{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T19:22:59Z","timestamp":1774898579688,"version":"3.50.1"},"reference-count":45,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"DOI":"10.13039\/501100021856","name":"Ministero dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["CUP E11G18000350001"],"award-info":[{"award-number":["CUP E11G18000350001"]}],"id":[{"id":"10.13039\/501100021856","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we present a numerical method based on the coupling between a Curved Virtual Element Method (CVEM) and a Boundary Element Method (BEM) for the simulation of wave fields scattered by obstacles immersed in homogeneous infinite media.\nIn particular, we consider the 2D time-domain damped wave equation, endowed with a Dirichlet condition on the boundary (sound-soft scattering).\nTo reduce the infinite domain to a finite computational one, we introduce an artificial boundary on which we impose a Boundary Integral Non-Reflecting Boundary Condition (BI-NRBC).\nWe apply a CVEM combined with the Crank\u2013Nicolson time integrator in the interior domain, and we discretize the BI-NRBC by a convolution quadrature formula in time and a collocation method in space.\nWe present some numerical results to test the performance of the proposed approach and to highlight its effectiveness, especially when obstacles with complex geometries are considered.<\/jats:p>","DOI":"10.1515\/cmam-2022-0084","type":"journal-article","created":{"date-parts":[[2023,3,8]],"date-time":"2023-03-08T12:51:52Z","timestamp":1678279912000},"page":"353-372","source":"Crossref","is-referenced-by-count":16,"title":["CVEM-BEM Coupling for the Simulation of Time-Domain Wave Fields Scattered by Obstacles with Complex Geometries"],"prefix":"10.1515","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3924-0939","authenticated-orcid":false,"given":"Luca","family":"Desiderio","sequence":"first","affiliation":[{"name":"Department of Mathematical, Physical and Computer Sciences , University of Parma , Parma , Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4957-3972","authenticated-orcid":false,"given":"Silvia","family":"Falletta","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences \u201cG.\u2009L. Lagrange\u201d , Polytechnic of Turin , Turin , Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2577-1421","authenticated-orcid":false,"given":"Matteo","family":"Ferrari","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences \u201cG.\u2009L. Lagrange\u201d , Polytechnic of Turin , Turin , Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1685-9608","authenticated-orcid":false,"given":"Letizia","family":"Scuderi","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences \u201cG.\u2009L. Lagrange\u201d , Polytechnic of Turin , Turin , Italy"}]}],"member":"374","published-online":{"date-parts":[[2023,3,9]]},"reference":[{"key":"2023033113095706907_j_cmam-2022-0084_ref_001","doi-asserted-by":"crossref","unstructured":"B. Ahmed, A. Alsaedi, F. Brezzi, L. D. Marini and A. Russo,\nEquivalent projectors for virtual element methods,\nComput. Math. Appl. 66 (2013), 376\u2013391.","DOI":"10.1016\/j.camwa.2013.05.015"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_002","doi-asserted-by":"crossref","unstructured":"A. Aimi, L. Desiderio and G. Di Credico,\nPartially pivoted ACA based acceleration of the energetic BEM for time-domain acoustic and elastic waves exterior problems,\nComput. Math. Appl. 119 (2022), 351\u2013370.","DOI":"10.1016\/j.camwa.2022.05.024"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_003","doi-asserted-by":"crossref","unstructured":"A. Aimi, L. Desiderio, M. Diligenti and C. Guardasoni,\nA numerical study of energetic BEM-FEM applied to wave propagation in 2D multidomains,\nPubl. Inst. Math. (Beograd) (N.\u2009S.) 96(110) (2014), 5\u201322.","DOI":"10.2298\/PIM1410005A"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_004","doi-asserted-by":"crossref","unstructured":"A. Aimi, L. Desiderio, P. Fedeli and A. Frangi,\nA fast boundary-finite element approach for estimating anchor losses in micro-electro-mechanical system resonators,\nAppl. Math. Model. 97 (2021), 741\u2013753.","DOI":"10.1016\/j.apm.2021.04.002"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_005","doi-asserted-by":"crossref","unstructured":"P. F. Antonietti, G. Manzini and M. Verani,\nThe conforming virtual element method for polyharmonic problems,\nComput. Math. Appl. 79 (2020), no. 7, 2021\u20132034.","DOI":"10.1016\/j.camwa.2019.09.022"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_006","doi-asserted-by":"crossref","unstructured":"E. Artioli, S. Marfia and E. Sacco,\nVEM-based tracking algorithm for cohesive\/frictional 2D fracture,\nComput. Methods Appl. Mech. Engrg. 365 (2020), Paper No. 112956.","DOI":"10.1016\/j.cma.2020.112956"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_007","doi-asserted-by":"crossref","unstructured":"A. Bamberger and T. H. Duong,\nFormulation variationnelle espace-temps pour le calcul par potentiel retard\u00e9 de la diffraction d\u2019une onde acoustique. I,\nMath. Methods Appl. Sci. 8 (1986), no. 3, 405\u2013435.","DOI":"10.1002\/mma.1670080127"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_008","doi-asserted-by":"crossref","unstructured":"L. Banjai,\nMultistep and multistage convolution quadrature for the wave equation: Algorithms and experiments,\nSIAM J. Sci. Comput. 32 (2010), no. 5, 2964\u20132994.","DOI":"10.1137\/090775981"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_009","doi-asserted-by":"crossref","unstructured":"L. Banjai,\nImplicit\/explicit, BEM\/FEM coupled scheme for acoustic waves with the wave equation in the second order formulation,\nComput. Methods Appl. Math. 22 (2022), no. 4, 757\u2013773.","DOI":"10.1515\/cmam-2021-0186"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_010","doi-asserted-by":"crossref","unstructured":"L. Banjai, C. Lubich and F.-J. Sayas,\nStable numerical coupling of exterior and interior problems for the wave equation,\nNumer. Math. 129 (2015), no. 4, 611\u2013646.","DOI":"10.1007\/s00211-014-0650-0"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_011","doi-asserted-by":"crossref","unstructured":"L. Beir\u00e3o da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini and A. Russo,\nBasic principles of virtual element methods,\nMath. Models Methods Appl. Sci. 23 (2013), no. 1, 199\u2013214.","DOI":"10.1142\/S0218202512500492"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_012","doi-asserted-by":"crossref","unstructured":"L. Beir\u00e3o da Veiga, F. Brezzi, L. D. Marini and A. Russo,\nThe hitchhiker\u2019s guide to the virtual element method,\nMath. Models Methods Appl. Sci. 24 (2014), no. 8, 1541\u20131573.","DOI":"10.1142\/S021820251440003X"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_013","doi-asserted-by":"crossref","unstructured":"L. Beir\u00e3o da Veiga, F. Brezzi, L. D. Marini and A. Russo,\nMixed virtual element methods for general second order elliptic problems on polygonal meshes,\nESAIM Math. Model. Numer. Anal. 50 (2016), no. 3, 727\u2013747.","DOI":"10.1051\/m2an\/2015067"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_014","doi-asserted-by":"crossref","unstructured":"L. Beir\u00e3o da Veiga, C. Lovadina and A. Russo,\nStability analysis for the virtual element method,\nMath. Models Methods Appl. Sci. 27 (2017), no. 13, 2557\u20132594.","DOI":"10.1142\/S021820251750052X"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_015","doi-asserted-by":"crossref","unstructured":"L. Beir\u00e3o da Veiga, A. Russo and G. Vacca,\nThe virtual element method with curved edges,\nESAIM Math. Model. Numer. Anal. 53 (2019), no. 2, 375\u2013404.","DOI":"10.1051\/m2an\/2018052"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_016","doi-asserted-by":"crossref","unstructured":"S. Berrone, A. Borio and F. Marcon,\nComparison of standard and stabilization free virtual elements on anisotropic elliptic problems,\nAppl. Math. Lett. 129 (2022), Paper No. 107971.","DOI":"10.1016\/j.aml.2022.107971"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_017","doi-asserted-by":"crossref","unstructured":"S. C. Brenner, Q. Guan and L.-Y. Sung,\nSome estimates for virtual element methods,\nComput. Methods Appl. Math. 17 (2017), no. 4, 553\u2013574.","DOI":"10.1515\/cmam-2017-0008"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_018","doi-asserted-by":"crossref","unstructured":"S. Chaillat, L. Desiderio and P. Ciarlet,\nTheory and implementation of \u210b-matrix based iterative and direct solvers for Helmholtz and elastodynamic oscillatory kernels,\nJ. Comput. Phys. 351 (2017), 165\u2013186.","DOI":"10.1016\/j.jcp.2017.09.013"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_019","doi-asserted-by":"crossref","unstructured":"B. Chen, F. Ma and Y. Guo,\nTime domain scattering and inverse scattering problems in a locally perturbed half-plane,\nAppl. Anal. 96 (2017), no. 8, 1303\u20131325.","DOI":"10.1080\/00036811.2016.1188288"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_020","doi-asserted-by":"crossref","unstructured":"M. Costabel,\nSymmetric methods for the coupling of finite elements and boundary elements (invited contribution),\nBoundary Elements IX, Vol. 1 (Stuttgart 1987),\nComputational Mechanics, Southampton (1987), 411\u2013420.","DOI":"10.1007\/978-3-662-21908-9_26"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_021","doi-asserted-by":"crossref","unstructured":"L. Desiderio and S. Falletta,\nEfficient solution of two-dimensional wave propagation problems by CQ-wavelet BEM: Algorithm and applications,\nSIAM J. Sci. Comput. 42 (2020), no. 4, B894\u2013B920.","DOI":"10.1137\/19M1287614"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_022","doi-asserted-by":"crossref","unstructured":"L. Desiderio, S. Falletta, M. Ferrari and L. Scuderi,\nCVEM-BEM coupling with decoupled orders for 2D exterior Poisson problems,\nJ. Sci. Comput. 92 (2022), no. 3, Paper No. 96.","DOI":"10.1007\/s10915-022-01951-3"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_023","doi-asserted-by":"crossref","unstructured":"L. Desiderio, S. Falletta, M. Ferrari and L. Scuderi,\nOn the coupling of the curved virtual element method with the one-equation boundary element method for 2D exterior Helmholtz problems,\nSIAM J. Numer. Anal. 60 (2022), no. 4, 2099\u20132124.","DOI":"10.1137\/21M1460776"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_024","doi-asserted-by":"crossref","unstructured":"L. Desiderio, S. Falletta and L. Scuderi,\nA virtual element method coupled with a boundary integral non reflecting condition for 2D exterior Helmholtz problems,\nComput. Math. Appl. 84 (2021), 296\u2013313.","DOI":"10.1016\/j.camwa.2021.01.002"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_025","doi-asserted-by":"crossref","unstructured":"H. Eruslu and F. J. Sayas,\nPolynomially bounded error estimates for trapezoidal rule convolution quadrature,\nComput. Math. Appl. 79 (2020), no. 6, 1634\u20131643.","DOI":"10.1016\/j.camwa.2019.09.020"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_026","doi-asserted-by":"crossref","unstructured":"S. Falletta and G. Monegato,\nAn exact non reflecting boundary condition for 2D time-dependent wave equation problems,\nWave Motion 51 (2014), no. 1, 168\u2013192.","DOI":"10.1016\/j.wavemoti.2013.06.001"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_027","doi-asserted-by":"crossref","unstructured":"S. Falletta and G. Monegato,\nExact non-reflecting boundary condition for 3D time-dependent multiple scattering\u2013multiple source problems,\nWave Motion 58 (2015), 281\u2013302.","DOI":"10.1016\/j.wavemoti.2015.06.002"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_028","doi-asserted-by":"crossref","unstructured":"S. Falletta, G. Monegato and L. Scuderi,\nA space-time BIE method for nonhomogeneous exterior wave equation problems. The Dirichlet case,\nIMA J. Numer. Anal. 32 (2012), no. 1, 202\u2013226.","DOI":"10.1093\/imanum\/drr008"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_029","doi-asserted-by":"crossref","unstructured":"S. Falletta, G. Monegato and L. Scuderi,\nA space-time BIE method for wave equation problems: The (two-dimensional) Neumann case,\nIMA J. Numer. Anal. 34 (2014), no. 1, 390\u2013434.","DOI":"10.1093\/imanum\/drs040"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_030","doi-asserted-by":"crossref","unstructured":"S. Falletta and S. A. Sauter,\nThe panel-clustering method for the wave equation in two spatial dimensions,\nJ. Comput. Phys. 305 (2016), 217\u2013243.","DOI":"10.1016\/j.jcp.2015.10.033"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_031","doi-asserted-by":"crossref","unstructured":"G. N. Gatica and S. Meddahi,\nCoupling of virtual element and boundary element methods for the solution of acoustic scattering problems,\nJ. Numer. Math. 28 (2020), no. 4, 223\u2013245.","DOI":"10.1515\/jnma-2019-0068"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_032","doi-asserted-by":"crossref","unstructured":"C. Geuzaine and J.-F. Remacle,\nGmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities,\nInternat. J. Numer. Methods Engrg. 79 (2009), no. 11, 1309\u20131331.","DOI":"10.1002\/nme.2579"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_033","doi-asserted-by":"crossref","unstructured":"H. Gimperlein, C. \u00d6zdemir and E. P. Stephan,\nA time-dependent FEM-BEM coupling method for fluid-structure interaction in \n                  \n                     \n                        \n                           3\n                           \u2062\n                           d\n                        \n                     \n                     \n                     3d\n                  \n               ,\nAppl. Numer. Math. 152 (2020), 49\u201365.","DOI":"10.1016\/j.apnum.2020.01.023"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_034","doi-asserted-by":"crossref","unstructured":"H. Gimperlein, C. \u00d6zdemir and E. P. Stephan,\nError estimates for FE-BE coupling of scattering of waves in the time domain,\nComput. Methods Appl. Math. 22 (2022), no. 4, 839\u2013859.","DOI":"10.1515\/cmam-2021-0162"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_035","unstructured":"D. Givoli,\nNumerical Methods for Problems in Infinite Domains,\nStud. Appl. Math. 33,\nElsevier Scientific, Amsterdam, 2013."},{"key":"2023033113095706907_j_cmam-2022-0084_ref_036","unstructured":"H. D. Han,\nA new class of variational formulations for the coupling of finite and boundary element methods,\nJ. Comput. Math. 8 (1990), no. 3, 223\u2013232."},{"key":"2023033113095706907_j_cmam-2022-0084_ref_037","doi-asserted-by":"crossref","unstructured":"C. Johnson and J.-C. N\u00e9d\u00e9lec,\nOn the coupling of boundary integral and finite element methods,\nMath. Comp. 35 (1980), no. 152, 1063\u20131079.","DOI":"10.1090\/S0025-5718-1980-0583487-9"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_038","doi-asserted-by":"crossref","unstructured":"C. Lubich,\nConvolution quadrature and discretized operational calculus. II,\nNumer. Math. 52 (1988), no. 4, 413\u2013425.","DOI":"10.1007\/BF01462237"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_039","doi-asserted-by":"crossref","unstructured":"G. Monegato and L. Scuderi,\nNumerical integration of functions with boundary singularities,\nJ. Comput. Appl. Math. 112 (1999), 201\u2013214.","DOI":"10.1016\/S0377-0427(99)00230-7"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_040","doi-asserted-by":"crossref","unstructured":"F.-J. Sayas,\nThe validity of Johnson\u2013N\u00e9d\u00e9lec\u2019s BEM-FEM coupling on polygonal interfaces,\nSIAM J. Numer. Anal. 47 (2009), no. 5, 3451\u20133463.","DOI":"10.1137\/08072334X"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_041","doi-asserted-by":"crossref","unstructured":"M. Schanz,\nFast multipole method for poroelastodynamics,\nEng. Anal. Bound. Elem. 89 (2018), 50\u201359.","DOI":"10.1016\/j.enganabound.2018.01.014"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_042","doi-asserted-by":"crossref","unstructured":"A. Sommariva and M. Vianello,\nProduct Gauss cubature over polygons based on Green\u2019s integration formula,\nBIT 47 (2007), no. 2, 441\u2013453.","DOI":"10.1007\/s10543-007-0131-2"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_043","doi-asserted-by":"crossref","unstructured":"A. Sommariva and M. Vianello,\nGauss\u2013Green cubature and moment computation over arbitrary geometries,\nJ. Comput. Appl. Math. 231 (2009), no. 2, 886\u2013896.","DOI":"10.1016\/j.cam.2009.05.014"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_044","doi-asserted-by":"crossref","unstructured":"O. Steinbach,\nA note on the stable one-equation coupling of finite and boundary elements,\nSIAM J. Numer. Anal. 49 (2011), no. 4, 1521\u20131531.","DOI":"10.1137\/090762701"},{"key":"2023033113095706907_j_cmam-2022-0084_ref_045","doi-asserted-by":"crossref","unstructured":"F. Xie, Y. Qu, M. A. Islam and G. Meng,\nA sharp-interface Cartesian grid method for time-domain acoustic scattering from complex geometries,\nComput. & Fluids 202 (2020), Paper No. 104498.","DOI":"10.1016\/j.compfluid.2020.104498"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2022-0084\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2022-0084\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T17:41:26Z","timestamp":1680284486000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2022-0084\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,9]]},"references-count":45,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,10,6]]},"published-print":{"date-parts":[[2023,4,1]]}},"alternative-id":["10.1515\/cmam-2022-0084"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2022-0084","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,3,9]]}}}