Asynchronous Communications Library for the Parallel-in-Time Solution of Black-Scholes Equation

Abstract

The advent of asynchronous iterative scheme gives high efficiency to numerical computations. However, it is generally difficult to handle the problems of resource management and convergence detection. This paper uses JACK2, an asynchronous communication kernel library for iterative algorithms, to implement both classical and asynchronous parareal algorithms, especially the latter. We illustrate the measures whereby one can tackle the problems above elegantly for the time-dependent case. Finally, experiments are presented to prove the availability and efficiency of such application.

Recent Developments in Iterative Methods for Reducing Synchronization

“…For the time domain decomposition methods, the derivation of asynchronous waveform relaxation can be found in [27]. Magoulès et al [43,40] proposed the asynchronous variant of Parareal algorithm (see also [57,56]). Another asynchronous time-parallel method based on Laplace transform can be found in [46].…”

Using Asynchronous Simulation Approach for Interactive Simulation

“…Recent developments have extended asynchronous iterations to parallel in time domain decomposition [18] [19]to parallel in space domain decomposition method like sub-structuring method [22]or like optimized Schwarz method [21]In order to monitor asynchronous iterations, stopping criteria is a real bottleneck. One example shows how we realize the domain decomposition in methods applied to European option pricing [26] and for a time-dependent case [25].…”