Algorithm 965

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 library 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.

Time‐parallel integration and phase averaging for the nonlinear shallow‐water equations on the sphere

“…Peddle et al (2019) proved convergence of the iterative Parareal procedure for highly oscillatory PDEs with quadratic nonlinearity, making use of the optimal averaging window T at finite Rossby number. Bauer et al (2022) created a hierarchy of higher-order averaged models that increase accuracy through increasing the number of variables; this type of hierarchy is ideal for predictor-corrector approaches such as revisionist integral deferred correction methods (Ong et al, 2016) and the parallel full approximation scheme in space and time algorithm (Minion, 2011) that compute more accurate correction steps in parallel as new predictor steps are being taken. These are motivations for the work in this article, but here we focus on the impact of the averaging on the rotating shallow-water solution.…”

Inexact Spectral Deferred Corrections

“…While this typically results in small-scale parallelization in the time-domain, parallel efficiency and applicability of these methods are often more favorable. Most notably, the "revisionist integral deferred correction method" (RIDC) by Christlieb et al [Christlieb et al 2010;Ong et al 2016] makes use of integral deferred corrections in order to compute multiple iterations in a pipelined way. Also within the SDC context, parallelization across the method is possible: In [Speck 2018c], two strategies for computing updates on multiple collocation nodes simultaneously is presented.…”

“…XBraid -a C/C++ time-parallel multigrid solver (or, actually, more like a framework) generalizing the Parareal idea to multiple levels [LLNL 2018], RIDC -a C++-implementation of the revisionist integral deferred correction method [Ong et al 2016], PFASST -different implementations of the parallel full approximation scheme in space and time [LLBL 2018].…”

A Pipeline-Based ODE Solving Framework

“…In the second experiment, we use 32 groups of two equations with 1000, 10000 and 100000 sampling point, comparing explicit Fourth-order Euler and Fourth-order Runger-Kutta on the CPU side, Julia's RK4 and CPU version RIDC in [28] with explicit Euler algorithm on the GPU side, the equations are as eq.10 shows, then set the equations number to 10 and conduct the same experiment. The results are shown in TABLE 1 and 2…”