{"id":12,"date":"2018-08-23T17:58:55","date_gmt":"2018-08-23T21:58:55","guid":{"rendered":"https:\/\/sciencescosmaincms.cm.ucf.edu\/math\/borges\/?page_id=12"},"modified":"2024-11-15T16:02:51","modified_gmt":"2024-11-15T21:02:51","slug":"research","status":"publish","type":"page","link":"https:\/\/sciences.ucf.edu\/math\/borges\/research\/","title":{"rendered":"Research"},"content":{"rendered":"<h2>Research Interests<\/h2>\n<p>These are some of my Research Interests:<\/p>\n<ul>\n<li>Inverse and Direct Scattering Problems.<\/li>\n<li>Numerical Analysis.<\/li>\n<li>Wave Propagation.<\/li>\n<li>Domain Decomposition.<\/li>\n<li>Fast Direct Solvers.<\/li>\n<li>Integral Equations.<\/li>\n<li>Neural Networks.<\/li>\n<\/ul>\n<hr \/>\n<h2>Software<\/h2>\n<p>These are the links to GitHub repositories to software that I contributed to:<\/p>\n<ul>\n<li><a href=\"https:\/\/github.com\/flatironinstitute\/inverse-obstacle-scattering2d\">Inverse acoustic scattering solver for 2D problems.<\/a><\/li>\n<li><a href=\"https:\/\/github.com\/flatironinstitute\/inverse-volume-scattering2d\">Inverse volume solver for 2D problems.<\/a><\/li>\n<\/ul>\n<hr \/>\n<h2>Publications<\/h2>\n<ul>\n<li>C. Borges, L. Greengard, M.O&#8217;Neil, M. Rachh. <a href=\"https:\/\/link.springer.com\/article\/10.1007\/s10915-024-02727-7\">On the construction of scattering matrices for irregular or <em>elongated<\/em> enclosures using Green&#8217;s representation formula.<\/a> <i>Journal of \u00a0Scientific Computing<\/i> <strong>102<\/strong>, 2 (2025).<\/li>\n<li>T. Askham, C. Borges. <a href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6420\/ad6284\">Reconstructing the shape and material parameters of dissipative obstacles using an impedance model<\/a>. <em>Inverse Problems<\/em> 40.9 (2024): 095004.<\/li>\n<li>T. Askham, C. Borges, J. Hoskins, M. Rachh. <a href=\"https:\/\/link.springer.com\/article\/10.1007\/s10915-023-02406-z\">Random walks in frequency and the reconstruction of obstacles with cavities from multi-frequency data<\/a>.\u00a0<span dir=\"ltr\" role=\"presentation\"><i>Journal of \u00a0Scientific Computing<\/i> <b>98<\/b>, 15 (2024).<\/span><\/li>\n<li>M. Zhou, J. Han, M. Rachh, C. Borges. <a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0021999123004369?casa_token=pEhiyiZnxwYAAAAA:GGIJe4GyOS07r0wKxLP1XlY587TCn7rhGWbF3BkHGZD567xLN5OVRfINi_wvfZ8_EHP6GqGZzAE\">A Neural Network Warm-Start Approach for the Inverse Acoustic Obstacle Scattering Problem<\/a>. <i>Journal of Computational Physics<\/i> 490 (2023): 112341.<\/li>\n<li>C. Borges, M. Rachh, L. Greengard. <a href=\"http:\/\/iopscience.iop.org\/article\/10.1088\/1361-6420\/acb2ec\">On the robustness of inverse scattering for penetrable, homogeneous objects with complicated boundary<\/a>.\n<div><i>Inverse Problems<\/i> 39.3 (2023): 035004.<\/div>\n<\/li>\n<li>C. Borges, M. Rachh. <a href=\"https:\/\/idp.springer.com\/authorize\/casa?redirect_uri=https:\/\/link.springer.com\/article\/10.1007\/s10444-021-09915-1&amp;casa_token=7318TE5up8MAAAAA:fF3LDl-DoA6b6A_ceJq12V2ZNnxtV3OgFTHsrHS2f5jLLTpwuA5zuPTGwAObuCV6neXADv6iWMzl6GJjLg\">Multifrequency inverse obstacle scattering with unknown impedance boundary conditions using recursive linearization<\/a>. Advances in Computational Mathematics 48.1 (2022): 1-32.<\/li>\n<li>C. Borges, J. Lai. <a href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6420\/abac9b\">Inverse scattering reconstruction of a three-dimensional sound-soft axis-symmetric impenetrable object<\/a>. <em>Inverse Problems<\/em>, 36.10 (2020): 105005.<\/li>\n<li>C. Borges, G. Biros. <a href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6420\/ab6e78\/pdf\">A domain decomposition preconditioning for an inverse volume scattering problem,<\/a> <em>Inverse Problems<\/em>, <span class=\"wd-jnl-art-breadcrumb-vol nowrap\">36.<\/span><span class=\"wd-jnl-art-breadcrumb-issue\"><span class=\"wd-jnl-art-breadcrumb-issue\">3 (2020): <\/span><\/span><span style=\"font-size: revert\">035016.<\/span><\/li>\n<li>C. Borges, G. Biros. <a href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6420\/aadbc5\">Reconstruction of a compactly supported sound profile in the presence of a random background medium<\/a>, <em>Inverse Problems<\/em>, 34.11 (2018): 115007.<\/li>\n<li>C. Borges, A. Gillman, L. Greengard. <a href=\"https:\/\/epubs.siam.org\/doi\/abs\/10.1137\/16M1093562\">High-resolution inverse scattering in two dimensions using recursive linearization<\/a>, SIAM J. Imaging Sciences, volume 10, no. 2, pp. 641-664, 2017.<\/li>\n<li>S. Ambikasaran, C. Borges, L. Imbert-Gerard, L. Greengard. <a href=\"https:\/\/epubs.siam.org\/doi\/abs\/10.1137\/15M102455X\">Fast, adaptive, high order accurate discretization of the Lippmann-Schwinger equation in two dimensions<\/a>, SIAM J. Sci. Comput., 38(3), A1770\u2013A1787.<\/li>\n<li>C. Borges, L. Greengard. <a href=\"https:\/\/epubs.siam.org\/doi\/abs\/10.1137\/140982787?journalCode=sjisbi\">Inverse obstacle scattering in two dimensions with multiple frequency data and multiple angles of incidence<\/a>, SIAM J. Imaging Sciences, vol. 8, no. 1, pp. 280\u2013298, 2015.<\/li>\n<li>C. Borges. A multifrequency method for the solution of the acoustic inverse scattering problem. Ph.D.dissertation, Worcester Polytechnic Institute, Worcester, MA, January 2013.<\/li>\n<li>C. Borges, M. Sarkis, C. Schaerer. Coarse grid correction operator splitting for parabolic partial differential equations. In proceedings: X Meeting in Computational Modeling, November 2007, Rio de Janeiro, Brazil.<\/li>\n<li>C. Borges. Coarse grid correction operator splitting for parabolic partial differential equations. M.Sc.Thesis, Institute of Pure and Applied Mathematics, Rio de Janeiro, Brazil, October 2007.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Research Interests These are some of my Research Interests: Inverse and Direct Scattering Problems. Numerical Analysis. Wave Propagation. Domain Decomposition. [&hellip;]<\/p>\n","protected":false},"author":39,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-publications.php","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-12","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sciences.ucf.edu\/math\/borges\/wp-json\/wp\/v2\/pages\/12","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sciences.ucf.edu\/math\/borges\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sciences.ucf.edu\/math\/borges\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sciences.ucf.edu\/math\/borges\/wp-json\/wp\/v2\/users\/39"}],"replies":[{"embeddable":true,"href":"https:\/\/sciences.ucf.edu\/math\/borges\/wp-json\/wp\/v2\/comments?post=12"}],"version-history":[{"count":20,"href":"https:\/\/sciences.ucf.edu\/math\/borges\/wp-json\/wp\/v2\/pages\/12\/revisions"}],"predecessor-version":[{"id":167,"href":"https:\/\/sciences.ucf.edu\/math\/borges\/wp-json\/wp\/v2\/pages\/12\/revisions\/167"}],"wp:attachment":[{"href":"https:\/\/sciences.ucf.edu\/math\/borges\/wp-json\/wp\/v2\/media?parent=12"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}