Scientific computation

Elmer - Finite Element Analysis for Multiphysics Problems

Friday, 22 July 2011 20:58

Elmer is a Finite Element Analysis (FEA) software package for the solution of partial differential equations developed by CSC - IT (Center for Science). Elmer can deal with a great number of different equations, which may be coupled in a generic manner making Elmer a versatile tool for multiphysical simulations. As an open source software, Elmer also gives the user the means to modify the existing solution procedures and to develop new solvers for equations of interest to the user. Elmer offers a wide range of methods and techniques for the computational modeling of physical phenomena described by partial differential equations. In the following some of the most essential ones are summarized. The Elmer package contains solvers for a variety of mathematical models. The following list summarizes the capabilities of Elmer in specialized fields:

Heat transfer: models for conduction, radiation and phase change;
Fluid flow: the Navier-Stokes, Stokes and Reynolds equations, k-epsilon model;
Species transport: generic convection-diffusion equation;
Elasticity: general elasticity equations, dimensionally reduced models for plates and shells;
Acoustics: the Helmholtz equation;
Electromagnetism: electrostatics, magnetostatics, induction;
Microfluidics: slip conditions, the Poisson-Boltzmann equation;
Levelset method: Eulerian free boundary problems;
Quantum Mechanics: density functional theory (Kohn-Sham).

For approximation and linear system solution Elmer offers a great number of possibilities. The following list summarizes some of the most essential ones:

All basic element shapes in 1D, 2D and 3D with the Lagrange shape functions of degree k<=2;
Higher degree approximation using p-elements;
Time integration schemes for the first and second order equations;
Solution methods for eigenvalue problems;
Direct linear system solvers (Lapack & Umfpack);
Iterative Krylov subspace solvers for linear systems;
Multigrid solvers (GMG and AMG) for some basic equations;
ILU preconditioning of linear systems;
Parallelization of iterative methods;
The discontinuous Galerkin method;
Stabilized finite element formulations, including the methods of residual free bubbles and SUPG;
Adaptivity, particularly in 2D;
BEM solvers (without multipole acceleration).

Since Elmer is an open source product, it is possible to verify and modify the solution procedures! For more information about Elmer click here or on the official Wiki-Forum.

FreeMat - Rapid engineering and scientific prototyping

Thursday, 08 January 2009 22:08

FreeMat is a free numerical interpreted matrix-oriented computing environment and programming language for rapid engineering and scientific prototyping and data processing similar to MATLAB from Mathworks and GNU Octave. In addition to supporting many MATLAB functions and some IDL functionality, it features codeless interface to external C, C++, and Fortran code, further Freemat provides visualization, image manipulation, and plotting as well as parallel programming (parallel distributed algorithm development via MPI), and some extended volume and 3D visualization capabilities. Some features;

Support for 8,16, 32, and 64 bit integer types (signed and unsigned), 32 and 64 bit floating point types, and 64 and 128 bit complex types;
Support for solving linear systems of equations via the divide operators;
Arbitrary-size FFT support;
3D Plotting and visualization via OpenGL;
Full support for dynamic structure arrays;
Sparse Matrix native support;
Signal processing functions;
Numerical methods;
Optimization and Curve Fitting;
Object Oriented Programming;
...and many others!

FreeMat is available under the GNU GPL license. For more information (...and download) click here.

Gmsh - A three dimensional finite element

Tuesday, 27 January 2009 23:40

Gmsh is an automatic 3D finite element grid generator with built-in CAD with pre- and post-processing facilities. Its design goal is to provide a simple meshing tool for academic test cases with parametric input and up to date visualization capabilities. One of the strengths of Gmsh is its ability to respect a characteristic length field for the generation of adapted meshes on lines, surfaces and volumes. These adapted meshes can be mixed with simple structured (transfinite, elliptic, etc.) meshes in order to augment the flexibility. It is structured around four modules: geometry, mesh, solver, and post-processing. The specification of any input to these modules is done either interactively using the graphical user interface (based on FLTK and OpenGL) or in ASCII text files using Gmsh's own scripting language. The accessibility of most features in the ASCII text file makes it possible to automate all treatments (loops, tests and external access methods permit advanced scripting capabilities). Gmsh is developed by University of Liège and Catholic University of Louvain. Complete list of credits here. For more information click here.

Maxima - A complete Computer Algebra System

Tuesday, 28 October 2008 23:29

Maxima is a CAS (Computer Algebra System) similar to systems like Mathematica and Maple. Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors. Maxima yields high precision numeric results by using exact fractions, arbitrary precision integers, and variable precision floating point numbers. Maxima can plot functions and data in two and three dimensions. Maxima however, is a commandline application, which makes it a bit harder to use. Here is where a GUI (Graphical User Interface) for Maxima made to make using Maxima simpler and more enjoyable. Possible GUI are:

Kayali.
wxMaxima.

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