5121

4811

كارشناسي ارشد

رياضي كاربردي﴿آناليز عددي﴾

اصفهان: دانشگاه صنعتي اصفهان،دانشكده رياضي

1388

[هفت]،123ص.:مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

رضا مختاري،مهدي تاتاري

89/1/29

مصطفي شمسي،حميدرضا مرزبان

رياضي

ID4811

به فارسي و انگليسي:قابل رويت در نسخه ديجيتالي

Domain decomposition for solving PDEs using RBF collocation methods Saeed Torabi Ziaratgahi saeed torabi@math iut ac ir January 26 2010 Master of Science Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranFirst supervisor Dr Reza Mokhtari mokhtari@cc iut ac irSecond supervisor Dr Mehdi Tatari mtatari@cc iut ac ir2000 MSC 65M55Key words Radial Basis Function RBF RBF collocation methods Domain Decomposi tion DD AbstractIn this thesis we present an expanded account of domain decomposition for solving PDEsusing RBF collocation methods based on two articles by Chinchapatnam and coworkers 2006 and Mai Duy et al 2008 The well known nite di erence nite element and nite volume methods in solving par tial di erential equations are based on a mesh discretization which is a complicated and timeconsuming process particularly for complex higher dimensional geometries The meshfree ormeshless methods try to circumvent the cumbersome issues of mesh generation One of themeshless methods is due to the pioneering e ort of Kansa 1990 who directly collocated theRBFs for the approximate solutions of di ertial equations Kansa method which is known as DRBF Di erentiated RBF collocation method hasseveral advantages in comparison with traditional methods and has been applied successfullyto obtain numerical solution of various type of ordinary and partial di erential equations Also Mai Duy Tran Cong presented similar method which is known as IRBF IntegratedRBF collocation method 1999 RBF collocation methods are very simple to implement because they are truly meshlessin the sense of that collocation points need not have any connectivity requirement as neededtraditional methods They are spatial dimension independent which is very attractive formodelling high dimensional problems They possess superior rate of convergence too Therefore for small to moderate sized problems RBF collocation methods do outperformtraditional methods but for large scale problems the resultant coe cient matrix is highlyill conditioned which hinders the applicability of the RBF collocation methods One of thebest remedies to ill conditioning problem is domain decomposition which has presented byDubal for DRBF 1994 and Mai Duy et al for IRBF 2008 We rst study the interpolation by radial basis functions which is used to constructingRBF collocation methods We then o er the DRBF and IRBF collocation methods for solvingODEs and PDEs After that we present di erent type of DD and combine them with RBFcollocation methods Finally we show the e ciency of the presented methods by variouskinds of numerical examples 1

رضا مختاري،مهدي تاتاري

مصطفي شمسي،حميدرضا مرزبان