arXiv subjects

Thilina Ratnayaka

Publications and source records attributed to Thilina Ratnayaka.

3 recordsLinked to original sources

arXiv2026

Coarse Solvers for Exascale Solution of Poisson Problems

We present a two-level Schwarz method as an alternative to Algebraic Multigrid method(AMG) used as the last level (coarse) solver of the p-multigrid pMG preconditioner for pressure Poisson equation resulting from Spectral/Finite element descretization of incompressible Navier-Stokes equation. Proposed Schwarz method consits of a local problem in the original pMG coarse space and a global coarse problem. Main contribution of the paper is a novel, structured and a non-nested coarse space for the global coarse problem. Structured nature of the proposed global coarse space enable communication-free interpolation between the original p-multgrid coarse space and the global coarse problem. We demonstrate the effectiveness of the proposed method compared to the state of the art AMG solver BoomerAMG by a series of experiments performed using Nek5000/RS, a suite of highly scalable incompressible Navier-Stokes solvers, on Summit/Frontier supercomputers at Oak Ridge Leadership Computing Facility.

math.NA↗

arXiv2026

parRSB: Exascale Spectral Element Mesh Partitioning

We introduce parRSB - a parallel, highly scalable graph partitioner for spectral element meshes that produce high quality partitions. parRSB is based on Recursive Spectral Bisection (RSB) algorithm implemented on the dual graph of the input mesh. RSB uses the Fiedler vector, which is the eigenvector associated with the smallest non-zero eigenvalue of the Laplacian matrix of the dual graph for making partitioning decisions and tries to minimize the communication volume between the partitions. We implemented two numerical methods: Lanczos, and Inverse iteration using Conjugate Gradient method to compute the Fiedler vector. We present partitioning results using parRSB on Summit and Frontier supercomputers at Oak Ridge National Laboratory to illustrate the quality of the partitions produced by parRSB and the scalability of our implementation. We also present results for some of the optimizations we did to speed up the partitioning process.

cs.DC↗

arXiv2026

nomp: A Framework for Building Domain Specific Compilers

The low-level GPU programming models (CUDA, HIP, OpenCL, etc.) provide detailed control of the data flow and execution plan of a program in order to extract close-to-metal performance. However, these have a steep learning curve due to the intricacies of their syntax and semantics. This reduces programmer productivity. On the other hand, high-level models (OpenMP, OpenACC, etc.) that serve as abstractions over the low-level models are aimed at improving programmer productivity but achieving performance on-par with the low-level models is a challenge. There are inherent trade-offs between productivity, portability and performance in both approaches and there is no one-size-fits-all solution which achieves all three simultaneously. However, we believe there is room to improve programmer productivity without sacrificing performance and portability by reusing optimization patterns specific to a given domain. To this end, we propose nomp: a framework for building domain specific compilers. nomp consists of a pragma based programming model and a runtime capable of code transformation and generation based on user provided metadata.

cs.PL↗