8389

7770

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1392

هشت،107ص.: مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

مهدي تاتاري

داود ميرزايي

15/10/92

كيوان مهاجر، فريد بهرامي

رياضي

ID7770

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Methodology for the boundary methodsfor solving partial di erntial equations Fatemeh Ghasemi fatemeh ghasemi@math iut ac ir 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mehdi Tatari mtatari@cc iut ac ir Advisor Dr Davoud Mirzaei d mirzaei@sci ui ac ir 2013 MSC 65N99 65N38 Keywords Boundary methods Boundary integral equations Meshless Methods Moving leastsquares Abstract This thesis is an extension and generalization of the work done by Li and Zhu 25 Allthe numerical methods for solving partial di erential equations PDEs can be classi ed into twocategories the domain type and the boundary type In this thesis some boundary type methods forsolving PDEs such as boundary element BEM and Galerkin boundary node method GBNM arepresented The boudary methods have some advantages over domain type methods Only the boundary of the domain needs to be discretized Especially in two dimensions where the boundary is just a curve this allows very simple data input and storage methods Exterior problems with unbounded domains but bounded boundaries are handled as easily as interior problems In some applications the physically relevant data are needed not by the solution in the interior of the domain but rather by the boundary values of the solution or its derivatives These data can be obtained directly from the solution of boundary integral equations whereas boundary values obtained from domain methods solutions are in general not very accurate The solution in the interior of the domain is approximated with a rather high convergence rate and moreover the same rate of convergence holds for all derivatives of any order of the solution

مهدي تاتاري

داود ميرزايي

كيوان مهاجر، فريد بهرامي