{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:32:22Z","timestamp":1772296342465,"version":"3.50.1"},"reference-count":20,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2012,8,1]],"date-time":"2012-08-01T00:00:00Z","timestamp":1343779200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["10901157\/A0117"],"award-info":[{"award-number":["10901157\/A0117"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["DMS-1016092"],"award-info":[{"award-number":["DMS-1016092"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002855","name":"Ministry of Science and Technology of the People's Republic of China","doi-asserted-by":"publisher","award":["973 Program 2012CB025904863 Program 2012 AA01A309"],"award-info":[{"award-number":["973 Program 2012CB025904863 Program 2012 AA01A309"]}],"id":[{"id":"10.13039\/501100002855","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2012,8]]},"abstract":"<jats:p>Transmission eigenvalue problem has important applications in inverse scattering. Since the problem is non-self-adjoint, the computation of transmission eigenvalues needs special treatment. Based on a fourth-order reformulation of the transmission eigenvalue problem, a mixed finite element method is applied. The method has two major advantages: 1) the formulation leads to a generalized eigenvalue problem naturally without the need to invert a related linear system, and 2) the nonphysical zero transmission eigenvalue, which has an infinitely dimensional eigenspace, is eliminated. To solve the resulting non-Hermitian eigenvalue problem, an iterative algorithm using restarted Arnoldi method is proposed. To make the computation efficient, the search interval is decided using a Faber-Krahn type inequality for transmission eignevalues and the interval is updated at each iteration. The algorithm is implemented using Matlab. The code can be easily used in the qualitative methods in inverse scattering and modified to compute transmission eigenvalues for other models such as elasticity problem.<\/jats:p>","DOI":"10.1145\/2331130.2331137","type":"journal-article","created":{"date-parts":[[2012,9,4]],"date-time":"2012-09-04T12:50:47Z","timestamp":1346763047000},"page":"1-8","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":49,"title":["Algorithm 922"],"prefix":"10.1145","volume":"38","author":[{"given":"Xia","family":"Ji","sequence":"first","affiliation":[{"name":"Chinese Academy of Sciences"}]},{"given":"Jiguang","family":"Sun","sequence":"additional","affiliation":[{"name":"Delaware State University"}]},{"given":"Tiara","family":"Turner","sequence":"additional","affiliation":[{"name":"Delaware State University"}]}],"member":"320","published-online":{"date-parts":[[2012,8]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1017\/S000192400008489X"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2010.4.39"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/00036810802713966"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/26\/7\/074004"},{"key":"e_1_2_2_5_1","doi-asserted-by":"crossref","unstructured":"Ciarlet P. G. 2002. The Finite Element Method for Elliptic Problems. Classics in Applied Mathematics 40 SIAM Philadelphia PA. Ciarlet P. G. 2002. The Finite Element Method for Elliptic Problems . Classics in Applied Mathematics 40 SIAM Philadelphia PA.","DOI":"10.1137\/1.9780898719208"},{"key":"e_1_2_2_6_1","volume-title":"Proceedings of the Symposium on Mathematical Aspects of Finite Elements in Partial Differential Equations. C. de Boor Ed.","author":"Ciarlet P. G."},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2007.1.13"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/26\/4\/045011"},{"key":"e_1_2_2_9_1","unstructured":"Golub G. H. and Loan C. F. V. 1989. Matrix Computations 2nd Ed. Johns Hopkins University Press Baltimore MD. Golub G. H. and Loan C. F. V. 1989. Matrix Computations 2nd Ed. Johns Hopkins University Press Baltimore MD."},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.4310\/MRL.2011.v18.n2.a7"},{"key":"e_1_2_2_11_1","doi-asserted-by":"crossref","unstructured":"Hitrik M. Krupchyk K. Ola P. and P\u00e4iv\u00e4rinta L. 2011b. Transmission eigenvalues for elliptic operators. arXiv:1007.0503 physics.math-ph. Hitrik M. Krupchyk K. Ola P. and P\u00e4iv\u00e4rinta L. 2011b. Transmission eigenvalues for elliptic operators. arXiv:1007.0503 physics.math-ph.","DOI":"10.1137\/110827867"},{"key":"e_1_2_2_12_1","doi-asserted-by":"crossref","unstructured":"Hitrik M. Krupchyk K. Ola P. and P\u00e4iv\u00e4rinta L. 2011c. Transmission eigenvalues for operators with constant coefficients. arXiv:1004.5105 physics.math-ph. Hitrik M. Krupchyk K. Ola P. and P\u00e4iv\u00e4rinta L. 2011c. Transmission eigenvalues for operators with constant coefficients. arXiv:1004.5105 physics.math-ph.","DOI":"10.1137\/110827867"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2011.05.011"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2009.3.155"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/0724048"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1137\/070697525"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(80)90169-X"},{"key":"e_1_2_2_18_1","first-page":"1","article-title":"A new family of high regularity elements","volume":"28","author":"Sun J.","year":"2010","journal-title":"Num. Meth. Partial Diff. Eq."},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/27\/1\/015009"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1137\/100785478"}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2331130.2331137","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2331130.2331137","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T08:49:12Z","timestamp":1750236552000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2331130.2331137"}},"subtitle":["A Mixed Finite Element Method for Helmholtz Transmission Eigenvalues"],"short-title":[],"issued":{"date-parts":[[2012,8]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["10.1145\/2331130.2331137"],"URL":"https:\/\/doi.org\/10.1145\/2331130.2331137","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"value":"0098-3500","type":"print"},{"value":"1557-7295","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,8]]},"assertion":[{"value":"2011-01-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-11-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-08-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}