Geometrically Reduced Modelling of Pulsatile Flow in Perivascular Networks

Flow of cerebrospinal fluid in perivascular spaces is a key mechanism underlying brain transport and clearance. In this paper, we present a mathematical and numerical formalism for reduced models of pulsatile viscous fluid flow in networks of generalized annular cylinders. We apply this framework to study cerebrospinal fluid flow in perivascular spaces induced by pressure differences, cardiac pulse wave-induced vascular wall motion and vasomotion. The reduced models provide approximations of the cross-section average pressure and cross-section flux, both defined over the topologically one-dimensional centerlines of the network geometry. Comparing the full and reduced model predictions, we find that the reduced models capture pulsatile flow characteristics and provide accurate pressure and flux predictions across the range of idealized and image-based scenarios investigated—at a fraction of the computational cost of the corresponding full models. The framework presented thus provides a robust and effective computational approach for large scale in-silico studies of pulsatile perivascular fluid flow and transport.publishedVersio

Simultaneous empirical interpolation and reduced basis method for non-linear problems

In this paper, we focus on the reduced basis methodology in the context of non-linear non-affinely parametrized partial differential equations in which affine decomposition necessary for the reduced basis methodology are not obtained [4, 3]. To deal with this issue, it is now standard to apply the EIM methodology [8, 9] before deploying the Reduced Basis (RB) methodology. However the computational cost is generally huge as it requires many finite element solves, hence making it inefficient, to build the EIM approximation of the non-linear terms [9, 1]. We propose a simultaneous EIM Reduced basis algorithm, named SER, that provides a huge computational gain and requires as little as N + 1 finite element solves where N is the dimension of the RB approximation. The paper is organized as follows: we first review the EIM and RB methodologies applied to non-linear problems and identify the main issue, then we present SER and some variants and finally illustrates its performances in a benchmark proposed in [9]

Reduced Order modeling of high magnetic field magnets

International audienceWe present applications of the reduced basis method (RBM) to large-scale non-linear multi-physics problems connected to real industrial applications arising from the High Field Resistive Magnets development at the Laboratoire National des Champs Magnétiques Intenses

Reduced basis methods and high performance computing. Applications to non-linear multi-physics problems

International audienceWe present an open-source framework for the reduced basis methods implemented in the library Feel++ [3,4] and we consider in particular multi-physics, possibly non-linear, applications [1,2] which require high performance computing. We present how the mathematical methodology and technology scale with respect to complexity and the gain obtained in industrial context [1]. We present also briefly our first developments on low-rank methods within our framework with our colleagues from ECN. One of the main application presented is developed with the Laboratoire National des Champs Magnétiques Intenses (LNCMI), a large french equipment, allowing researchers to do experiments with magnetic fields up to 35T provided by water cooled resistive electro-magnet. Existing technologies (material properties,...) are pushed to the limits and users require now specific magnetic field profiles or homogeneous fields. These constraints and the international race for higher magnetic fields demand conception tools which are reliable and robust. The reduced basis methodology is now part of this tool chain. Another domain of application we will consider in the talk is fluid flows, both Stokes and Navier-Stokes.[1] Cécile Daversin, Stéphane Veys, Christophe Trophime, Christophe Prud'Homme. A Reduced Basis Framework: Application to large scale non-linear multi-physics problems http://hal.archives-ouvertes.fr/hal-00786557 [2] Elisa Schenone, Stéphane Veys, Christophe Prud'Homme. High Performance Computing for the Reduced Basis Method. Application to Natural Convection http://hal.archives-ouvertes.fr/hal-00786560[3] http://www.feelpp.org [4] C. Prudhomme, V. Chabannes, V. Doyeux, M. Ismail, A. Samake, G. Pena. Feel++ :A Computational Framework for Galerkin Methods and Advanced NumericalMethods, ESAIM Proc., Multiscale Coupling of Complex Models in Scientific Computing, 38 (2012), 429–455

Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo

Efficient uncertainty quantification algorithms are key to understand the propagation of uncertainty -- from uncertain input parameters to uncertain output quantities -- in high resolution mathematical models of brain physiology. Advanced Monte Carlo methods such as quasi Monte Carlo (QMC) and multilevel Monte Carlo (MLMC) have the potential to dramatically improve upon standard Monte Carlo (MC) methods, but their applicability and performance in biomedical applications is underexplored. In this paper, we design and apply QMC and MLMC methods to quantify uncertainty in a convection-diffusion model of tracer transport within the brain. We show that QMC outperforms standard MC simulations when the number of random inputs is small. MLMC considerably outperforms both QMC and standard MC methods and should therefore be preferred for brain transport models.Comment: Multilevel Monte Carlo, quasi Monte Carlo, brain simulation, brain fluids, finite element method, biomedical computing, random fields, diffusion-convectio

High intensity neutrino oscillation facilities in Europe

The EUROnu project has studied three possible options for future, high intensity neutrino oscillation facilities in Europe. The first is a Super Beam, in which the neutrinos come from the decay of pions created by bombarding targets with a 4 MW proton beam from the CERN High Power Superconducting Proton Linac. The far detector for this facility is the 500 kt MEMPHYS water Cherenkov, located in the Fréjus tunnel. The second facility is the Neutrino Factory, in which the neutrinos come from the decay of μ+ and μ− beams in a storage ring. The far detector in this case is a 100 kt magnetized iron neutrino detector at a baseline of 2000 km. The third option is a Beta Beam, in which the neutrinos come from the decay of beta emitting isotopes, in particular He6 and Ne18, also stored in a ring. The far detector is also the MEMPHYS detector in the Fréjus tunnel. EUROnu has undertaken conceptual designs of these facilities and studied the performance of the detectors. Based on this, it has determined the physics reach of each facility, in particular for the measurement of CP violation in the lepton sector, and estimated the cost of construction. These have demonstrated that the best facility to build is the Neutrino Factory. However, if a powerful proton driver is constructed for another purpose or if the MEMPHYS detector is built for astroparticle physics, the Super Beam also becomes very attractive

Bases réduites pour des problèmes multi-physiques non-linéaires de grande taille : application au design d'aimants à haut champ

The magnetic field constitutes a powerfull tool for researchers, especially to determine the properties of the matter. This kind of applications requires magnetic fields of high intensity. The "Laboratoire National des Champs Magnetiques Intenses" (LNCMI) develops resistive magnets providing such magnetic field to scientists. The design of these magnets represents a challenge interms of design. We have developed a range of non-linear coupled models taking into account the whole involved physics, implemented through the Feel++ library. Designed for many query context, the reduced basis method applied to the multi-physics model aims to circumvent the complexity of the problem. lts efficiency allows to move towards parametric studies and sensitivity analysis in various concrete applications. Especially, the method SER we introduce in this thesis is a significant breakthrough for non-linear and non-affine problems in an industrial context.Le LNCMI est un grand équipement du CNRS. Il met à la disposition de la communauté scientifique internationale des aimants produisant des champs magnétiques intenses (entre 24 et 36 Teslas pendant plusieurs heures), utilisés par les chercheurs comme un moyen d'exploration et de contrôle de la matière. Dans la thèse, nous nous intéressons à la simulation de ce type d'aimants, dans le but de les étudier, d'optimiser leur design, ou encore de faire des analyses d'incidents. Ces modèles 30 sont basés sur des équations aux dérivées partielles couplées non-linéaires. Au vu de leur complexité, nous avons développé des méthodes de réduction d'ordre, permettant de réduire considérablement les temps de calcul associés. En particulier, nous pensons avoir levé un verrou majeur de l'utilisation du cadre méthodologique de réduction d'ordre pour des problèmes multi-physiques non-linéaires

Simultaneous empirical interpolation and reduced basis method for non-linear problems

In this paper, we focus on the reduced basis methodology in the context of non-linear non-affinely parametrized partial differential equations in which affine decomposition necessary for the reduced basis methodology are not obtained [4, 3]. To deal with this issue, it is now standard to apply the EIM methodology [8, 9] before deploying the Reduced Basis (RB) methodology. However the computational cost is generally huge as it requires many finite element solves, hence making it inefficient, to build the EIM approximation of the non-linear terms [9, 1]. We propose a simultaneous EIM Reduced basis algorithm, named SER, that provides a huge computational gain and requires as little as N + 1 finite element solves where N is the dimension of the RB approximation. The paper is organized as follows: we first review the EIM and RB methodologies applied to non-linear problems and identify the main issue, then we present SER and some variants and finally illustrates its performances in a benchmark proposed in [9]

Full 3D MultiPhysics Model of High Field PolyHelices Magnets

International audienceHigh field Resistive magnets for static field developed at the Laboratoire National des Champs Magnétiques Intenses (LNCMI) are based on the so-called polyhelix technique. Their design relies on non-linear 3D multi-physic 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 en Mathématique Avancée (IRMA). 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 Tesla in a 34 mm bore