Parallel-in-time high-order multiderivative IMEX solvers

TL;DR

This paper introduces a new class of parallelizable high-order time integration methods for additive ODEs, combining multiderivative quadrature and predictor-corrector schemes to enable efficient parallel computation in time.

Contribution

The work develops a novel parallel-in-time high-order multiderivative IMEX solver framework with thorough analysis and demonstrated scaling benefits.

Findings

Methods achieve high order accuracy.

Numerical results show effective parallel scaling.

Framework applicable to additive ODEs.

Abstract

In this work, we present a novel class of parallelizable high-order time integration schemes for the approximate solution of additive ODEs. The methods achieve high order through a combination of a suitable quadrature formula involving multiple derivatives of the ODE's right-hand side and a predictor-corrector ansatz. The latter approach is designed in such a way that parallelism in time is made possible. We present thorough analysis as well as numerical results that showcase scaling opportunities of methods from this class of solvers.