What is Mefisto?
Mefisto is an OpenSource Software downloadable at
https://www.ljll.math.upmc.fr/perronnet/mefistoa.charger.php
which can solve some Partial Differential Equations
by Finite Element methods on 1d or 2d or 3d objects or a 6d-cube.
What problems can be solved with Mefisto?
From MEFISTO-INITIER & MEFISTO-MESHER:
- The creation of 1d or 2d or 3d meshes from POINTS, LINES, SURFACES, VOLUMES;
- The construction of an OBJECT with an ISOPARAMETRIC LAGRANGE INTERPOLATION
from polynomials of degree 1 or 2
(the middle point of edges are added for each finite element (FE)
- The Mefisto METHODOLOGY to CONSTRUCT OBJECT MESHES
From MEFISTO-FLUIDER, computation of the
- The STEADY STOKES equations
- The UNSTEADY STOKES equations
- The STEADY NAVIER-STOKES equations
- The UNSTEADY NAVIER-STOKES equations
for a 2d or 3d incompressible flow by Taylor-Hood or Brezzi-Fortin finite elements,
solved by a Crout's factorization of the global matrix assembled in a skyline storage.
Remark: AXI-SYMMETRIC HEAT and ELASTICITY SOLVERS are also AVAILABLE in Mefisto.
How to use Mefisto?
The execution of these modules is users' friendly by the using of menus, mouse and drawings of numerical results
on the display or in a PostScript file.
A User Language, named LU permits during data input the using of
algebraic expressions with parenthesis ( pi * ( r**2 ); );
user's function declarations ( definition by typing of
deffunc f(x); if x>0; then f=x; else f=-x; endfunc;
then, using with the form : sqrt(f(x)) )
Variables et functions permit, for example, to have the same edge number of 2 lines,
to parameter with x, y, z, physical data, ...
How to program finite element methods with Mefisto?
The source of the software, version October 2014, has
257848 fortran 77 instruction lines;
192314 comment lines;
3607 C instruction lines for drawings with the X11-Window System;
1 call 'convert' of the package ImageMagick.
The module sources are structured in
libraries according to their functionalities:
bin : Commands;
doc : Documentation;
elas: Elasticity Solver;
flui: Fluid Flow Solver;
incl: Include Files;
mail: Mesher;
pp : Executable Programs;
prpr: Programs Sources;
reso: Linear Systems Solvers;
td : Data Descriptors;
test: Tests;
ther: Heat Transfer Solver and Non Linear Schrodinger Equation Solver;
util: Utilities;
xvue: Drawings Utilities;
The fortran 77 language has been completed by notions such that
the dynamic adresses of arrays in main memory ( named TMC );
the automatic saving of arrays on direct access files between 2 executions ( named TMS );
each TMS has a name named TMS.
The named TMS are structured in a tree (as directories) which permits to access to TMS (as a file of the system).
Each node of the tree is a Lexique;
the description of the semantic of each named TMS in a TD (descriptor array)
is done with a grammar permits
the full structuration of data;
the interactive reading of data;
the automatic printing of the numerical values of a TMS;
the value modification of any variable of a TMS;
the inline documentation of any TMS and menu.
the module in which are programmed the steps of
the reading of data with the TMS;
the declaration of auxiliary arrays TMC and the result TMS;
the call to the algorithm which is written from Fortran 77 standards;
the destruction of auxiliary arrays TMC;
the closing of result TMS.
the using of documented menus with the mouse or the keyboard;
the automatic saving of full user's data.
How to install Mefisto?
The Mefisto software is available on UNIX system, or MAC system 10, or MICROSOFT system under CYGWIN.
The Mefisto load-modules or the sources may be downloaded here
The authors of Mefisto:
The software has been written at Laboratoire Jacques-Louis Lions of the
Université Pierre et Marie CURIE at Paris, France.
This software, based on Finite element methods to solve Partial Differential Equations,
has been conceived, written and is managed by
Alain PERRONNET.
Many options to construct meshes, to solve linear systems, sub-domains have been written by
Pascal JOLY.
The algebraic elliptic quadrangle or hexahedron meshers and a PostScript drawer have been written by
Christophe DOURSAT.
Several students have developed options.
Page written by Alain Perronnet Last update: August 23, 2016