André Chambarel

Finite element formulation for Maxwell's equations with space dependent electric properties

ABSTRACT The Time Domain Reflectometry—TDR- probe is a new technique applied to moisture measurement. It is a wave guide constituted by two or three parallel metallic rods stuck in the ground. An electromagnetic wave propagates all along the wave guide and crosses a variable electric properties medium. In that way the reflecting wave is disrupted and we detect the electric singularities. We study the transverse magneti- mode. We simulate this wave guide in this medium thanks to the Finite Element Method and present the used matricial structure. For time integration we compare a semi-implicit or Runge-Kutta method with variable time-step. This process is driven by the Automatic Multigrid System with an unknown time-dependent number.

A General Parallel Computing Approach Using the Finite Element Method and the Objects Oriented Programming by Selected Data Technique

We develop a coherent set of techniques for parallel computing. We use the Finite Element Method associated with the C++ Objects Oriented Programming with only one database. A technique of data selection called AMS - Automatic Multigrid System - is used for the determination of the data dedicated to each processor. This method is performed by a SIMD technology associated with the MPI capabilities. This parallel computing is applied to very large CPU cost problems particularly the unsteady problems or steady problems using iterative methods. Different results in Computational Fluid Dynamics are presented.

Parallel Computation of an Unsteady Compressible Flow

In the present paper, a general background is presented for developping parallel applications in the domain of Computational Fluid Dynamics. This frame of work is based upon block Jacobi preconditioned iterative methods for solving partial differential equations. It is shown how the parallelism potential of such a preconditioning can be efficiently exploited by associating it with Finite Element discretization and Object Oriented Programming. The resulting parallel applications are characterized by coarse granularity, ease of maintaining good load balance and the possibility of using the same object in both a serial or a parallel computing context. As an application of our parallel approach, the simulation of an unsteady compressible flow is discussed.

Numerical modelling of poroviscoelastic grounds in the time domain using a parallel approach

In this paper, we present a parallelized finite element code developed to study wave propagation phenomena, specifically in porous soils problems which usually require millions of degrees of freedom. The parallelization technique uses an algebraic grid partitioning managed by a Single Program Multiple Data (SPMD) programming model. Message Passing Interface (MPI) library specification is the standard used to exchange data between processors. The architecture of the code is explained and numerical results show its performance.

Application of the Parallel Computing Technology to a Wave Front Model Using the Finite Element Method

The Time Domain Reflectometry probe is a new technique applied to moisture measurement. It is a wave guide stuck in the ground. The wave crosses a variable electric properties medium. We develop a model based on the resolution of Maxwells equations which allows to determine the electromagnetic field and the energy density. The problem of a wave front propagation presents a very large CPU cost. So we develop a parallel computing approach based on C++ Objects Oriented Programming, Finite Element Method and selected data technique. We associate the SIMD technology with the MPI C++ library for software implementation. High performances computing are obtained.

Simulation of a Compressible Flow by the Finite Element Method Using a General Parallel Computing Approach

We have developed a coherent set of techniques for parallel computing. We have used the Finite Element Method associated with the C++ Object-Oriented Programming with only one database. A technique of data selection is used in the determination of the data dedicated to each processor. This method is performed by SIMD technology associated with MPI capabilities. This parallel computing is applied to very large CPU cost problems particularly the unsteady problems or steady problems using iterative methods. Different results in Computational Fluid Dynamics are presented.

Numerical Model of Complex Porous Media

In complex porous media we often notice a percolation phenomenon [KIR 71] [GRI 89]. Usually these media present discontinuous characteristics and a random space distribution [LET 00] [BIR 95]. There results that the classical models based on the resolution of a partial differential problem become inefficient because we have non-derivable function [MAU 01]. Statistical approaches based on the resolution of partial differential problems pose notably the questions concerning the continuity of the functions representing the physical properties of the medium. In this work we propose to study a numerical model of porous media based on a mixture of 2 components in a percolation context. In practice, the main difficulty is based on the complex physical properties. We present also a model of homogenization. Our numerical model is based on the Finite Element approach.Copyright

Modeling of electromagnetic waves in media with dirac distribution of electric properties

We develop a new numerical approach of the electromagnetic wave propagation in a complex media model. We use a new Finite Element Method for space discretization and a finite difference method in time domain. This study is applied to TDR (Time Domain Reflectometry) which appears as a wave guide. In this context, the experimental approach is very uneasy and the numerical study brings about very interesting results, particularly for local values of the electromagnetic field. Moreover we test models of an heterogeneous medium. Dielectric properties of the medium are represented by an homogeneous component associated with Dirac distribution. We present wave front profiles with useable signals simulation.

Cellular Model of Complex Porous Media Application to Permeability Determination

In soil science we need complex porous media models. Usually these media present discontinuous characteristics with random space distribution. So we propose to study a medium based on a cellular model. In this work we represent the soil as a compact matter associated with vacuum areas. Under these conditions we study the flux of water through this medium. We formulate the hypothesis that it is composed of a mixture of two different permeability values. The medium is discretized with tetrahedral cells and we dedicate permeability to each cell with a random space distribution. We associate to each cell an inner and an outer physical law and we test the flux of water through this medium. So we introduce a physical consideration in a cellular model. We also present a study for several scales of the problem.

Optimization of the Communications between Processors in a General Parallel Computing Approach Using the Selected Data Technique

A large variety of problems that are out of reach of single processor computer capabilities. Many approaches are offered today to get round this. Each of these has its own strengths and weaknesses : a compromise has to be found. We will introduce a general parallel computing method for engineering problems dedicated to all users. We have searched an easy method for code development. A technique of data selection (Selected Data Technique – SDT) is used for the determination of the data dedicated to each processor. Several problems associated with the communication times are posed and solutions are proposed in accordance with the number of processors. This method is applied to very large CPU cost problems, particularly the unsteady problems or steady problems using an iterative method. So the domain of potential applications is very wide. The SDT-parallelization is performed by an expert system called AMS (Automatic Multi-grid System) included in the software. This new concept is a natural way for the standardization of parallel codes. An example is presented hereafter.