Communication-Efficient Algorithms for Solving Pressure Poisson Equation for Multiphase Flows using Parallel Computers

TL;DR

This paper introduces communication-efficient parallel algorithms for solving the Pressure Poisson equation in multiphase flows, reducing synchronization and communication overhead on distributed systems.

Contribution

It presents an asynchronous and an event-triggered communication algorithm that improve efficiency while maintaining accuracy in solving PDEs on parallel computers.

Findings

Reduced communication overhead in parallel PDE solving

Improved time and energy efficiency in multiphase flow simulations

Maintained solution accuracy with fewer messages

Abstract

Numerical solution of partial differential equations on parallel computers using domain decomposition usually requires synchronization and communication among the processors. These operations often have a significant overhead in terms of time and energy. In this paper, we propose communication-efficient parallel algorithms for solving partial differential equations that alleviate this overhead. First, we describe an asynchronous algorithm that removes the requirement of synchronization and checks for termination in a distributed fashion while maintaining the provision to restart iterations if necessary. Then, we build on the asynchronous algorithm to propose an event-triggered communication algorithm that communicates the boundary values to neighboring processors only at certain iterations, thereby reducing the number of messages while maintaining similar accuracy of solution. We demonstrate our algorithms on a successive over-relaxation solver for the Pressure Poisson equation arising from variable density incompressible multiphase flows in 3-D and show that our algorithms improve time and energy efficiency.