Efficient Parallel Implementation of Radial Basis Functions Generated Finite Differences using Asynchronous Techniques

June 16, 2025

Radial Basis Function - generated Finite Difference (RBF-FD) method is a powerful meshless technique for solving Partial Differential Equations (PDEs), particularly in domains with complex or dynamic geometries. By operating on scattered nodes, RBF-FD circumvents the need for mesh generation while achieving high-order accuracy through localized stencils and radial basis function interpolation. However, its flexibility comes at the cost of substantial computational demands, especially for large-scale problems where node generation, stencil computation, matrix assembly, and sparse linear system solution dominate runtime. This thesis addresses these performance bottlenecks by exploring the parallelization of RBF-FD using OpenMP, with a specific focus on task-based asynchronous execution. Two critical stages identified in prior benchmarks of the Medusa library are examined: (i) interior node discretization and (ii) sparse system solution. While both are costly, this work concentrates on the first—domain filling—given its dominant role in point-based discretizations. The proposed strategy leverages OpenMP task dependencies to accelerate the interior node generation phase, aiming to minimize synchronization overhead and enhance parallel scalability. A custom C implementation is developed and directly compared against Medusa, an open-source C++ framework for strong-form meshless PDE solvers. The evaluation includes detailed timing analyses, memory usage profiling, and strong scaling tests across various node densities and domain sizes. By focusing on efficient domain discretization, this work demonstrates that carefully structured asynchronous tasking can outperform traditional approaches, offering a scalable alternative for meshless PDE solvers.

Authors in the community:

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  A

  António Quirino Soares de Carvalho Falacho

  ist196164

Supervisors of this institution:

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  J

  Juan António Acebron de Torres

  ist24873

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  J

  José Carlos Alves Pereira Monteiro

  ist12850

electrical-engineering-electronic-engineering-information-engineering - Electrical engineering, electronic engineering, information engineering

eng - English

Instituto Superior Técnico