Distributed local spline simulator for wave propagation

TL;DR

The paper introduces a distributed local spline simulator (LOSS) for efficient and accurate wave propagation simulation in elastic media, suitable for high-performance computing environments.

Contribution

It proposes a novel LOSS method using patched cubic B-splines with boundary conditions for distributed wavefield simulation, improving efficiency and accuracy.

Findings

Achieves accurate spatial derivatives with linear complexity.

Demonstrates high convergence and accuracy in 2D and 3D wave simulations.

Shows good parallel scalability in numerical experiments.

Abstract

Numerical simulation of wave propagation in elastic media faces the challenges arising from increasing demand of high resolution in modern 3-D imaging applications, which requires a balance between efficiency and accuracy in addition to being friendly to the distributed high-performance computing environment. In this paper, we propose a distributed local spline simulator (LOSS) for solving the wave equation. LOSS uses patched cubic B-splines to represent the wavefields and attains an accurate evaluation of spatial derivatives with linear complexity. In order to link the adjacent patches, a perfectly matched boundary condition is introduced to give a closure of local spline coefficients. Owing to the rapid decay property of the local wavelets in dual space, it can recover the global spline as accurately as possible only at the cost of local communications among adjacent neighbors. Several typical numerical examples, including 2-D acoustic wave equation and P- and S- wave propagation in 3-D homogenous or heterogenous media, are provided to validate its convergence, accuracy and parallel scalability.