Preconditioning

AJ Wathen - Acta Numerica, 2015 - cambridge.org
The computational solution of problems can be restricted by the availability of solution
methods for linear (ized) systems of equations. In conjunction with iterative methods …

A review of the spectral, pseudo‐spectral, finite‐difference and finite‐element modelling techniques for geophysical imaging

J Virieux, H Calandra, RÉ Plessix - Geophysical Prospecting, 2011 - earthdoc.org
Modelling methods are nowadays at the heart of any geophysical interpretation approach.
These are heavily relied upon by imaging techniques in elastodynamics and …

Fast full-wavefield seismic inversion using encoded sources

JR Krebs, JE Anderson, D Hinkley, R Neelamani… - Geophysics, 2009 - library.seg.org
Full-wavefield seismic inversion (FWI) estimates a subsurface elastic model by iteratively
minimizing the difference between observed and simulated data. This process is extremely …

A class of iterative solvers for the Helmholtz equation: Factorizations, swee** preconditioners, source transfer, single layer potentials, polarized traces, and …

MJ Gander, H Zhang - Siam Review, 2019 - SIAM
Solving time-harmonic wave propagation problems by iterative methods is a difficult task,
and over the last two decades an important research effort has gone into develo** …

Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

SN Chandler-Wilde, IG Graham, S Langdon… - Acta …, 2012 - cambridge.org
In this article we describe recent progress on the design, analysis and implementation of
hybrid numerical-asymptotic boundary integral methods for boundary value problems for the …

Swee** preconditioner for the Helmholtz equation: moving perfectly matched layers

B Engquist, L Ying - Multiscale Modeling & Simulation, 2011 - SIAM
This paper introduces a new swee** preconditioner for the iterative solution of the
variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow …

A parametrization study for surface seismic full waveform inversion in an acoustic vertical transversely isotropic medium

RE Plessix, Q Cao - Geophysical Journal International, 2011 - academic.oup.com
Full waveform inversion (FWI) of surface seismic data requires low-frequency and long-offset
data, namely diving waves or post-critical reflections, to update the long wavelength features …

Swee** preconditioner for the Helmholtz equation: hierarchical matrix representation

B Engquist, L Ying - Communications on pure and applied …, 2011 - Wiley Online Library
The paper introduces the swee** preconditioner, which is highly efficient for iterative
solutions of the variable‐coefficient Helmholtz equation including very‐high‐frequency …

Preconditioners for Krylov subspace methods: An overview

JW Pearson, J Pestana - GAMM‐Mitteilungen, 2020 - Wiley Online Library
When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

Three-dimensional frequency-domain full-waveform inversion with an iterative solver

RÉ Plessix - Geophysics, 2009 - library.seg.org
With the acquisition of wide-aperture seismic data sets, full-waveform inversion is an
attractive method for deriving velocity models. Three-dimensional implementations require …