Welcome to the web site of the NACHOS team!

Numerical modeling and high performAnce computing for evolution problems
in Complex domains and HeterogeneOuS media

NACHOS is a joint project-team between INRIA, the CNRS and the University of Nice/Sophia Antipolis
via the J.A. Dieudonné Mathematics Laboratory (UMR 6621)

Our research activities are concerned with the formulation, analysis and evaluation of numerical methods and high performance resolution algorithms for the computer simulation of evolution problems in complex domains and heterogeneous media. We consider in the first place mathematical models that rely on first-order linear systems of partial differential equations with variable coefficients and more particularly those pertaining to electrodynamics and elastodynamics with applications to computational electromagnetics and computational geoseismics.

We focus on applications in these domains which involve the interaction of the underlying physical fields with media exhibiting space and time heterogeneities such as when studying the propagation of electromagnetic waves in biological tissues or the propagation of seismic waves in complex geological media. Moreover, in most of the situations of practical relevance, the computational domain is irregularly shaped or/and it includes geometrical singularities. Both the heterogeneity and the complex geometrical features of the underlying media motivate the use of numerical methods working on non-uniform discretizations of the computational domain.

In this context, our research efforts aim at the development of unstructured (or hybrid unstructured/structured) mesh based methods with activities ranging from the mathematical analysis of numerical methods for the discretization of systems of partial differentail equations of electrodynamics and elastodynamics, to the development of prototype 3D simulation software that efficiently exploit the capabilities of modern high performance computing platforms.

From the point of view of applications, our objective is to demonstrate the capabilities of the proposed numerical methodologies for the study of realistic wave propagation problems in complex domains and heterogeneous media. Three physical situations currently attract our attention which respectively involve the interaction of:

• electromagnetic waves with dispersive media focussing on biological tissues,
• electromagnetic waves with charged particles considering particle-in-cell methods,
• seismic waves with viscoelastic geological media.

Recent publications

L. Moya and J. Verwer
Temporal convergence of a locally implicit discontinuous Galerkin method for Maxwell's equations
Available as INRIA RR-7533 on Hyper Article Online

S. Lanteri and R. Perrussel
An implicit hybridized discontinuous Galerkin method for time-domain Maxwell's equations
Available as INRIA RR-7578 on Hyper Article Online

T. Cabel, J. Charles and S. Lanteri
Multi-GPU acceleration of a DGTD method for modeling human exposure to electromagnetic waves
Available as INRIA RR-7592 on Hyper Article Online

C. Scheid and S. Lanteri
Convergence of a Discontinuous Galerkin scheme for the mixed time domain Maxwell's equations in dispersive media
Available as INRIA RR-7634 on Hyper Article Online

S. Lanteri, L. Li and R. Perrussel
A hybridizable discontinuous Galerkin method for time-harmonic Maxwell's equations
Available as INRIA RR-7649 on Hyper Article Online

Numerical simulation of the exposure of a pregnant women to electromagnetic waves emitted by multiple localized sources, using DGTD-P1 and DGTD-P2 methods (Discontinuous Galerkin Time Domain methods with linear and quadratic interpolation of electromagnetic field components). This calculation is performed on an heterogeneous geometrical model of 3 tissues (body of the women, body of the foetus and brain of the foetus) consisting of an unstructured tetrahedral mesh with 5,536,852 tetrahedra (the total number of degrees of freedom for this problem is 132,884,448 for the DGTD-P1 method and 332,211,120 for the DGTD-P2 method).

The geometrical model has been built starting from MRI mdedical images provided by the FEMONUM project.

The unstructured tetrahedral mesh has been generated using the TetMesh-GHS3D software developed by the Distene company and the GAMMA3 INRIA project-team.

The underlying DGTD method has been ported to a multiple GPU (Graphical Processing Unit) BULL Novascale R422 computing system.
The single precision floating point performance of the DGTD-P1 and DGTD-P2 calculation is 4.7 Tflops and 8.9 Tflops on 128 GPUs.
This work was granted access to the HPC resources of CCRT under the allocation 2010-t2010065004 made by GENCI (Grand Equipement National de Calcul Intensif).

Numerical simulation of the exposure of head tissues to an electromagnetic wave emitted by a mobile phone, using a DGTD-P1 method (Discontinuous Galerkin Time Domain method with linear interpolation of electromagnetic field components). This calculation is performed on an heterogeneous geometrical model of 4 head tissues (skin, skull, cerebro spinal fluid and brain) consisting of an unstructured tetrahedral mesh with 7,894,172 tetrahedra (the total number of degrees of freedom for this problem is 189,460,128).

The simulation was run on 512 cores of a Bull Novascale 3045 parallel system consisting of Intel Itanium 2/1.6 GHz nodes interconnected by a high performance Infiniband network.
The corresponding elapsed computing time is 761 sec.
This work was granted access to the HPC resources of CCRT under the allocation 2009-t2009065004 made by GENCI (Grand Equipement National de Calcul Intensif).

Numerical simulation of the exposure of a full body to electromagnetic waves emitted by multiple localized sources, using a DGTD-P2 method (Discontinuous Galerkin Time Domain method with quadratic interpolation of electromagnetic field components). This calculation is performed on a homogeneous geometrical model consisting of an unstructured tetrahedral mesh with 5,335,521 tetrahedra (the total number of degrees of freedom for this problem is 320,131,260).

The simulation was run on 512 cores of a Bull Novascale 3045 parallel system consisting of Intel Itanium 2/1.6 GHz nodes interconnected by a high performance Infiniband network.
The corresponding elapsed computing time is 7903 sec.
This work was granted access to the HPC resources of CCRT under the allocation 2008-t2009065004 made by GENCI (Grand Equipement National de Calcul Intensif).

Scattering of a plane wave by a spherical cavity with a hole at one of its pole. This numerical simulation is performed using a hybrid explicit-implicit DGTD-P2 method. The elements of the underlying tetrahedral mesh are partitioned into two sets based on a geometric criterion: the set of implicit elements is composed of tetrahedra for which the geometric criterion is below a given threshold, while the explicit set is composed of the remaining elements. Numerical simulations have been conducted on a cluster of Intel Xeon 2.33 GHz based nodes interconnected by a high performance Myrinet network. The hybrid-explicit time stepping scheme combines a Leap-Frog scheme for time advancing the set of unknowns associated to the explicit part with a Crank-Nicolson scheme for time advancing the set of unknowns associated to the implicit part. This hybrid time integration strategy allows to reduce the simulation time from 4 h 24 mn (fully explicit DGTD-P2 method) to 56 mn. The elements treated implicitly represent here 0.2 % of the whole set of 301,116 mesh elements. A parallel direct (sparse LU factorization) method is used for solving the implicit system at each time step.

INRIA, NACHOS project-team
2004 Route des Lucioles, B.P. 93
06902 Sophia Antipolis Cedex, France
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