Wavelet-Based Adaptive Solvers on Multi-core Architectures for the Simulation of Complex Systems

Abstract

We build wavelet-based adaptive numerical methods for the simulation of advection dominated flows that develop multiple spatial scales, with an emphasis on fluid mechanics problems. Wavelet based adaptivity is inherently sequential and in this work we demonstrate that these numerical methods can be implemented in software that is capable of harnessing the capabilities of multi-core architectures while maintaining their computational efficiency. Recent designs in frameworks for multi-core software development allow us to rethink parallelism as task-based, where parallel tasks are specified and automatically mapped into physical threads. This way of exposing parallelism enables the parallelization of algorithms that were considered inherently sequential, such as wavelet-based adaptive simulations. In this paper we present a framework that combines wavelet-based adaptivity with the task-based parallelism. We demonstrate good scaling performance obtained by simulating diverse physical systems on different multi-core and SMP architectures using up to 16 cores.