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Weighted integral solvers for elastic scattering by open arcs in two dimensions

Bruno, Oscar P. and Xu, Liwei and Yin, Tao (2019) Weighted integral solvers for elastic scattering by open arcs in two dimensions. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20190906-093843706

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Abstract

We present a novel approach for the numerical solution of problems of elastic scattering by open arcs in two dimensions. Our methodology relies on the composition of weighted versions of the classical operators associated with Dirichlet and Neumann boundary conditions in conjunction with a certain "open-arc elastic Calderón relation" whose validity is demonstrated in this paper on the basis of numerical experiments, but whose rigorous mathematical proof is left for future work. Using this Calderón relation in conjunction with spectrally accurate quadrature rules and the Krylov-subspace linear algebra solver GMRES, the proposed overall open-arc elastic solver produces results of high accuracy in small number of iterations---for low and high frequencies alike. A variety of numerical examples in this paper demonstrate the accuracy and efficiency of the proposed methodology.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1902.08687arXivDiscussion Paper
ORCID:
AuthorORCID
Bruno, Oscar P.0000-0001-8369-3014
Additional Information:OB gratefully acknowledge support by NSF, AFOSR and DARPA through contracts DMS-1411876 and FA9550-15-1-0043 and HR00111720035, and the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. LX is partially supported by a Key Project of the Major Research Plan of NSFC (No. 91630205), and a NSFC Grant (No. 11771068).
Funders:
Funding AgencyGrant Number
NSFDMS-1411876
Air Force Office of Scientific Research (AFOSR)FA9550-15-1-0043
Defense Advanced Research Projects Agency (DARPA)HR00111720035
National Security Science and Engineering Faculty FellowshipN00014-16-1-2808
Vannever Bush Faculty FellowshipUNSPECIFIED
National Natural Science Foundation of China91630205
National Natural Science Foundation of China11771068
Record Number:CaltechAUTHORS:20190906-093843706
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190906-093843706
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98477
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:06 Sep 2019 16:53
Last Modified:03 Oct 2019 21:41

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