Accelerating 3D Unstructured Mesh Deformation Based on Radial Basis Functions Interpolations Using Tile Low-Rank Matrix Computation

Hatem Ltaief, Youssef MESRI, Rabab M. Alomairy, Wael BADER, David E. Keyes

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We leverage the performance of 3D unstructured mesh deformation in the context of fluid-structure interactions. We employ the Radial Basis Function (RBF) interpolations as a well-known numerically robust approach that produces deformed meshes with high fidelity. The resulting operator is a dense symmetric matrix of size N, with N the number of nodes in the boundary of the mesh. The cubic arithmetic complexity and the quadratic memory footprint often make the system challenging to solve using a direct method. In this paper, we accelerate the computations of 3D unstructured mesh deformation based on RBF interpolations using tile low-rank matrix computations. The idea consists in exploiting the data sparsity of the matrix operator of the linear system by approximating off-diagonal tiles up to an application-dependent accuracy threshold. We demonstrate the effectiveness of our implementation by assessing the numerical accuracy of the mesh deformation. We then provide preliminary performance benchmarking on two shared-memory systems. The high performance tile low-rank solver permits to achieve up to 20-fold performance speedup over the state-of-the-art dense matrix solvers
Original languageEnglish (US)
Title of host publication32nd International Conference on Parallel Computational Fluid Dynamics
PublisherParCFD’2020
StatePublished - May 11 2020

Bibliographical note

KAUST Repository Item: Exported on 2022-09-14

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