Sweeping preconditioners for elastic wave propagation with spectral element methods

Tsuji, Paul H.; Poulson, Jack; Engquist, Björn; Ying, Lexing

doi:10.1051/m2an/2013114

Cited by 20 publications

(10 citation statements)

References 23 publications

(31 reference statements)

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“…The first linear complexity claim was perhaps made in the work of Engquist and Ying (2011), followed by Stolk (2013). Other authors have since then proposed related methods with similar properties, including Chen and Xiang (2013) and Vion and Geuzaine (2014); however, they are often difficult to parallelize, and they usually rely on distributed linear algebra such as Poulson et al (2013) and Tsuji et al (2014), or highly tuned multigrid methods such as Stolk et al (2013) and Calandra et al (2013). As we put the final touches to this note, Liu and Ying (2015) proposed a recursive sweeping algorithm closely related to the one presented in this note.…”

Section: Introductionmentioning

confidence: 99%

A short note on the nested-sweep polarized traces method for the 2D Helmholtz equation

Zepeda-Núñez

Demanet

2015

SEG Technical Program Expanded Abstracts 2015

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SUMMARYWe present a variant of the solver in Zepeda-Núñez and Demanet (2014), for the 2D high-frequency Helmholtz equation in heterogeneous acoustic media. By changing the domain decomposition from a layered to a grid-like partition, this variant yields improved asymptotic online and offline runtimes and a lower memory footprint. The solver has online parallel complexity that scales sublinearly as O N P , where N is the number of volume unknowns, and P is the number of processors, provided that P = O (N 1/5 ). The variant in Zepeda-Núñez and Demanet (2014) only afforded P = O (N 1/8 ). Algorithmic scalability is a prime requirement for wave simulation in regimes of interest for geophysical imaging.

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Section: Introductionmentioning

confidence: 99%

A short note on the nested-sweep polarized traces method for the 2D Helmholtz equation

Zepeda-Núñez

Demanet

2015

SEG Technical Program Expanded Abstracts 2015

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“…The application of such ideas to the Helmholtz problem can be traced back, to great extent, to the AILU preconditioner of Gander and Nataf [43], in which a layered domain decomposition was used; and to Plessix and Mulder [76] in which a similar idea is used using separation of variables. However, it was Engquist and Ying who showed in [33,32] that such ideas could yield fast methods to solve the high-frequency Helmholtz equation, by introducing the sweeping preconditioner, which was then extended by Tsuji and collaborators to different discretizations and physics [89,90,91]. Since then, many other papers have proposed methods with similar claims.…”

Section: Related Workmentioning

confidence: 99%

Nested Domain Decomposition with Polarized Traces for the 2D Helmholtz Equation

Zepeda-Núñez¹,

Demanet²

2018

SIAM J. Sci. Comput.

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We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous, constant density, acoustic media, with online parallel complexity that scales empirically as O( N P ), where N is the number of volume unknowns, and P is the number of processors, as long as P = O(N 1/5 ). This sublinear scaling is achieved by domain decomposition, not distributed linear algebra, and improves on the P = O(N 1/8 ) scaling reported earlier in [99]. The solver relies on a two-level nested domain decomposition: a layered partition on the outer level, and a further decomposition of each layer in cells at the inner level. The Helmholtz equation is reduced to a surface integral equation (SIE) posed at the interfaces between layers, efficiently solved via a nested version of the polarized traces preconditioner [99]. The favorable complexity is achieved via an efficient application of the integral operators involved in the SIE.

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“…[3,46]. When domain decomposition is considered, the sweeping preconditioner [42] is an attractive alternative.…”

Section: Introductionmentioning

confidence: 99%

An MSSS-preconditioned matrix equation approach for the time-harmonic elastic wave equation at multiple frequencies

et al. 2017

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In this work, we present a new numerical framework for the efficient solution of the time-harmonic elastic wave equation at multiple frequencies. We show that multiple frequencies (and multiple right-hand sides) can be incorporated when the discretized problem is written as a matrix equation. This matrix equation can be solved efficiently using the preconditioned IDR(s) method. We present an efficient and robust way to apply a single preconditioner using MSSS matrix computations. For 3D problems, we present a memory-efficient implementation that exploits the solution of a sequence of 2D problems. Realistic examples in two and three spatial dimensions demonstrate the performance of the new algorithm.

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Sweeping preconditioners for elastic wave propagation with spectral element methods

Cited by 20 publications

References 23 publications

A short note on the nested-sweep polarized traces method for the 2D Helmholtz equation

A short note on the nested-sweep polarized traces method for the 2D Helmholtz equation

Nested Domain Decomposition with Polarized Traces for the 2D Helmholtz Equation

An MSSS-preconditioned matrix equation approach for the time-harmonic elastic wave equation at multiple frequencies

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