Some Specific Projects Modeling and HPC US France Young Engineering Scientists symposium

The Life Sciences Session US France Young Engineering Scientists symposium

Common features complex problems (multiphase, multiphysics, multidomain, multi scale), often "early stage" in modelization. Life Sciences Session

Common interest Four subjects Soft tissue/fluid (medical image driven problems); Contact model/moving boundaries; Concentrate suspension; Complex geometry and (medical...) imaging.

Medical image driven problems Georges Biros, Didier Auroux, Marcela Szopos, Benjamin Mauroy, Mourad Ismail, Boyce Griffith. Right now: integration of existing codes in an open source framework; development of benchmarks for arterial flows; sharing image-driven model datasets (when possible); development of novel parameter estimation algorithms.

Contact model /moving boundaries Judith Hill, Vincent Martin, Marcela Szopos, Arnaud Ducrot, Olivier Saut, Benjamin Mauroy, Boyce Griffith. Right now: a discussion of methods for moving boundaries (we all use different ones) a beginning of a discussion on the theory behind the contact problem (what's the right thing to do).

Concentrate suspension Mourad Ismail, Judith Hill, Olivier Saut, Benjamin Mauroy. Right now: compare different numerical methods for complex fluids simulation include some US researchers in our ANR project "MOSICOB" on numerical simulation of complex fluids. share experimental data for validation of numerical methods.

Complex geometry and imaging Olivier Saut, Boyce Griffith, Arnaud Ducrot. Right now: discuss methods for mesh generation; discuss compare methods for interpolation of medical data on the mesh (and image reconstruction).

The Algorithm Session US France Young Engineering Scientists symposium

Error estimate-based adaptivity for fluid structure problems Martin Vohralik, Virginie Bonnaillie-Noel, Mourad Ismail, Martin Campos-Pinto, Boyce Griffith, Sreekanth Pannala

Develop and implement a general parallel adaptive scheme based on local error estimate for problems involving fluid structure interactions. Some of the properties desirable in this scheme are: a) Optimal geometric and hierarchical adaptivity based on local error b) Load balanced to ensure scalability c) Amenable to implicit fluid structure coupling

Numerical methods for singular reaction diffusion equations arising in population dynamics Arnaud Ducrot Mayya Tokman

We want to construct numerical schemes using the weak formulation of pray-predator models with Holling-Tanner like interaction. The scheme will capture the singular behaviour of thesolutions

Inverse problems, parameter estimation and data assimilation Didier Auroux George Biros

In most life and physical sciences, a crucial issue in the modelisation process is the estimation and identification of the model parameters (or some boundary conditions, or some unknown terms in the model equations). Inverse problem and data assimilation techniques (e.g. optimal control theory, Kalman filters, dual variational algorithm) allow us to calibrate the model parameters from real data sets and identify more precisely the system state. We will combine Kalman filters with dual variational methods to explore novel methodologies for large scale data assimilation. We will conduct numerical experiments to compare the new methods with the existing state of the art.

Development of Parallel Solvers for Highly Anisotropic Parabolic Linear Systems Arising in Resistive MHD and Radiation Transport Frederic Magoules Daniel Reynolds Bronson Messer

We consider linear systems arising from highly anisotropic, parabolic differential equations relevant to fusion plasmas and astrophysical radiation transport. We will investigate parallel Domain Decomposition algorithms on these problems. Such approaches may promise increased robustness over multigrid methods for highly anisotropic and spatially adaptive systems on such problems.

“Non-life sciences” and “Software and libraries” Sessions US France Young Engineering Scientists symposium

Parallel in Time and Space Algorithms for Fluid Mechanics F. Magoules K. Evans G. Staffelbach R. Mills

Parallel in Time and Space Algorithms for Fluid Mechanics We will investigate computational efficiency improvements for computational fluid dynamics through an adaptation of the parallel method both in time and space. First, development of an implicit solver will allow larger time steps on relatively coarse grids to create 'seed' values along a time dependent run. The seed values allow a subsequent refinement of decomposed time domains to occur in parallel. An investigation of the treatment will be performed to determine the feasibility of scalability to 500K processors using space and time decomposition.

Combined Finite Element and Finite Volume Schemes for Subsurface Flows Martin Vohralik Richard Mills Sreekanta Parmala

Combined Finite Element and Finite Volume Schemes for Subsurface Flows Develop and implement a scalable scheme based on combined Finite Element (FE) and Finite Volume (FV) method for subsurface flow and transport with full anisotropic heterogeneous tensor and the following properties: 1.One unknown/element 2.Symmetric Positive Definite matrix 3.With proven existence and uniqueness 4.General mesh (non-convex, non-matching) 5.Local conservation 6.Linear 7.Discrete maximum principle

Efficient Preconditioning Strategies for Neutral Particle Transport Dinesh Kaushik Broson Messer Laura Grigori Julien Salomon

Efficient Preconditioning Strategies for Neutral Particle Transport The neutron transport equation is seven dimensional (three in space, two in angle, one in energy, and the last in time). The discretized form of this equation gives rise to massive linear systems that need to be solved on large-scale parallel machines. In order to do this in reasonable amount of time, efficient preconditioners are essential. In this collaborative effort, we will work on custom precondtioners that take advantage of the matrix structure. These preconditioners will be applied to the astrophysics (neutrino transport) and nuclear reactor applications (neutron transport). We will also explore the opportunities for preconditioning using techniques from parallelization in the time dimension.

Theoretical Analysis of the Eigenspectrum of the Dirac Equation James Brannick Virginie Bonnaillie-Noel

Theoretical Analysis of the Eigenspectrum of the Dirac Equation The aim of the project is to analyze the properties of the eigenspectrum of the Dirac equation of QCD. Initially, we propose to study the simplified Schwinger model of Quantum Electrodynamics with a U(1) potential. The goals will be as follows: –Conduct theoretical analysis to determine the behavior and localization of the eigenfuntions –Develop a gauge invariant discretization using Finite Elements -- –current discretizations are essentially limited to finite difference schemes. –Explore the theoretical results using this numerical model. –Generalize the results obtained for this model to the QCD equation with SU(3) gauge.

Integrating Adaptive Grids with Nonlinear Solvers for Problems in Plasma Physics Martin Compos-Pinto Mayya Tokman Daniel Reynolds

Integrating Adaptive Grids with Nonlinear Solvers for Problems in Plasma Physics The presence of complex nonlinear interactions of multiple spacial and tem- poral scales make numerical solutions of equations such as Vlasov or MHD a challenging task. To address this problem, it is highly desirable to construct numerical schemes which integrate efficient adaptive approaches to discreti- zations in space and time. By combining expertise of French researchers in time evolution of adaptive space discretizations and American counterparts in efficient time integrators for nonlinear systems, we plan to investigate pos- sibilities for designing innovative numerical methods for problems in plasma physics.

Exploring Coupling Strategies Using PALM for Multiphysics Nuclear Reactor Simulations Dinesh Kaushik Gabriel Staffelbach Laura Grigori

Exploring Coupling Strategies Using PALM for Multiphysics Nuclear Reactor Simulations Nuclear reactor core simulations require coupling among different physics areas such as neutronics, thermal hydraulics, and structural mechanics. This coupling needs to be accurate (not to compromise accuracy from each physics component) and parallel (to support large- scale simulations). We will explore using PALM software for coupling mutiphysics codes from Argonne. PALM is developed by the PALM Team at CERFACS ( Various coupling approaches will be tested with scalability and ease of use in mind. We will also attempt to construct accurate interpolation schemes and preconditioning techniques designed for the coupled systems.