Virtual Marine Arsenal


Multiphysics | RANS-URANS | Linear | Nonlinear | FEM | BEM

Elmer is a finite element software package for the solution of partial differential equations.  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 is an open source multiphysical simulation software mainly developed by CSC; IT Center for Science. Elmer development was started 1995 in collaboration with Finnish Universities, research institutes and industry. After it's open source publication in 2005, the use and development of Elmer has become international.

Elmer includes physical models of fluid dynamics, structural mechanics, electromagnetics, heat transfer and acoustics, for example. These are described by partial differential equations which Elmer solves by the Finite Element Method (FEM).


Physical models in Elmer

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, linearized Navier–Stokes equations in the frequency domain and large-amplitude wave motion of an ideal gas
  • Electromagnetism: Electrostatics, magnetostatics, the A-V formulation, magnetic induction, the vectorial Helmholtz equation
  • Microfluidics: Slip conditions, the Poisson-Boltzmann equation
  • Levelset method: Eulerian free boundary problems
  • Quantum Mechanics: Density functional theory (Kohn-Sham)


Numerical methods in Elmer

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 finite elements based on the Lagrange interpolation of degree k≤ 3 (1D and 2D) or k ≤ 2 (3D).
  • Higher degree approximation using p-elements
  • Curl-conforming (edge) finite elements of the lowest degree for all basic element shapes
  • Triangular, quadrilateral and tetrahedral div-conforming (face) finite elements of the lowest degree
  • 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)
License: Open Source
Operating System(s):
  • Linux
  • Windows

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