scientific computing.

Community / Mesh tools

• SciComp StackExchange - Computational Science on the StackExchange network.

• Nick Trefethen's Video Lectures - 36 video lectures on approximation theory/practice and scientific computing.

Multi-purpose toolkits

• DUNE Numerics - Toolbox for solving PDEs with grid-based methods. (C++, GPL 2, GitLab)

• SciPy - Python modules for statistics, optimization, integration, linear algebra, etc. (Python, mostly BSD, GitHub (⭐14k))

• NumPy - Fundamental package needed for scientific computing with Python. (Python, BSD, GitHub (⭐31k))

Finite Elements

• libMesh - Framework for the numerical simulation of PDEs using unstructured discretizations. (C++, LGPL 2.1, GitHub (⭐736))

• deal.II - Software library supporting the creation of finite element codes. (C++, LGPL 2.1, GitHub (⭐1.6k))

• Netgen/NGSolve - High performance multiphysics finite element software. (C++, LGPL 2.1, GitHub (⭐366))

• Firedrake - Automated system for the solution of PDEs using the finite element method. (Python, LGPL 3, GitHub (⭐631))

Meshing / Triangular and tetrahedral meshing

• Gmsh - Three-dimensional finite element mesh generator with pre- and post-processing facilities. (C++, GPL, GitLab)

• MeshPy - Quality triangular and tetrahedral mesh generation. (Python, MIT, GitHub (⭐572))

• CGAL - Algorithms for computational geometry. (C++, mixed LGPL/GPL, GitHub (⭐5.7k))

• TetGen - Quality tetrahedral mesh generator and 3D Delaunay triangulator. (C++, AGPLv3)

Sparse linear solvers / Mesh tools

• SuperLU - Direct solution of large, sparse, nonsymmetric systems of linear equations. (C, mostly BSD, GitHub (⭐326))

• PyAMG - Algebraic Multigrid Solvers in Python. (Python, MIT, GitHub (⭐636))

Other libraries and tools / Mesh tools

• FFTW - Discrete Fourier transforms in one or more dimensions, of arbitrary input size, real and complex. (C, GPL2, GitHub (⭐3k))

• Qhull - Convex hull, Delaunay triangulation, Voronoi diagram, halfspace intersection about a point, etc. (C/C++, custom open source license, GitHub (⭐807))

• GSL - Random number generators, special functions, and least-squares fitting etc. (C/C++, GPL 3, Savannah)

• OpenFOAM - Free, open source CFD (computational fluid dynamics) software. (C++, GPL 3, GitHub (⭐2k))

• FiPy - Finite-volume PDE solver. (Python, custom open-source license, GitHub (⭐599))