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A multiscale domain decomposition algorithm for boundary value problems for eikonal equations
Univ Texas Austin, Dept Math, Austin, TX 78712 USA..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. Univ Texas Austin, Dept Math, Austin, TX 78712 USA.;Univ Texas Austin, Oden Inst Computat Engn & Sci, Austin, TX 78712 USA.
2019 (English)In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 17, no 2, p. 620-649Article in journal (Refereed) Published
Abstract [en]

In this paper, we present a new multiscale domain decomposition algorithm for computing solutions of static Eikonal equations. In our new method, the decomposition of the domain does not depend on the slowness function in the Eikonal equation or the boundary conditions. The novelty of our new method is a coupling of coarse grid and fine grid solvers to propagate information along the characteristics of the equation efficiently. The method involves an iterative parareal-like update scheme in order to stabilize the method and speed up convergence. One can view the new method as a general framework where an effective coarse grid solver is computed "on the fly" from coarse and fine grid solutions that are computed in previous iterations. We study the optimal weights used to define the effective coarse grid solver and the stable update scheme via a model problem. To demonstrate the framework, we develop a specific scheme using Cartesian grids and the fast sweeping method for solving Eikonal equations. Numerical examples are given to show the method's effectiveness on Eikonal equations involving a variety of multiscale slowness functions.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics Publications , 2019. Vol. 17, no 2, p. 620-649
Keywords [en]
Eikonal equation, parallel algorithms, domain decomposition, multiscale algorithms
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-255345DOI: 10.1137/18M1186927ISI: 000473063800002Scopus ID: 2-s2.0-85068460439OAI: oai:DiVA.org:kth-255345DiVA, id: diva2:1339870
Note

QC 20190731

Available from: 2019-07-31 Created: 2019-07-31 Last updated: 2019-07-31Bibliographically approved

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