OpenGL Mathematics (GLM) is a header-only C++ mathematics library for graphics software based on the OpenGL Shading Language (GLSL) specifications.

SCOTCH is a set of programs and libraries which implement the static mapping and sparse matrix reordering algorithms developed within the SCOTCH project. Its purpose is to apply graph theory, with a divide and conquer approach, to scientific computing problems such as graph and mesh partitioning, static mapping, and sparse matrix ordering, in application domains ranging from structural mechanics to operating systems or bio-chemistry.

DUNE, the Distributed and Unified Numerics Environment is a modular toolbox for solving partial differential equations (PDEs) with grid-based methods. It supports the easy implementation of methods like Finite Elements (FE), Finite Volumes (FV), and also Finite Differences (FD).

This package contains the basic DUNE geometry classes.

This package provides a range of SAT solvers, including the sequential lingeling and its parallel variants plingeling and treengeling. A bounded model checker is also included.

The SPQR (SuiteSparseQR) package provides sparse QR factorization based on the multifrontal method, using BLAS for the frontal matrices.

GLPK is a C library for solving large-scale linear programming (LP), mixed integer programming (MIP), and other related problems. It supports the GNU MathProg modeling language, a subset of the AMPL language, and features a translator for the language. In addition to the C library, a stand-alone LP/MIP solver is included in the package.

MUMPS (MUltifrontal Massively Parallel sparse direct Solver) solves a sparse system of linear equations A x = b using Gaussian elimination.

accupy is a Python library for accurately computing sums and (dot) products. It implements Kahan summation, Shewchuck's algorithm and summation in K-fold precision.

DUNE, the Distributed and Unified Numerics Environment is a modular toolbox for solving partial differential equations (PDEs) with grid-based methods. It supports the easy implementation of methods like Finite Elements (FE), Finite Volumes (FV), and also Finite Differences (FD).

This package contains the DUNE UG grid classes.

CyLP is a Python interface to COIN-OR’s Linear and mixed-integer program solvers (CLP, CBC, and CGL). CyLP’s unique feature is that you can use it to alter the solution process of the solvers from within Python. For example, you may define cut generators, branch-and-bound strategies, and primal/dual Simplex pivot rules completely in Python.

The General Cartographic Transformation Package (GCTP) is a system of software routines designed to permit the transformation of coordinate pairs from one map projection to another. The GCTP is the standard computer software used by the National Mapping Division for map projection computations.

Mongoose is a library for graph partitioning by computing edge cuts using a coarsening and refinement framework.

Deal.II is a C++ program library targeted at the computational solution of partial differential equations using adaptive finite elements. The main aim of deal.II is to enable rapid development of modern finite element codes, using among other aspects adaptive meshes and a wide array of tools often used in finite element programs.

libflame is a portable library for dense matrix computations, providing much of the functionality present in LAPACK, developed by current and former members of the SHPC group in the Institute for Computational Engineering and Sciences at The University of Texas at Austin. libflame includes a compatibility layer, lapack2flame, which includes a complete LAPACK implementation.

More than 1500 numerical integration schemes for line segments, circles, disks, triangles, quadrilaterals, spheres, balls, tetrahedra, hexahedra, wedges, pyramids, n-spheres, n-balls, n-cubes, n-simplices, and the 1D/2D/3D/nD spaces with weight functions exp(-r) and exp(-r2) for fast integration of real-, complex-, and vector-valued functions.

CVXOPT is a package for convex optimization based on the Python programming language. Its main purpose is to make the development of software for convex optimization applications straightforward by building on Python’s extensive standard library and on the strengths of Python as a high-level programming language.

Bonmin is a code for solving general MINLP (Mixed Integer NonLinear Programming) problems. It builds on top of Cbc and Ipopt.

PDELab is a partial differential equations solver toolbox built on top of DUNE, the Distributed and Unified Numerics Environment.

Openspecfun provides AMOS and Faddeeva. AMOS (from Netlib) is a portable package for Bessel Functions of a Complex Argument and Nonnegative Order; it contains subroutines for computing Bessel functions and Airy functions. Faddeeva allows computing the various error functions of arbitrary complex arguments (Faddeeva function, error function, complementary error function, scaled complementary error function, imaginary error function, and Dawson function); given these, one can also easily compute Voigt functions, Fresnel integrals, and similar related functions as well.

The dune-subgrid module marks elements of another hierarchical dune grid. The set of marked elements can then be accessed as a hierarchical dune grid in its own right. Dune-Subgrid provides the full grid interface including adaptive mesh refinement.

Aris is a program for performing logical proofs. It supports propositional and predicate logic, as well as Boolean algebra and arithmetical logic. In addition to its predefined inference and equivalence rules, Aris also supports references to older proofs. Its use of standard logical symbols and its natural deduction interface make it easy to use for beginners.

Vinci implements a number of volume computation algorithms for convex polytopes in arbitrary dimension. The polytopes can be given by their V-representation (as the convex hull of a finite number of vertices), by their H-representation (as the bounded intersection of a finite number of halfspaces) or by their double description with both representations.

This library provides portable Arbitrary-precision unsigned integer arithmetic in C, for calculating with large numbers. Basic arithmetic (+, -, *, /, %) and bitwise operations (&, |, ^. <<, >>) plus increments, decrements and comparisons are supported.

PETSc, the Portable, Extensible Toolkit for Scientific Computation, is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations. It employs the MPI standard for all message-passing communication. petsc4py provides Python bindings to almost all functions of PETSc.