{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T04:25:09Z","timestamp":1680323109664},"reference-count":20,"publisher":"Walter de Gruyter GmbH","issue":"2","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>We are concerned with the numerical computation of electrostatic forces\/torques in only piece-wise homogeneous materials using the boundary element method (BEM).\nConventional force formulas based on the Maxwell stress tensor yield functionals that fail to be continuous on natural trace spaces.\nThus their use in conjunction with BEM incurs slow convergence and low accuracy.\nWe employ the remedy discovered in [P. Panchal and R. Hiptmair,\nElectrostatic force computation with boundary element methods,\n<jats:italic>SMAI J. Comput. Math.<\/jats:italic>\n                  <jats:bold>8<\/jats:bold> (2022), 49\u201374].\nMotivated by the virtual work principle which is interpreted using techniques of shape calculus, and using the adjoint method from shape optimization, we derive stable interface-based force functionals suitable for use with BEM.\nThis is done in the framework of single-trace direct boundary integral equations for second-order transmission problems.\nNumerical tests confirm the fast asymptotic convergence and superior accuracy of the new formulas for the computation of total forces and torques.<\/jats:p>","DOI":"10.1515\/cmam-2022-0112","type":"journal-article","created":{"date-parts":[[2023,3,7]],"date-time":"2023-03-07T10:36:38Z","timestamp":1678185398000},"page":"425-444","source":"Crossref","is-referenced-by-count":1,"title":["Force Computation for Dielectrics Using Shape Calculus"],"prefix":"10.1515","volume":"23","author":[{"given":"Piyush","family":"Panchal","sequence":"first","affiliation":[{"name":"Department of Mathematics , ETH Zurich , Zurich , Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ning","family":"Ren","sequence":"additional","affiliation":[{"name":"Department of Mathematics , ETH Zurich , Zurich , Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ralf","family":"Hiptmair","sequence":"additional","affiliation":[{"name":"Department of Mathematics , ETH Zurich , Zurich , Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,3,8]]},"reference":[{"key":"2023033113095820391_j_cmam-2022-0112_ref_001","doi-asserted-by":"crossref","unstructured":"A. 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Griffiths,\nIntroduction to Electrodynamics,\nPearson, London, 2013."},{"key":"2023033113095820391_j_cmam-2022-0112_ref_008","unstructured":"P. Grisvard,\nElliptic Problems in Nonsmooth Domains,\nMonogr. Stud. Math. 24,\nPitman, Boston, 1985."},{"key":"2023033113095820391_j_cmam-2022-0112_ref_009","doi-asserted-by":"crossref","unstructured":"W. Hackbusch,\nIntegral Equations,\nInternat. Ser. Numer. Math. 120,\nBirkh\u00e4user, Basel, 1995.","DOI":"10.1007\/978-3-0348-9215-5"},{"key":"2023033113095820391_j_cmam-2022-0112_ref_010","doi-asserted-by":"crossref","unstructured":"F. Henrotte, G. Deli\u00e9ge and K. Hameyer,\nThe eggshell approach for the computation of electromagnetic forces in 2D and 3D,\nCOMPEL 23 (2004), no. 4, 996\u20131005.","DOI":"10.1108\/03321640410553427"},{"key":"2023033113095820391_j_cmam-2022-0112_ref_011","doi-asserted-by":"crossref","unstructured":"F. Henrotte and K. Hameyer,\nComputation of electromagnetic force densities: Maxwell stress tensor vs. virtual work principle,\nJ. Comput. Appl. Math. 168 (2004), no. 1\u20132, 235\u2013243.","DOI":"10.1016\/j.cam.2003.06.012"},{"key":"2023033113095820391_j_cmam-2022-0112_ref_012","doi-asserted-by":"crossref","unstructured":"F. Henrotte and K. Hameyer,\nA theory for electromagnetic force formulas in continuous media,\nIEEE Trans. Magn. 43 (2007), no. 4, 1445\u20131448.","DOI":"10.1109\/TMAG.2007.892457"},{"key":"2023033113095820391_j_cmam-2022-0112_ref_013","unstructured":"M. Hinze, R. Pinnau, M. Ulbrich and S. Ulbrich,\nOptimization with PDE Constraints,\nMath. Model. Theory Appl. 23,\nSpringer, New York, 2009."},{"key":"2023033113095820391_j_cmam-2022-0112_ref_014","unstructured":"J. D. Jackson,\nClassical Electrodynamics, 3rd ed.,\nJohn Wiley & Sons, New York, 1998."},{"key":"2023033113095820391_j_cmam-2022-0112_ref_015","doi-asserted-by":"crossref","unstructured":"S. McFee, J. P. Webb and D. A. 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