Useful resources for scientific computing and numerical analysis.
Scientific computing and numerical analysis are research fields that aim to provide
methods for solving large-scale problems from various areas of science with the help of
computers. Typical problems are ordinary and partial differential equations (ODEs,
PDEs), their discretizations, and the solution of linear algebra problems arising from
them.
Standard building blocks for performing basic vector and matrix operations.
Optimized BLAS library based on GotoBLAS2.
High-performance BLAS-like dense linear algebra libraries.
Routines for solving systems of linear equations, linear least-squares, eigenvalue problems, etc.
C++ template library for linear algebra.
High-performance manycore linear algebra library, focus on sparse systems.
High-performance C++ math library for dense and sparse arithmetic.
(Fortran, public domain, GitHub)
(C and Assembly, BSD, GitHub)
(C, BSD, GitHub)
(Fortran, BSD, GitHub)
(C++, MPL 2, GitLab)
(C++, BSD, GitHub)
(C++, BSD, Bitbucket)
Parallel solution of scientific applications modeled by PDEs.
Toolbox for solving PDEs with grid-based methods.
Python modules for statistics, optimization, integration, linear algebra, etc.
Fundamental package needed for scientific computing with Python.
Toolbox for solving different types of differential equations numerically. (Julia, MIT, [GitHub](https://github.com/SciML/DifferentialEquations.jl))
(C, 2-clause BSD, GitLab)
(C++, GPL 2, GitLab)
(Python, mostly BSD, GitHub)
(Python, BSD, GitHub)
Computing platform for solving PDEs in Python and C++.
Framework for the numerical simulation of PDEs using unstructured discretizations.
Software library supporting the creation of finite element codes.
High performance multiphysics finite element software.
Automated system for the solution of PDEs using the finite element method.
Multiphysics Object Oriented Simulation Environment.
Free, lightweight, scalable C++ library for finite element methods.
Simple Finite Elements in Python.
High level multiphysics-multimesh finite element language.
Code for Efficient Extensible Discretizations.
Simple finite element assemblers.
(C++/Python, LGPL 3, GitHub/Bitbucket)
(C++, LGPL 2.1, GitHub)
(C++, LGPL 2.1, GitHub)
(C++, LGPL 2.1, GitHub)
(Python, LGPL 3, GitHub)
(C++, LGPL 2.1, GitHub)
(C++, BSD-3-Clause, GitHub)
(Python, BSD, GitHub)
(C++, LGPL, GitHub)
(C, 2-clause BSD, GitHub)
(Python, BSD/GPL, GitHub)
Three-dimensional finite element mesh generator with pre- and post-processing facilities.
Python interface for Gmsh.
Quality triangular and tetrahedral mesh generation.
Algorithms for computational geometry.
Python interface for CGAL's 3D meshing capabilities.
Quality tetrahedral mesh generator and 3D Delaunay triangulator.
Two-dimensional quality mesh generator and Delaunay triangulator.
Simple generator for unstructured triangular and tetrahedral meshes.
Loading and using triangular meshes with an emphasis on watertight surfaces.
Simple generator for unstructured triangular meshes, inspired by distmesh.
Generate tetrahedral meshes for triangular surface meshes.
Robust triangulation with curve constraints.
Same as TetWild, but faster.
Parallel 2D/3D triangle/tetrahedral mesh generation with sliver removal.
(C++, GPL, GitLab)
(Python, GPL 3, GitHub)
(Python, MIT, GitHub)
(C++, mixed LGPL/GPL, GitHub)
(Python, GPL 3, GitHub)
(C++, AGPLv3)
(C, nonfree software)
(MATLAB, GPL 3)
(Python, MIT, GitHub)
(Python, proprietary, GitHub)
(C++, GPL 3, GitHub)
(C++, MPL 2, GitHub)
(C++, MPL 2, GitHub)
(Python and C++, GPL 3, GitHub)
Scalable and robust quadrangulation from triangulation.
(C++, BSD, GitHub)
I/O for various mesh formats, file conversion.
Representing and evaluating mesh data.
Triangular mesh smoothing.
Polygon mesh processing library.
Robust, open-source & multidisciplinary software for remeshing.
Fast tools for simplex meshes.
(Python, MIT, GitHub)
(C++, mostly LGPL 3, Bitbucket)
(Python, proprietary, GitHub)
(C++, MIT with Employer Disclaimer, GitHub)
(C, LGPL 3, GitHub)
(Python, proprietary, GitHub)
Software libraries and data formats for array-oriented scientific data.
Data model, library, and file format for storing and managing data.
eXtensible Data Model and Format for data from High Performance Computing codes.
Format for the storage of chunked, compressed, N-dimensional arrays.
(C/C++/Fortran/Java/Python, custom open-source
license,
GitHub)
(C/Fortran, BSD, GitHub)
(C++, GitLab)
(Python, MIT, GitHub)
Direct solution of large, sparse, nonsymmetric systems of linear equations.
Algebraic Multigrid Solvers in Python.
Library of high-performance preconditioners and solvers.
(C, mostly BSD, GitHub)
(Python, MIT, GitHub)
(C, Apache 2.0/MIT, GitHub)
Multi-platform data analysis and visualization application based on VTK.
Process images and create 3D computer graphics.
3D scientific data visualization and plotting in Python.
Viewer and user interface for 3D geometry processing.
3D plotting and mesh analysis through a streamlined interface for VTK.
Library for scientific analysis and visualization of 3D objects based on VTK.
Toolkit for analysis and visualization of volumetric data.
Cross-platform, fast, and minimalist 3D viewer with scientific visualization tools.
Topological data analysis and visualization.
Header-only, modern OpenGL code to visualize numerical simulations at runtime. (C++, Apache 2.0, GitHub)
(C++, BSD, GitLab)
(C++, BSD, GitLab)
(Python, BSD, GitHub)
(C++, MIT, GitHub)
(Python, MIT, GitHub)
(Python, MIT, GitHub)
(Python, BSD, GitHub)
(C++, BSD, GitHub)
(C++/Python, BSD, GitHub)
Discrete Fourier transforms in one or more dimensions, of arbitrary input size, real and complex.
Convex hull, Delaunay triangulation, Voronoi diagram, halfspace intersection about a point, etc.
Random number generators, special functions, and least-squares fitting etc.
Free, open source CFD (computational fluid dynamics) software.
Numerical integration (quadrature, cubature) in Python.
Finite-volume PDE solver.
Accurate sums and dot products for Python.
Scalable Library for Eigenvalue Problem Computations.
Computing with functions to about 15-digit accuracy.
Model Order Reduction with Python.
Modeling language for convex optimization problems.
Wavelet transforms in Python.
Nonequispaced fast Fourier transform.
Coupling library for partitioned multi-physics simulations (FSI, CHT, and more).
Compute orthogonal polynomials efficiently.
Generalized Additive Models in Python.
Solve partial differential equations with spectral methods.
Massively parallel optimization.
High-performance Python library for the spectral Galerkin method.
Dynamic Mode Decomposition (DMD) in Python.
High-performance unified framework for domain decomposition methods.
(C, GPL2, GitHub)
(C/C++, custom open source license,
GitHub)
(C/C++, GPL 3, Savannah)
(C++, GPL 3, GitHub)
(Python, proprietary, GitHub)
(Python, custom open-source
license,
GitHub)
(Python, GPL 3, GitHub)
(C, 2-clause BSD, GitLab)
(MATLAB, BSD, GitHub)
(Python, 2-clause BSD, GitHub)
(Python, Apache 2.0, GitHub)
(Python, MIT, GitHub)
(C/MATLAB, GPL 2, GitHub)
(C++, LGPL 3, GitHub)
(Python, proprietary, GitHub)
(Python, Apache 2.0, GitHub)
(Python, GPL 3, GitHub)
(Python/C++, MPL 2, GitHub)
(Python, BSD-2, GitHub)
(Python, MIT, GitHub)
(C++, LGPL 3, GitHub)
Computational Science on the StackExchange network.
MATH 676: Finite element methods in scientific computing.
Mostly on MATLAB, general computing advice.
36 video lectures on approximation theory/practice and scientific computing.
Feats of scientific computing.
List of freely available software for the solution of linear algebra problems.
Collection of articles on topics related to numerical analysis and those who practice it.
One post a day on computational mathematics.
Discord messaging server on numerical software.