arXiv subjects

Srinath Kailasa

Publications and source records attributed to Srinath Kailasa.

3 recordsLinked to original sources

arXiv2026

A Simple Communication Scheme for Distributed Fast Multipole Methods

We present a simple hierarchical communication scheme for distributed Fast Multipole Methods (FMMs) based on MPI neighborhood collectives and uniform trees. The method targets the common case of extending an existing high-performance shared-memory uniform-tree FMM implementation to distributed memory with minimal redesign while preserving any shared memory optimizations. Benchmarks on the ARCHER2 supercomputer demonstrate that our method can scale to very large problem sizes, we demonstrate weak-scaling up to 3.2e10 uniformly distributed points on 512 nodes of the machine in our largest runs. Our simplifications based on uniform trees result in worse asymptotic scaling for non-uniform points, however we still obtain practically useful runtimes due to the ability to retain our shared memory optimizations.

cs.DC↗

arXiv2024

M2L Translation Operators for Kernel Independent Fast Multipole Methods on Modern Architectures

Hardware trends favor algorithm designs that maximize data reuse per FLOP. We develop and benchmark high-performance Multipole-to-Local (M2L) translation operators for the kernel-independent Fast Multipole Method (kiFMM), a widely adopted FMM variant that supports a broad class of kernels and has been favored by recent implementations for its simple specification. Naively implemented, M2L is bandwidth-limited and therefore a key bottleneck in the FMM. State-of-the-art FFT-based M2L implementations, though elegant and with a fast setup time, suffer from low operational intensity and require architecture-specific optimizations. We demonstrate that a BLAS-based M2L, combined with randomized low-rank compression, achieves competitive performance with greater portability and a simpler implementation leveraging existing BLAS infrastructure, at the cost of higher setup times-especially for high-accuracy settings in double precision. Our Rust-based implementation enables seamless switching between strategies for fair benchmarking. Results on CPUs show that FFT-based M2L is favorable in low-accuracy settings or dynamic particle simulations, while BLAS-based M2L is favored for high-accuracy settings for static particle distributions, where its higher setup costs are amortized in many practical applications of the FMM.

cs.CE↗

arXiv2023

PyExaFMM: an exercise in designing high-performance software with Python and Numba

Numba is a game-changing compiler for high-performance computing with Python. It produces machine code that runs outside of the single-threaded Python interpreter and that fully utilizes the resources of modern CPUs. This means support for parallel multithreading and auto vectorization if available, as with compiled languages such as C++ or Fortran. In this article we document our experience developing PyExaFMM, a multithreaded Numba implementation of the Fast Multipole Method, an algorithm with a non-linear data structure and a large amount of data organization. We find that designing performant Numba code for complex algorithms can be as challenging as writing in a compiled language.

cs.SE↗