{"id":14357,"date":"2022-11-18T14:23:07","date_gmt":"2022-11-18T06:23:07","guid":{"rendered":"https:\/\/virtual.math.ntnu.edu.tw\/?p=14357"},"modified":"2022-11-18T14:23:07","modified_gmt":"2022-11-18T06:23:07","slug":"20221130_speech","status":"publish","type":"post","link":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/2022\/11\/18\/20221130_speech\/","title":{"rendered":"<span style=\"color:#3566BD\">[\u5c08\u984c\u6f14\u8b1b] <\/span>\u301011\u670830\u65e5\u3011\u6797\u4f73\u5a01 \/ FFT-based fast algorithms for solving Maxwell eigenvalue problems"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"14357\" class=\"elementor elementor-14357\">\n\t\t\t\t\t\t<div class=\"elementor-inner\">\n\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7d6336ad elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7d6336ad\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-75f7fd9c\" data-id=\"75f7fd9c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-16918fed elementor-widget elementor-widget-heading\" data-id=\"16918fed\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">FFT-based fast algorithms for solving Maxwell eigenvalue problems<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-319459a8 elementor-widget elementor-widget-spacer\" data-id=\"319459a8\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-48c3dcea elementor-widget elementor-widget-text-editor\" data-id=\"48c3dcea\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"color: #000080; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-size: 18px; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: bold;\">\u6642\u3000\u9593\uff1a2022-11-30 14:00 (\u661f\u671f\u4e09) \/ \u5730\u3000\u9ede\uff1aM212 \/ \u8336\u3000\u6703\uff1aM107 (13:30)<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-565a0277 elementor-widget elementor-widget-image\" data-id=\"565a0277\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-image\">\n\t\t\t\t\t\t\t\t\t\t\t\t<img width=\"1125\" height=\"1442\" src=\"https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2022\/11\/\u6797\u4f73\u5a01.jpg\" class=\"attachment-full size-full\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2022\/11\/\u6797\u4f73\u5a01.jpg 1125w, https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2022\/11\/\u6797\u4f73\u5a01-234x300.jpg 234w, https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2022\/11\/\u6797\u4f73\u5a01-799x1024.jpg 799w, https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2022\/11\/\u6797\u4f73\u5a01-768x984.jpg 768w\" sizes=\"(max-width: 1125px) 100vw, 1125px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-55c03457 elementor-widget elementor-widget-text-editor\" data-id=\"55c03457\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<div style=\"list-style: none; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; margin-top: 10px; font-size: 22px; line-height: 26px; text-align: center; color: #cc6633; font-weight: bold;\">\u6797\u4f73\u5a01 \u535a\u58eb<\/div><div style=\"list-style: none; font-family: \u5fae\u8edf\u6b63\u9ed1\u9ad4; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; margin-top: 10px; font-size: 18px; line-height: 22px; text-align: center; color: #cc9966; font-weight: bold;\">(\u570b\u7acb\u967d\u660e\u4ea4\u901a\u5927\u5b78)<\/div>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3e7b18a3 elementor-widget elementor-widget-spacer\" data-id=\"3e7b18a3\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3364b956 elementor-widget elementor-widget-text-editor\" data-id=\"3364b956\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p>In this talk, we will introduce how the Fast Fourier Transform (FFT) is used to solve the discrete Maxwell eigenvalue problem (MEP). We first take a one-dimensional Poisson equation as an example to introduce the relationship between Fourier transform and discrete operators. Then, aiming at the discrete Maxwell eigenvalue problem introduced by Yee&#8217;s finite difference method, we will show the role of Fourier transform in matrix decomposition of discrete curl operators. In our numerical experiments, the computation times for FFT-based matrix-vector multiplications with matrices of dimension 7 million are only 0.33 and 3.6 \u00d7 10 \u2212 3 seconds using MATLAB with an Intel Xeon CPU and CUDA C++ programming with a single NVIDIA Tesla P100 GPU, respectively. Such multiplications significantly reduce the computational costs of the conjugate gradient method for solving linear systems. These results demonstrate the potential of our proposed algorithm to enable large-scale numerical simulations for novel physical discoveries and engineering applications of photonic crystals.<\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-43cd1cd4 elementor-widget elementor-widget-image\" data-id=\"43cd1cd4\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-image\">\n\t\t\t\t\t\t\t\t\t\t\t\t<img width=\"1240\" height=\"758\" src=\"https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e.jpg\" class=\"attachment-full size-full\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e.jpg 1240w, https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-300x183.jpg 300w, https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-768x469.jpg 768w, https:\/\/virtual.math.ntnu.edu.tw\/wp-content\/uploads\/2020\/08\/\u6f14\u8b1b\u6a19\u5c3e-1024x626.jpg 1024w\" sizes=\"(max-width: 1240px) 100vw, 1240px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<p class=\"wpf_wrapper\"><a class=\"print_link\" href=\"\" target=\"_blank\">\u53cb\u5584\u5217\u5370<\/a><\/p><!-- .wpf_wrapper -->","protected":false},"excerpt":{"rendered":"<p>FFT-based fast algorithms for solving Maxwell eigenvalu [&hellip;]<\/p>\n","protected":false},"author":18,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[1,124],"tags":[],"_links":{"self":[{"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/14357"}],"collection":[{"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/users\/18"}],"replies":[{"embeddable":true,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/comments?post=14357"}],"version-history":[{"count":11,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/14357\/revisions"}],"predecessor-version":[{"id":15302,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/14357\/revisions\/15302"}],"wp:attachment":[{"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/media?parent=14357"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/categories?post=14357"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/virtual.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/tags?post=14357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}