arXiv subjects

Serhii Yaskovets

Publications and source records attributed to Serhii Yaskovets.

2 recordsLinked to original sources

arXiv2025

Integrating Odeint Time Stepping into OpenFPM for Distributed and GPU Accelerated Numerical Solvers

We present a software implementation integrating the time-integration library Odeint from Boost with the OpenFPM framework for scalable scientific computing. This enables compact and scalable codes for multi-stage, multi-step, and adaptive explicit time integration on distributed-memory parallel computers and on Graphics Processing Units (GPUs). The present implementation is based on extending OpenFPM's metaprogramming system to Odeint data types. This makes the time-integration methods from Odeint available in a concise template-expression language for numerical simulations distributed and parallelized using OpenFPM. We benchmark the present software for exponential and sigmoidal dynamics and present application examples to the 3D Gray-Scott reaction-diffusion problem and the "dam break" problem from fluid mechanics. We find a strong-scaling efficiency of 80% on up to 512 CPU cores and a five-fold speedup on a single GPU.

cs.MS↗

arXiv2025

An Overview of Meshfree Collocation Methods

We provide a comprehensive overview of meshfree collocation methods for numerically approximating differential operators on continuously labeled unstructured point clouds. Meshfree collocation methods do not require a computational grid or mesh. Instead, they approximate smooth functions and their derivatives at potentially irregularly distributed collocation points, often called particles, to a desired order of consistency. We review several meshfree collocation methods from the literature, trace the historical development of key concepts, and propose a classification of methods according to their principle of derivation. Although some of the methods reviewed are similar or identical, there are subtle yet important differences between many, which we highlight and discuss. We present a unifying formulation of meshfree collocation methods that renders these differences apparent and show how each method can be derived from this formulation. Finally, we propose a generalized derivation for meshfree collocation methods going forward.

math.NA↗