Benjamin W. Ong

Parallel High-Order Integrators

In this work we discuss a class of defect correction methods which is easily adapted to create parallel time integrators for multicore architectures and is ideally suited for developing methods which can be order adaptive in time. The method is based on integral deferred correction (IDC), which was itself motivated by spectral deferred correction by Dutt, Greengard, and Rokhlin [BIT, 40 (2000), pp. 241-266]. The method presented here is a revised formulation of explicit IDC, dubbed revisionist IDC (RIDC), which can achieve

Integral deferred correction methods constructed with high order Runge-Kutta integrators

p

A Parallel Space-Time Algorithm

th-order accuracy in “wall-clock time” comparable to a single forward Euler simulation on problems where the time to evaluate the right-hand side of a system of differential equations is greater than latency costs of interprocessor communication, such as in the case of the

Implicit Parallel Time Integrators

N

Method of lines transpose: An implicit solution to the wave equation

-body problem. The key idea is to rewrite the defect correction framework so that, after initial start-up costs, each correction loop can be lagged behind the previous correction loop in a manner that facilitates running the predictor and

A Distributed and Incremental SVD Algorithm for Agglomerative Data Analysis on Large Networks

M=p-1

MPI–OpenMP Algorithms for the Parallel Space–Time Solution of Time Dependent PDEs

correctors in parallel on an interval which has

An Asymptotic Preserving Maxwell Solver Resulting in the Darwin Limit of Electrodynamics

K

REVISIONIST INTEGRAL DEFERRED CORRECTION WITH ADAPTIVE STEP-SIZE CONTROL

steps, where

Pipeline Schwarz Waveform Relaxation

K\gg p