{"id":79,"date":"2014-11-25T17:02:23","date_gmt":"2014-11-26T01:02:23","guid":{"rendered":"\/wp\/apde\/?p=79"},"modified":"2014-11-25T17:02:23","modified_gmt":"2014-11-26T01:02:23","slug":"naoki-saito","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/apde\/2014\/11\/25\/naoki-saito\/","title":{"rendered":"Naoki Saito (December 1)"},"content":{"rendered":"<p>\t\t\t\tNote: this talk will not take place in the usual room. Location TBA.<\/p>\n<p>Speaker: Naoki Saito (UC Davis)<\/p>\n<p>Title: Laplacian eigenfunctions that do not feel the boundary: Theory, Computation, and Applications<\/p>\n<p>Abstract: I will discuss Laplacian eigenfunctions defined on a Euclidean<br \/>\ndomain of general shape, which &#8220;do not feel the boundary.&#8221;<br \/>\nThese Laplacian eigenfunctions satisfy the Helmholtz equation inside the domain,<br \/>\nand can be extended smoothly and harmonically outside of the domain.<br \/>\nAlthough these eigenfunctions do not satisfy the usual Dirichlet or Neumann<br \/>\nboundary conditions, they can be computed via the eigenanalysis of the<br \/>\nintegral operator (with the potential kernel) commuting with the Laplace<br \/>\noperator. Compared to directly solving the Helmholtz equations on such<br \/>\ndomains, the eigenanalysis of this integral operator has several advantages<br \/>\nincluding the numerical stability and amenability to modern fast numerical<br \/>\nalgorithms (e.g., the Fast Multipole Method).<br \/>\nIn this talk, I will discuss their properties, the relationship with the<br \/>\nKrein-von Neumann self-adjoint extension of unbounded symmetric operators, and<br \/>\ncertain applications including image extrapolation and characterization of<br \/>\nbiological shapes.\t\t<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Note: this talk will not take place in the usual room. Location TBA. Speaker: Naoki Saito (UC Davis) Title: Laplacian eigenfunctions that do not feel the boundary: Theory, Computation, and Applications Abstract: I will discuss Laplacian eigenfunctions defined on a Euclidean domain of general shape, which &#8220;do not feel the boundary.&#8221; These Laplacian eigenfunctions satisfy [&hellip;]<\/p>\n","protected":false},"author":103,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-79","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/79","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/users\/103"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/comments?post=79"}],"version-history":[{"count":0,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/posts\/79\/revisions"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/media?parent=79"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/categories?post=79"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/apde\/wp-json\/wp\/v2\/tags?post=79"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}