CARP-CG: A robust and efficient parallel solver for linear systems, applied to strongly convection dominated PDEs

Gordon, Dan; Gordon, Rachel

doi:10.1016/j.parco.2010.05.004

Cited by 37 publications

(42 citation statements)

References 23 publications

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“…CARP-CG is a CG acceleration of CARP (component-averaged row projections) [11], which is a block-parallel extension of KACZ -the Kaczmarz algorithm [17]. KACZ is inherently sequential: starting from an arbitrary initial point, it sweeps through the equations by successively projecting the current iterate towards the hyperplane defined by the next equation.…”

Section: Solvermentioning

confidence: 99%

Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number

Turkel

Gordon

et al. 2013

Journal of Computational Physics

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132

102

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Section: Solvermentioning

confidence: 99%

Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number

Turkel

Gordon

et al. 2013

Journal of Computational Physics

Self Cite

132

102

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“…This algorithm is mainly suitable for parallel architectures. Further advancement in increasing the rate of convergence was achieved by the Component Average Row Projection (CARP) method introduced by Gordon and Gordon (2005). From all the above methods, CARP is more generalized and places no restriction on the system matrix or the selection of blocks.…”

Section: Distributed Tomography Algorithmsmentioning

confidence: 99%

“…This algorithm also contains landlords; however, information in these landlords differs from those of DMET as we are performing row partitioning. Few iterations of stable KACZ for inconsistent systems are run on each landlord and the intermediate results are later combined with others using a technique called component average (Gordon & Gordon, 2005). The information exchanged at each iteration is less compared to what is required to transfer the raw data, and for this reason we use a treebased aggregation scheme similar to the one used in the OASIS project.…”

Section: Component-average Distributed Multiresolution Evolving Tomogmentioning

confidence: 99%

Tomographic imaging in sensor networks

Kamath

Song

2015

Industrial Tomography

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“…The latter does not make these approaches very attractive for inversion since the medium parameters will change from one iteration to the next, possibly requiring the tuning parameters to be changed as well. Instead, we use CARP-CG [14,15], a generic, iterative solution technique for sparse linear systems based on the CGMN method [5]. Convergence of this method is guaranteed, making it an attractive solver for inversion purposes.…”

Section: Iterative Solvermentioning

confidence: 99%

“…As such, its implementation resembles an additive Schwarz approach, however, CARP-CG is guaranteed to converge. For details we refer the reader to [14,15]. The use of CARP-CG to solve the Helmholtz equation specifically is described by [16,17].…”

Section: Cgmnmentioning

confidence: 99%

3D Frequency-Domain Seismic Inversion with Controlled Sloppiness

Leeuwen¹,

Herrmann²

2014

SIAM J. Sci. Comput.

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Abstract. Seismic waveform inversion aims at obtaining detailed estimates of subsurface medium parameters, such as the spatial distribution of soundspeed, from multiexperiment seismic data. A formulation of this inverse problem in the frequency domain leads to an optimization problem constrained by a Helmholtz equation with many right-hand sides. Application of this technique to industry-scale problems faces several challenges: First, we need to solve the Helmholtz equation for high wave numbers over large computational domains. Second, the data consist of many independent experiments, leading to a large number of PDE solves. This results in high computational complexity both in terms of memory and CPU time as well as input/output costs. Finally, the inverse problem is highly nonlinear and a lot of art goes into preprocessing and regularization. Ideally, an inversion needs to be run several times with different initial guesses and/or tuning parameters. In this paper, we discuss the requirements of the various components (PDE solver, optimization method, . . . ) when applied to large-scale three-dimensional seismic waveform inversion and combine several existing approaches into a flexible inversion scheme for seismic waveform inversion. The scheme is based on the idea that in the early stages of the inversion we do not need all the data or very accurate PDE solves. We base our method on an existing preconditioned Krylov solver (CARP-CG) and use ideas from stochastic optimization to formulate a gradient-based (quasi-Newton) optimization algorithm that works with small subsets of the right-hand sides and uses inexact PDE solves for the gradient calculations. We propose novel heuristics to adaptively control both the accuracy and the number of right-hand sides. We illustrate the algorithms on synthetic benchmark models for which significant computational gains can be made without being sensitive to noise and without losing the accuracy of the inverted model. 1. Introduction. Detailed estimates of subsurface properties such as soundspeed and density can be obtained from seismic data by solving a PDE-constrained optimization problem [44]-also known as full-waveform inversion (FWI) in the seismic community-that involves multiple source experiments. The data in this setting consist of a collection of time series for many source-receiver pairs and are the result of either passive or active source experiments. The PDE is a wave equation with as many right-hand sides as there are sources. Applications of this technique include oil and gas exploration and global seismology. A common characteristic of these applications is the need to propagate the waves over large distances (i.e., several hundred wavelenghts) through strongly inhomogeneous media for a large number of sources.

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CARP-CG: A robust and efficient parallel solver for linear systems, applied to strongly convection dominated PDEs

Cited by 37 publications

References 23 publications

Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number

Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number

Tomographic imaging in sensor networks

3D Frequency-Domain Seismic Inversion with Controlled Sloppiness

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