Bérenger Bramas soutiendra sa thèse le lundi 15 février à 14h30 salle Ada Lovelace.
“Optimization and Parallelization of the Boundary Element Method for the Wave Equation in Time Domain”
George Biros – Professor – The University of Texas at Austin
Coulaud Olivier (Advisor) – Research Director – Inria Bordeaux – Sud-Ouest
Pascal Havé – Researcher – IFP Energies nouvelles
Stéphane Lanteri – Research Director – Inria Sophia Antipolis
Raymond Namyst – Professor – The University of Bordeaux
Guillaume Sylvand (Advisor) – Researcher – Airbus Group Innovations
Isabelle Terrasse – Research Director – Airbus Group
Richard Vuduc – Associate Professor – Georgia Institute of Technology
Abstract:
The time-domain BEM for the wave equation in acoustics and electromagnetism is used to simulate the propagation of a wave with a discretization in time. It allows to obtain several frequency-domain results with one solve. In this thesis, we investigate the implementation of an efficient TD-BEM solver using different approaches. We describe the context of our study and the TD-BEM formulation expressed as a sparse linear system composed of multiple interaction/convolution matrices. This system is naturally computed using the sparse matrix-vector product (SpMV). We work on the limits of the SpMV kernel by looking at the matrix reordering and the behavior of our SpMV kernels using vectorization (SIMD) on CPUs and an advanced blocking-layout on Nvidia GPUs. We show that this operator is not appropriate for our problem, and we then propose to reorder the original computation to get a special matrix structure. This new structure is called a slice matrix and is computed with a custom matrix/vector product operator. We present an optimized implementation of this operator on CPUs and Nvidia GPUs for which we describe advanced blocking schemes. The resulting solver is parallelized with a hybrid strategy above heterogeneous nodes and relies on a new heuristic to balance the work among the processing units. Due to the quadratic complexity of this matrix approach, we study the use of the fast multipole method (FMM) for our time-domain BEM solver. We investigate the parallelization of the general FMM algorithm using several paradigms in both shared and distributed memory, and we explain how modern runtime systems are well-suited to express the FMM computation. Finally, we investigate the implementation and the parametrization of an FMM kernel specific to our TD-BEM, and we provide preliminary results.
