7507

7002

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1391

يازده،75ص.: مصور

ص.ع.به فارسي و انگليسي

مهدي تاتاري

داوود ميرزايي

23/11/91

رضا مختاري، محمدرضا رئوفي

رياضي

ID7002

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Element free Galerkin and Petrov Galerkin methods for solving partial di erential equations Zahra Jannesari z jannesary@math iut ac ir 08 09 2012 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mehdi Tatari mtatari@cc iut ac ir Keywords meshfree methods element free Galerkin method meshless local Petrov GalerkinmethodAbstractThis thesis is an extension and generalization of the work done by Belytschko et al 7 and thework done by Atluri and Zhu 4 Traditionally partial di erential equations PDEs are solvedby using numerical methods such as the nite di erence method FDM the nite element method FEM and the nite volume method FVM They relied on the use of interlaced grids elementsor nite volumes as the underlying structures upon which to discretize governing PDEs actuallydomain of the problem discretized into a mesh Mesh generation has always posed challenges forcomputational scientists because of its time consuming and complication Nowadays a new class ofnumerical methods known commonly as meshless methods have gained a considerable attention dueto their exibility and capacity to solve the systems of PDEs These methods do not have di cultiesof the FDM the FEM and the FVM Compatibility of these methods with deformations is relativelyeasy since it is necessary to add nodes in a part of domain for decreasing error Meshless methods areused to set up a system of algebraic equations for the whole problem domain without mesh generation These methods utilize a set of arbitrarily distributed nodes within the problem domain and on thedomain boundaries to represent the problem domain and its boundaries All of them reduce necessityto mesh generation but most of these methods are not truly meshfree methods because they need amesh for integration purpose These methods are called pseudomeshfree methods One of the most powerful meshless methods that is investigated in this work is element free Galerkin EFG method This method employes the moving least squares MLS approximation to create shapefunctions and uses a background cells for evaluation the integrals appeared in the its global weak form

مهدي تاتاري

داوود ميرزايي

رضا مختاري، محمدرضا رئوفي