Séminaire "Multirésolution adaptative pour la simulation de problème multi-échelles et parallélisme"

Programme

lundi 30/05

13:30 13:40

Accueil (café)

13:40 13:45

Introduction

13:45 14:45

Multiresolution Flow Simulations Using Grids and Particles

Petros Koumoutsakos (Chair of Computational Science, ETH Zurich)

We present finite volume and remeshed vortex methods for flow simulations based on wavelet adapted grids. These methods have been integrated in open source software framework, for multiresolution simulations of two-dimensional, compressible and incompressible, viscous flows on multicore architectures. I will discuss in particular incompressible vortical flows where the spatiotemporal scales of the flow field are captured by remeshed particles enhanced by high order average-interpolating wavelets and local time-stepping. The multiresolution solver of the Poisson equation relies on the development of a novel, tree-based multi-pole method. The software (MRAG-I2D) implements a number of HPC strategies to map efficiently the irregular computational workload of wavelet-adapted grids on multicore nodes. Examples of flow simulations include flows past cylinders and self-propelled anguilliform swimmers. Finally, I will discuss steps towards multiresolution simulations of 3D flows and the extension of the software to distributed memory architectures.

14:45 15:45

Dedicated time integration schemes on multiresolution adapted grids for stiff PDEs

Max Duarte (CD-adapco, previously Lawrence Berkeley National Laboratory)

Special care must be taken to address the numerical integration of stiff, time-dependent PDEs. In this talk we focus on some alternatives to efficiently solve stiff PDEs modeling unsteady problems with localized fronts, from operator splitting schemes to high order fully implicit discretizations. In all cases the time integration is performed on dynamically adapted grids generated by multiresolution analysis using a conservative finite volume discretization. The multiresolution finite volume scheme yields highly compressed representations within a user-defined accuracy tolerance. Time adaptivity based on accuracy criteria can be also achieved, thus defining a time-space adaptive solver. Numerical evidence is provided of the computational efficiency of the numerical strategy to cope with highly unsteady problems modeling various physical scenarios with a broad spectrum of time and space scales. The strategy is particularly relevant to carry out numerical simulations with very limited computational resources.

15:45 16:00

Pause café

16:00 17:00

Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures

Thierry Dumont (Institut Camille Jordan, Université Claude Bernard Lyon 1)

Reaction-diffusion systems involving a large number of unknowns and a wide spectrum of scales in space and time are numerically difficult to solve. New techniques featuring adaptation in space and time as well as error control, based on operator splitting, finite volume adaptive multiresolution and high order time integrators have been introduced recently and applied to combustion, plasma physics, nonlinear chemical dynamics and biomedical engineering. Parallel computation with these methods is challenging: we present here a new implementation in shared memory, based on specific data structures, using the TBB library. The performance of our implementation is assessed in a series of test-cases of increasing difficulty in two and three dimensions, demonstrating high scalability.

17:00 18:00

Understanding the CPU performance of irregular HPC codes

Thomas Guillet (Intel France)

Modern CPU architectures provide an ever increasing amount of computing power, with more and more integrated cores and higher peak flops. However, this performance is most readily accessible to codes with a regular CPU execution behavior. Many numerical methods, including multiresolution or adaptive mesh refinement techniques, are intrinsically irregular, and implementations struggle to achieve high efficiency even at the level of a single compute node. In this presentation, we will discuss some of the mechanisms that make regular codes run well on modern CPUs, and cover the corresponding performance challenges of irregular codes. We will discuss some key principles, which can help extract performance from irregular applications.