High-performance modeling acoustic and elastic waves using the Parallel Dichotomy Algorithm

TL;DR

This paper introduces a high-performance parallel algorithm for modeling acoustic and elastic wave propagation in inhomogeneous media, utilizing the Dichotomy Algorithm and integral Laguerre transform for efficient and accurate simulations.

Contribution

It presents a novel parallel algorithm that combines the Dichotomy Algorithm with integral Laguerre transform for efficient wave modeling in complex media.

Findings

High accuracy in wave simulation demonstrated.

Algorithm scales efficiently up to 8192 processors.

Effective for real seismic problem applications.

Abstract

A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant elliptic operator and different right-hand sides via the integral Laguerre transform. It is proposed to solve difference equations by the conjugate gradient method for acoustic equations and by the GMRES$(k)$ method for modeling elastic waves. A preconditioning operator was the Laplace operator that is inverted using the variable separation method. The novelty of the proposed algorithm is using the Dichotomy Algorithm (Terekhov, 2010), which was designed for solving a series of tridiagonal systems of linear equations, in the context of the preconditioning operator inversion. Via considering analytical solutions, it is shown that modeling wave processes for long instants of time requires high-resolution meshes. The proposed parallel fine-mesh algorithm enabled to solve real application seismic problems in acceptable time and with high accuracy. By solving model problems, it is demonstrated that the considered parallel algorithm possesses high performance and efficiency over a wide range of the number of processors (from 2 to 8192).