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HiFlow³
HiFlow³ is a multi-purpose finite element software providing powerful tools for efficient and accurate solution of a wide range of problems modeled by partial differential equations. Based on object-oriented concepts and the full capabilities of C++ the HiFlow³ project follows a modular and generic approach for building efficient parallel numerical solvers. It provides highly capable modules dealing with the mesh setup, finite element spaces, degrees of freedom, linear algebra routines, numerical solvers, and output data for visualization. Parallelism – as the basis for high performance simulations on modern computing systems – is introduced on two levels: coarse-grained parallelism by means of distributed grids and distributed data structures, and fine-grained parallelism by means of platform-optimized linear algebra back-ends.
More informationMaple
Maple is an environment for scientific and engineering problem-solving, mathematical exploration, data visualization and technical authoring.
More informationPLTMG
PLTMG is a package for solving elliptic partial differential equations in general regions of the plane. It is based on continuous piecewise linear triangular finite elements, and features adaptive local mesh refinement, multigraph iteration, and pseudo-arclength continuation options for parameter dependencies. It also provides options for solving several classes of optimal control and obstacle problems. The package includes an initial mesh generator and several graphics packages. Support for the Bank-Holst parallel adaptive meshing strategy is also provided. PLTMG is provided as Fortran (and a little C) source code, in both single and double precision versions. The code has interfaces to X-Windows, MPI, and Michael Holst's OpenGL image viewer SG. The X-Windows, MPI, and SG interfaces require libraries that are NOT provided as part of the PLTMG package.
More informationrbMIT
The rbMIT © MIT software package implements in Matlab® all the general reduced basis algorithms. The rbMIT © MIT software package is intended to serve both (as Matlab® source) "Developers" — numerical analysts and computational tool-builders — who wish to further develop the methodology, and (as Matlab® "executables") "Users" — computational engineers and educators — who wish to rapidly apply the methodology to new applications. The rbMIT software package was awarded with the Springer Computational Science and Engineering Prize in 2009.
More informationTheorema
The Theorema project aims at extending current computer algebra systems by facilities for supporting mathematical proving. The present early-prototype version of the Theorema software system is implemented in Mathematica . The system consists of a general higher-order predicate logic prover and a collection of special provers that call each other depending on the particular proof situations. The individual provers imitate the proof style of human mathematicians and produce human-readable proofs in natural language presented in nested cells. The special provers are intimately connected with the functors that build up the various mathematical domains. The long-term goal of the project is to produce a complete system which supports the mathematician in creating interactive textbooks, i.e. books containing, besides the ordinary passive text, active text representing algorithms in executable format, as well as proofs which can be studied at various levels of detail, and whose routine parts can be automatically generated. This system will provide a uniform (logic and software) framework in which a working mathematician, without leaving the system, can get computer-support while looping through all phases of the mathematical problem solving cycle.
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