{"title":"环域泊松方程的快速谱解","authors":"Te-Sheng Lin, C-Y. He, Wei-Fan Hu","doi":"10.4310/amsa.2020.v5.n1.a3","DOIUrl":null,"url":null,"abstract":"A simple and efficient spectral method is formulated to solve Poisson equation in an annular domain. The solver relies on the Fourier expansion, where the differential equations for the Fourier coefficients are solved using an ultraspherical spectral method. For a domain with N grid points in the polar direction and M grid points in the radial direction, the solver only requires O ( NM log 2 N ) arith-metic operations.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fast spectral solver for Poisson equation in an annular domain\",\"authors\":\"Te-Sheng Lin, C-Y. He, Wei-Fan Hu\",\"doi\":\"10.4310/amsa.2020.v5.n1.a3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A simple and efficient spectral method is formulated to solve Poisson equation in an annular domain. The solver relies on the Fourier expansion, where the differential equations for the Fourier coefficients are solved using an ultraspherical spectral method. For a domain with N grid points in the polar direction and M grid points in the radial direction, the solver only requires O ( NM log 2 N ) arith-metic operations.\",\"PeriodicalId\":42896,\"journal\":{\"name\":\"Annals of Mathematical Sciences and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Mathematical Sciences and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4310/amsa.2020.v5.n1.a3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Mathematical Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/amsa.2020.v5.n1.a3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Fast spectral solver for Poisson equation in an annular domain
A simple and efficient spectral method is formulated to solve Poisson equation in an annular domain. The solver relies on the Fourier expansion, where the differential equations for the Fourier coefficients are solved using an ultraspherical spectral method. For a domain with N grid points in the polar direction and M grid points in the radial direction, the solver only requires O ( NM log 2 N ) arith-metic operations.