Algorithm xxx: RIDC Methods -- A Family of Parallel Time-Integrators

TL;DR

RIDC methods are a family of parallel-in-time algorithms that efficiently produce high-order solutions for initial value problems, leveraging existing lower-order integrators and a C++ framework for easy implementation.

Contribution

This paper introduces RIDC methods as a novel parallel-in-time approach and provides a flexible C++ framework for their implementation.

Findings

Achieves high-order accuracy with parallel efficiency.

Provides a versatile C++ framework for various integrators.

Includes multiple example templates for user adaptation.

Abstract

Revisionist integral deferred correction (RIDC) methods are a family of parallel--in--time methods to solve systems of initial values problems. The approach is able to bootstrap lower order time integrators to provide high order approximations in approximately the same wall clock time, hence providing a multiplicative increase in the number of compute cores utilized. Here we provide a C++ framework which automatically produces a parallel--in--time solution of a system of initial value problems given user supplied code for the right hand side of the system and a sequential code for a first-order time step. The user supplied time step routine may be explicit or implicit and may make use of any auxiliary libraries which take care of the solution of any nonlinear algebraic systems which may arise or the numerical linear algebra required. The code contains six examples of increasing complexity which also serve as templates to solve user defined problems.