{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T11:29:31Z","timestamp":1787225371302,"version":"build-2736575974"},"reference-count":14,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1908602"],"award-info":[{"award-number":["DMS-1908602"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2024,2,29]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We analyze the well-posedness of certain field-only boundary integral equations (BIEs) for frequency domain electromagnetic scattering from perfectly conducting spheres. Starting from the observations that (1) the three components of the scattered electric field [Formula: see text] and (2) scalar quantity [Formula: see text] are radiative solutions of the Helmholtz equation, we see that novel boundary integral equation formulations of electromagnetic scattering from perfectly conducting obstacles can be derived using Green\u2019s identities applied to the aforementioned quantities and the boundary conditions on the surface of the scatterer. The unknowns of these formulations are the normal derivatives of the three components of the scattered electric field and the normal component of the scattered electric field on the surface of the scatterer, and thus these formulations are referred to as field-only BIEs. In this paper we use the combined field methodology of Burton and Miller within the field-only BIE approach, and we derive new boundary integral formulations that feature only Helmholtz boundary integral operators, which we subsequently show to be well posed for all positive frequencies in the case of spherical scatterers. Relying on the spectral properties of Helmholtz boundary integral operators in spherical geometries, we show that the combined field-only boundary integral operators are diagonalizable in the case of spherical geometries and their eigenvalues are nonzero for all frequencies. Furthermore, we show that for spherical geometries one of the field-only integral formulations considered in this paper exhibits eigenvalues clustering at one\u2014a property similar to second-kind integral equations.<\/jats:p>","DOI":"10.1137\/23m1561865","type":"journal-article","created":{"date-parts":[[2024,1,12]],"date-time":"2024-01-12T04:03:29Z","timestamp":1705032209000},"page":"19-38","source":"Crossref","is-referenced-by-count":1,"title":["Combined Field-Only Boundary Integral Equations for PEC Electromagnetic Scattering Problem in Spherical Geometries"],"prefix":"10.1137","volume":"84","author":[{"given":"Luiz","family":"Maltez-Faria","sequence":"first","affiliation":[{"name":"POEMS Laboratory (CNRS\/INRIA\/ENSTA Paris), Institut Polytechnique de Paris, 91120 Palaiseau, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1647-4019","authenticated-orcid":true,"given":"Carlos","family":"P\u00e9rez-Arancibia","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, University of Twente, Enschede, The Netherlands."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Catalin","family":"Turc","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,1,12]]},"reference":[{"key":"ref1","series-title":"National Bureau of Standards Appl. Math. Ser. 55","volume-title":"Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables","author":"Abramowitz M.","year":"1964"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2006.02.049"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2014.04.003"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/BF01220037"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1002\/nme.4302"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1971.0097"},{"key":"ref7","unstructured":"D. Y. Chan, A. J. Yuffa, E. Klaseboer, and Q. Sun, Efficient Field-Only Surface Integral Equations for Electromagnetics, preprint, arXiv:1901.01602, 2019."},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20313"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1109\/8.558648"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.2016.2632619"},{"key":"ref11","first-page":"157","volume":"32","author":"Mavtz J.","year":"1978","journal-title":"AEU"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4393-7"},{"key":"ref13","volume-title":"Department of Statistics","author":"Woodbury M. A.","year":"1950"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.2018.2855671"}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/23M1561865","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T11:09:39Z","timestamp":1787224179000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M1561865"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,12]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,2,29]]}},"alternative-id":["10.1137\/23M1561865"],"URL":"https:\/\/doi.org\/10.1137\/23m1561865","relation":{},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,12]]}}}