Parallel Semi-Implicit Time Integrators

TL;DR

This paper introduces parallel semi-implicit RIDC methods for solving time-dependent PDEs, leveraging multiple GPUs to achieve high-order accuracy efficiently in wall clock time.

Contribution

It develops a semi-implicit RIDC framework that efficiently utilizes multiple GPUs for high-order solutions of PDEs, demonstrating significant computational speedups.

Findings

Fourth order solutions achieved with four GPUs and CPUs

Parallel implementation matches single GPU/CPU performance for lower order

Effective use of CUBLAS libraries for matrix operations

Abstract

In this paper, we further develop a family of parallel time integrators known as Revisionist Integral Deferred Correction methods (RIDC) to allow for the semi-implicit solution of time dependent PDEs. Additionally, we show that our semi-implicit RIDC algorithm can harness the computational potential of multiple general purpose graphical processing units (GPUs) in a single node by utilizing existing CUBLAS libraries for matrix linear algebra routines in our implementation. In the numerical experiments, we show that our implementation computes a fourth order solution using four GPUs and four CPUs in approximately the same wall clock time as a first order solution computed using a single GPU and a single CPU.