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

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