{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:41:58Z","timestamp":1787330518332,"version":"build-2736575974"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/100008917","name":"Colorado School of Mines","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008917","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>In this article, we develop a novel computer model for the constant coefficient Helmholtz equation based on a sign-definite formulation [A. Moiola and E. A. Spence, SIAM Rev., 56 (2014), pp. 274--312], finite element methods (FEMs), and iterative solvers. This includes (i) a variant parameter version of the formulation for improved performance of the GMRES iterates compared to the standard formulation; (ii) development of a new frequency-robust sign-definite preconditioned high-order FEM model for the simulation of acoustic wave propagation in bounded homogeneous media; and (iii) efficient use of domain decomposition methods in conjunction with our preconditioned model. For simulations, we use a nonconvex star-shaped geometry comprising curved and nonsmooth boundaries and a non-star-shaped nonsmooth geometry and demonstrate our approach for medium- to high-frequency incident waves.<\/jats:p>","DOI":"10.1137\/16m1072061","type":"journal-article","created":{"date-parts":[[2017,10,26]],"date-time":"2017-10-26T16:24:40Z","timestamp":1509035080000},"page":"S563-S586","source":"Crossref","is-referenced-by-count":9,"title":["A Sign-Definite Preconditioned High-Order FEM, Part I: Formulation and Simulation for Bounded\n                    <i>Homogeneous<\/i>\n                    Media Wave Propagation"],"prefix":"10.1137","volume":"39","author":[{"given":"M.","family":"Ganesh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C.","family":"Morgenstern","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,10,26]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1993-1146834-4"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1002\/9780470749081"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20358"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/100804644"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2004.01.009"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-015-0700-2"},{"key":"atypb7","volume-title":"Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods, preprint, https:\/\/arxiv.org\/abs\/1610.02270","author":"Gander M.","year":"2016"},{"key":"atypb8","unstructured":"M. Ganesh and C. Morgenstern,\n                      High-Order FEM Domain Decomposition Sign-Indefinite Models for High-Frequency Wave Propagation in Heterogeneous Media\n                      , preprint,http:\/\/inside.mines.edu\/~mganesh\/final_ddhelm_manuscript.pdf, 2016."},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2049"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3190"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/120887667"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717532"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0207(20010220)50:5<1077::AID-NME65>3.0.CO;2-P"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/120901301"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1080\/02726340903485414"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160210206"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2015.11.040"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1072061","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:10:28Z","timestamp":1787328628000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1072061"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":17,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/16M1072061"],"URL":"https:\/\/doi.org\/10.1137\/16m1072061","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}