{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T11:11:10Z","timestamp":1680261070546},"reference-count":38,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1416742"],"award-info":[{"award-number":["DMS-1416742"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671340","91430213"],"award-info":[{"award-number":["11671340","91430213"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we first give a quick review of the current status of the invisibility cloak with metamaterials. Then we focus on the carpet cloak model and establish an elegant stability different from our previous work.\nA similar discrete stability is also proved for a new FETD scheme.\nThen we prove the optimal convergence for this new scheme.\nFinally, we implement a new discontinuous Galerkin method and demonstrate its effectiveness in simulating the carpet cloaking phenomena.<\/jats:p>","DOI":"10.1515\/cmam-2018-0001","type":"journal-article","created":{"date-parts":[[2018,2,27]],"date-time":"2018-02-27T10:45:34Z","timestamp":1519728334000},"page":"359-378","source":"Crossref","is-referenced-by-count":2,"title":["Improved Analysis and Simulation of a Time-Domain Carpet Cloak Model"],"prefix":"10.1515","volume":"19","author":[{"given":"Jichun","family":"Li","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences , University of Nevada Las Vegas , Las Vegas , NV 89154-4020 , USA"}]},{"given":"Chen","family":"Meng","sequence":"additional","affiliation":[{"name":"Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education , School of Mathematics and Computational Science , Xiangtan University , Xiangtan , P. R. China"}]},{"given":"Yunqing","family":"Huang","sequence":"additional","affiliation":[{"name":"Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education , School of Mathematics and Computational Science , Xiangtan University , Xiangtan , P. R. China"}]}],"member":"374","published-online":{"date-parts":[[2018,2,17]]},"reference":[{"key":"2023033110021966757_j_cmam-2018-0001_ref_001_w2aab3b7d590b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"H.  Ammari, H.  Kang, H.  Lee, M.  Lim and S.  Yu,\nEnhancement of near cloaking for the full Maxwell equations,\nSIAM J. Appl. Math. 73 (2013), no. 6, 2055\u20132076.","DOI":"10.1137\/120903610"},{"key":"2023033110021966757_j_cmam-2018-0001_ref_002_w2aab3b7d590b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"G.  Bao, H.  Liu and J.  Zou,\nNearly cloaking the full Maxwell equations: Cloaking active contents with general conducting layers,\nJ. Math. Pures Appl. 101 (2014), no. 5, 716\u2013733.","DOI":"10.1016\/j.matpur.2013.10.010"},{"key":"2023033110021966757_j_cmam-2018-0001_ref_003_w2aab3b7d590b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"A.-S.  Bonnet-Ben Dhia, L.  Chesnel and P.  Ciarlet, Jr.,\nTwo-dimensional Maxwell\u2019s equations with sign-changing coefficients,\nAppl. Numer. Math. 79 (2014), 29\u201341.","DOI":"10.1016\/j.apnum.2013.04.006"},{"key":"2023033110021966757_j_cmam-2018-0001_ref_004_w2aab3b7d590b1b6b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"S. C.  Brenner, J.  Gedicke and L.-Y.  Sung,\nAn adaptive P1P_{1} finite element method for two-dimensional transverse magnetic time harmonic Maxwell\u2019s equations with\ngeneral material properties and general boundary conditions,\nJ. Sci. Comput. 68 (2016), no. 2, 848\u2013863.","DOI":"10.1007\/s10915-015-0161-x"},{"key":"2023033110021966757_j_cmam-2018-0001_ref_005_w2aab3b7d590b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"X.  Chen, Y.  Luo, J.  Zhang, K.  Jiang, J. B.  Pendry and S.  Zhang,\nMacroscopic invisibility cloaking of visible light,\nNature Comm. 2 (2011), 10.1038\/ncomms1176.","DOI":"10.1038\/ncomms1176"},{"key":"2023033110021966757_j_cmam-2018-0001_ref_006_w2aab3b7d590b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"Z.  Chen, Q.  Du and J.  Zou,\nFinite element methods with matching and nonmatching meshes for Maxwell equations with discontinuous coefficients,\nSIAM J. Numer. Anal. 37 (2000), no. 5, 1542\u20131570.","DOI":"10.1137\/S0036142998349977"},{"key":"2023033110021966757_j_cmam-2018-0001_ref_007_w2aab3b7d590b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"P.  Ciarlet, H.  Wu and J.  Zou,\nEdge element methods for Maxwell\u2019s equations with strong convergence for Gauss\u2019 laws,\nSIAM J. Numer. Anal. 52 (2014), no. 2, 779\u2013807.","DOI":"10.1137\/120899856"},{"key":"2023033110021966757_j_cmam-2018-0001_ref_008_w2aab3b7d590b1b6b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"P.  Ciarlet, Jr. and J.  Zou,\nFully discrete finite element approaches for time-dependent Maxwell\u2019s equations,\nNumer. Math. 82 (1999), no. 2, 193\u2013219.","DOI":"10.1007\/s002110050417"},{"key":"2023033110021966757_j_cmam-2018-0001_ref_009_w2aab3b7d590b1b6b1ab2ab9Aa","doi-asserted-by":"crossref","unstructured":"L.  Demkowicz and J.  Li,\nNumerical simulations of cloaking problems using a DPG method,\nComput. Mech. 51 (2013), no. 5, 661\u2013672.","DOI":"10.1007\/s00466-012-0744-4"},{"key":"2023033110021966757_j_cmam-2018-0001_ref_010_w2aab3b7d590b1b6b1ab2ac10Aa","doi-asserted-by":"crossref","unstructured":"A.  Greenleaf, Y.  Kurylev, M.  Lassas and G.  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