Mathematical tools used to create items such as vacuums, cars and skyscrapers, make the design process streamlined, less expensive and safer.<\/p>\n
However, with advances in modern science increasingly pushing boundaries, these tools need to be adapted in order to keep up \u2013 and avoid potentially costly mistakes.<\/p>\n
The finite element method<\/strong> is a commonly used technique to solve mathematical problems.<\/p>\n However, well-established equations used by designers and computer models have limitations.<\/p>\n They don\u2019t account for imaginary numbers (known as complex-variables).<\/p>\n During his summer research project, Aaron Joy, visiting assistant professor of mechanical engineering, aims to extend the finite element method to solve complex-variable problems.<\/p>\n \u201cVariationally consistent finite element formulations for complex-valued differential equations\u201d examines the finite element method\u2019s scope and will test equations to formulate a base of ground rules for consistency.<\/p>\n Joy became interested in this work as an undergraduate at the University of Kansas. He credits inspiring teachers and advisers with spurring his fascination for solving complex-variable problems.<\/p>\n \u201cMy work right now is trying to extend current methods and compute solutions to problems that are [currently] impossible to solve \u2013 like equations that describe the motion of a fluid,\u201d he says.<\/p>\n Today, rules in most design processes only apply to real numbers. Real numbers are those we use normally; positive or negative, large or small, whole numbers or decimal numbers.<\/p>\n But modern innovations in electronics, optics, sensors, circuity, lasers, electromagnetics, quantum mechanics and advanced chemistry use imaginary numbers; numbers that when squared give a negative result.<\/p>\n Current computational infrastructure is not up to the task of solving for these problems.<\/p>\n Joy hopes his research, funded by the Summer Faculty Research Fund Program<\/a>, will continue past the exploratory phase in the fall to involve students using computer modeling and simulations.<\/p>\n The goal is to find one method that could solve any problem using real or imaginary numbers.<\/p>\n According to Joy, other researchers’ efforts are focused on seeking methods for single-use, specific problems \u2013 not a cost-saving or efficient use of innovators\u2019 time.<\/p>\n He seeks to find an overarching method in a single, well-contained framework that can be generalized and used by all future innovators.<\/p>\n Media Contact: Christel Peters<\/a>, 207.581.3571<\/p>\n","protected":false},"excerpt":{"rendered":" Mathematical tools used to create items such as vacuums, cars and skyscrapers, make the design process streamlined, less expensive and safer. However, with advances in modern science increasingly pushing boundaries, these tools need to be adapted in order to keep up \u2013 and avoid potentially costly mistakes. The finite element method is a commonly used […]<\/p>\n","protected":false},"author":1286,"featured_media":42805,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_seopress_robots_primary_cat":"65","_seopress_titles_title":"%%title%% %%page%%","_seopress_titles_desc":"91±¬ΑΟ researcher, Aaron Joy, has the ambitious goal to find mathematical solutions to complex, impossible-to-solve 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Mathematical tools used to create items such as vacuums, cars and skyscrapers, make the design process streamlined, less expensive and safer. However, with advances in modern science increasingly pushing boundaries, these tools need to be adapted in order to keep up \u2013 and avoid potentially costly mistakes. The finite element method is a commonly used technique to solve mathematical problems. However, well-established equations used by designers and computer models have limitations. They don\u2019t account for imaginary numbers (known as complex-variables). During his summer research project, Aaron Joy, visiting assistant professor of mechanical engineering, aims to extend the finite element method…<\/p>\n","category_list_v2":"Faculty Research Fund Awards<\/a>, Faculty Spotlight<\/a>, IMPACT Newsletter<\/a>, Research News<\/a>","author_info_v2":{"name":"","url":"https:\/\/umaine.edu\/research\/author\/"},"comments_num_v2":"0 comments","taxonomy_info":{"category":[{"value":7,"label":"Faculty Research Fund Awards"},{"value":572,"label":"Faculty Spotlight"},{"value":94,"label":"IMPACT Newsletter"},{"value":65,"label":"Research News"}],"post_tag":[{"value":408,"label":"Aaron Joy"},{"value":410,"label":"complex-variable"},{"value":10,"label":"FRF"},{"value":409,"label":"mathematics"},{"value":344,"label":"Mechanical Engineering"},{"value":78,"label":"Summer Research"}]},"featured_image_src_large":["https:\/\/umaine.edu\/research\/wp-content\/uploads\/sites\/281\/2019\/05\/AaronJoy-1024x683.jpg",1024,683,true],"author_info":{"display_name":"","author_link":"https:\/\/umaine.edu\/research\/author\/"},"comment_info":0,"category_info":[{"term_id":7,"name":"Faculty Research Fund Awards","slug":"frf-rrf-awards","term_group":0,"term_taxonomy_id":7,"taxonomy":"category","description":"","parent":0,"count":16,"filter":"raw","cat_ID":7,"category_count":16,"category_description":"","cat_name":"Faculty Research Fund Awards","category_nicename":"frf-rrf-awards","category_parent":0},{"term_id":572,"name":"Faculty Spotlight","slug":"faculty-spotlight","term_group":0,"term_taxonomy_id":572,"taxonomy":"category","description":"","parent":0,"count":36,"filter":"raw","cat_ID":572,"category_count":36,"category_description":"","cat_name":"Faculty Spotlight","category_nicename":"faculty-spotlight","category_parent":0},{"term_id":94,"name":"IMPACT Newsletter","slug":"impact-newsletter","term_group":0,"term_taxonomy_id":94,"taxonomy":"category","description":"","parent":0,"count":112,"filter":"raw","cat_ID":94,"category_count":112,"category_description":"","cat_name":"IMPACT Newsletter","category_nicename":"impact-newsletter","category_parent":0},{"term_id":65,"name":"Research News","slug":"research-news","term_group":0,"term_taxonomy_id":65,"taxonomy":"category","description":"","parent":0,"count":226,"filter":"raw","cat_ID":65,"category_count":226,"category_description":"","cat_name":"Research News","category_nicename":"research-news","category_parent":0}],"tag_info":[{"term_id":408,"name":"Aaron Joy","slug":"aaron-joy","term_group":0,"term_taxonomy_id":408,"taxonomy":"post_tag","description":"","parent":0,"count":1,"filter":"raw"},{"term_id":410,"name":"complex-variable","slug":"complex-variable","term_group":0,"term_taxonomy_id":410,"taxonomy":"post_tag","description":"","parent":0,"count":1,"filter":"raw"},{"term_id":10,"name":"FRF","slug":"frf","term_group":0,"term_taxonomy_id":10,"taxonomy":"post_tag","description":"","parent":0,"count":7,"filter":"raw"},{"term_id":409,"name":"mathematics","slug":"mathematics","term_group":0,"term_taxonomy_id":409,"taxonomy":"post_tag","description":"","parent":0,"count":2,"filter":"raw"},{"term_id":344,"name":"Mechanical Engineering","slug":"mechanical-engineering","term_group":0,"term_taxonomy_id":344,"taxonomy":"post_tag","description":"","parent":0,"count":2,"filter":"raw"},{"term_id":78,"name":"Summer Research","slug":"summer-research","term_group":0,"term_taxonomy_id":78,"taxonomy":"post_tag","description":"","parent":0,"count":7,"filter":"raw"}],"_links":{"self":[{"href":"https:\/\/umaine.edu\/research\/wp-json\/wp\/v2\/posts\/42804","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/umaine.edu\/research\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/umaine.edu\/research\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/umaine.edu\/research\/wp-json\/wp\/v2\/users\/1286"}],"replies":[{"embeddable":true,"href":"https:\/\/umaine.edu\/research\/wp-json\/wp\/v2\/comments?post=42804"}],"version-history":[{"count":15,"href":"https:\/\/umaine.edu\/research\/wp-json\/wp\/v2\/posts\/42804\/revisions"}],"predecessor-version":[{"id":43750,"href":"https:\/\/umaine.edu\/research\/wp-json\/wp\/v2\/posts\/42804\/revisions\/43750"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/umaine.edu\/research\/wp-json\/wp\/v2\/media\/42805"}],"wp:attachment":[{"href":"https:\/\/umaine.edu\/research\/wp-json\/wp\/v2\/media?parent=42804"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/umaine.edu\/research\/wp-json\/wp\/v2\/categories?post=42804"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/umaine.edu\/research\/wp-json\/wp\/v2\/tags?post=42804"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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