Christophe Prud'Homme

Simulation of two-fluid flows using a finite element/level set method. Application to bubbles and vesicle dynamics

A new framework for two-fluid flows using a finite element/level set method is presented and verified through the simulation of the rising of a bubble in a viscous fluid. This model is then enriched to deal with vesicles (which mimic red blood cells mechanical behavior) by introducing a Lagrange multiplier to constrain the inextensibility of the membrane. Moreover, high order polynomial approximation is used to increase the accuracy of the simulations. A validation of this model is finally presented on known behaviors of vesicles under flow such as tank treading and tumbling motions.

Scalable domain decomposition preconditioners for heterogeneous elliptic problems

Domain decomposition methods are, alongside multigrid methods, one of the dominant paradigms in contemporary large-scale partial differential equation simulation. In this paper, a lightweight implementation of a theoretically and numerically scalable preconditioner is presented in the context of overlapping methods. The performance of this work is assessed by numerical simulations executed on thousands of cores, for solving various highly heterogeneous elliptic problems in both 2D and 3D with billions of degrees of freedom. Such problems arise in computational science and engineering, in solid and fluid mechanics. While focusing on overlapping domain decomposition methods might seem too restrictive, it will be shown how this work can be applied to a variety of other methods, such as non-overlapping methods and abstract deflation based preconditioners. It is also presented how multilevel preconditioners can be used to avoid communication during an iterative process such as a Krylov method.

High-order fluid-structure interaction in 2D and 3D application to blood flow in arteries

This paper addresses the numerical approximation of fluid-structure interaction (FSI) problems through the arbitrary Lagrangian Eulerian (ALE) framework, high-order methods and a Dirichlet-Newmann approach for the coupling. The paper is divided into two main parts. The first part concerns the discretization method for the FSI problem. We introduce an improved ALE map, capable of handling curved geometries in 2D and 3D in a unified manner, that is based on a local differential operator. We also propose a minimal continuous interior penalty (CIP) stabilization term for the fluid discretization that accounts for a smaller computational effort, while stabilizing the flow regime. The second part is dedicated to validating our numerical strategy through a benchmark and some applications to blood flow in arteries.

High performance domain decomposition methods on massively parallel architectures with FreeFem

Abstract - In this document, we present a parallel implementation in freefem++ of scalable two-level domain decomposition methods. Numerical studies with highly heterogeneous problems are then performed on large clusters in order to assert the performance of our code.

Hemodynamic Forces Tune the Arrest, Adhesion, and Extravasation of Circulating Tumor Cells

Metastatic seeding is driven by cell-intrinsic and environmental cues, yet the contribution of biomechanics is poorly known. We aim to elucidate the impact of blood flow on the arrest and the extravasation of circulating tumor cells (CTCs) inxa0vivo. Using the zebrafish embryo, we show that arrest of CTCs occurs in vessels with favorable flow profiles where flow forces control the adhesion efficacy of CTCs to the endothelium. We biophysically identified the threshold values of flow and adhesion forces allowing successful arrest ofxa0CTCs. In addition, flow forces fine-tune tumor cellxa0extravasation by impairing the remodeling properties of the endothelium. Importantly, we also observe endothelial remodeling at arrest sites of CTCs in mouse brain capillaries. Finally, we observed that human supratentorial brain metastases preferably develop in areas with low perfusion. These results demonstrate that hemodynamic profiles at metastatic sites regulate key steps of extravasation preceding metastatic outgrowth.

Full Three-Dimensional Multiphysics Model of High-Field Polyhelices Magnets

High-field resistive magnets for static field developed at the Laboratoire National des Champs Magnétiques Intenses are based on the so-called polyhelix technique. Their design relies on nonlinear 3-D multiphysics models. As the user demands for higher magnetic field or specific field profile are growing, we have to revisit our numerical models. They need to include more physics and more precise geometry. In this context, we have rewritten our numerical model in the frame of a collaboration with Institut de Recherche Mathématique Avancćee. New models have been implemented with the finite-element library Feel++. This paper gives a status of these developments and the new features available. Results are presented for a 14 polyhelices insert targeting 36 T in a 34-mm bore.

Scalable Domain Decomposition Preconditioners for Heterogeneous Elliptic Problems

Domain decomposition methods are, alongside multigrid methods, one of the dominant paradigms in contemporary large-scale partial differential equation simulation. In this paper, a lightweight implementation of a theoretically and numerically scalable preconditioner is presented in the context of overlapping methods. The performance of this work is assessed by numerical simulations executed on thousands of cores, for solving various highly heterogeneous elliptic problems in both 2D and 3D with billions of degrees of freedom. Such problems arise in computational science and engineering, in solid and fluid mechanics. While focusing on overlapping domain decomposition methods might seem too restrictive, it will be shown how this work can be applied to a variety of other methods, such as non-overlapping methods and abstract deflation based preconditioners. It is also presented how multilevel preconditioners can be used to avoid communication during an iterative process such as a Krylov method.

Overlapping Domain Decomposition Methods with FreeFem

In this note, the performances of a framework for two-level overlapping domain decomposition methods are assessed. Numerical experiments are run on Curie, a Tier-0 system for PRACE, for two second order elliptic PDE with highly heterogeneous coefficients: a scalar equation of diffusivity and the system of linear elasticity. Those experiments yield systems with up to ten billion unknowns in 2D and one billion unknowns in 3D, solved on few thousands cores.

From Real MRA to Virtual MRA: Towards an Open-Source Framework

Angiographic imaging is a crucial domain of medical imaging. In particular , Magnetic Resonance Angiography (MRA) is used for both clinical and research purposes. This article presents the first framework geared toward the design of virtual MRA images from real MRA images. It relies on a pipeline that involves image processing, vascular modeling, computational fluid dynamics and MR image simulation, with several purposes. It aims to provide to the whole scientific community (1) software tools for MRA analysis and blood flow simulation ; and (2) data (computational meshes, virtual MRAs with associated ground truth), in an open-source / open-data paradigm. Beyond these purposes, it constitutes a versatile tool for progressing in the understanding of vascular networks, especially in the brain, and the associated imaging technologies.

Reduced Basis method applied to large scale non linear multiphysics problems

The Laboratoire National des Champs Magnetiques Intenses (LNCMI) is a French large scale nfacility enabling researchers to perform experiments in the highest possible magnetic field. The ndesign and optimization of such magnets require the prediction of performance metrics which can be nthe magnetic field in the center, maximum stresses, or maximum and average temperatures. These noutputs are expressed as functionals of field variables associated with a set of coupled parametrized nPDEs involving materials properties as well as magnet operating conditions. These inputs are not nexactly known and form uncertainties that are essential to consider, since existing magnet technologies nare pushed to the limits. nSolutions of a multi-physics model involving electro-thermal, magnetostatics and mechanics are nrequested to evaluate these implicit input-output relationships, but represent a huge computational ntime when applied on real geometries. The models typically include mesh (resp. finite element approximations) nwith (tens of) millions of elements (resp. degrees of freedom) requiring high performance ncomputing solutions. Moreover, the non affine dependance of materials properties on temperature nrender these models non linear and non affinely parametrized. nThe reduced basis (RB) method offers a rapid and reliable evaluation of this input-output relationship nin a real-time or many-query context for a large class of problems among which non linear nand non affinely parametrized ones. This methodology is well adapted to this context of many model nevaluations for parametric studies, inverse problems and uncertainty quantification. nIn this talk, we will present the RB method applied to the 3D non-linear and non affinely parametrized nmulti-physics model used in a real magnet design context. This reduced model enjoys features of reduced nbasis framework available with opensource library Feel++. (Finite Element method nEmbedded Language in C++, http://www.feelpp.org). Validations and examples will be presented nfor small to large magnet models, involving parametric studies and uncertainty quantifications.