5498

5157

كارشناسي ارشد

طراحي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده مكانيك

1389

نه،82ص.: مصور،جدول،نمودار

ص.ع.به فارسي و انگليسي

محمود فرزين، حميد هاشم الحسيني

حسين ديباجيان

11/8/89

بيژن برومند، محمد مشايخي

مهندسي مكانيك

ID5157

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Suggestion of a probabilistic error indicator and its application in refinement of a meshless method Shahrokh Sepehri Rahnama sm sepehrirahnama@me iut ac ir shahrokh sepehri@gmail com April 12 2010 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisors Farzin Mahmud Associate Professor Email Farzin@cc iut ac ir Hashemolhosseini Hamid Associate Professor Email hamidh@cc iut ac ir Advisor Dibajian Hussein PHD student Email dibajian@gmail com Abstract Calculation of error and its estimation over the problem domain is one of the most important concerns in numerical methods Many researchers have tried to propose a posteriori error estimators or error indicators to control the errors and the results In the mean time development of error estimator is usually based on smoothing of error field of the problem This means that they are some function of recovered error In this dissertation a probabilistic model is presented which can estimate the distribution of variance of absolute error and contains spatial structure of nodes This model is used as an error indicator Then a refinement strategy is developed based on the proposed error indicator According to the proposed refinement strategy the refinement can be performed many times based on the user defined percentage of error It should be noted that this refinement procedure has low computation costs The proposed refinement is a type of H refinement For the proposed model first a parameter is presented which contains the global trend of error field and is calculated by recovered values Then according to probabilistic concepts the covariance can present the correlation of nodes locations by considering the spatial structure of nodes and This property of covariance is used for error indicating and formulation of the proposed error indicator The validation procedure is performed by two types of examples firstly using mathematical random functions and secondly using an infinite plate with a circular hole as a physical problem According to the results presented in this dissertation the first advantage of this error indicator is definition of a specific formulation for assessment of local changes of the variance of the absolute error field which improves the evaluation of the error field and the second one is considering the field parameter itself instead of the gradient of field parameter for error indication process For the refinement of the problem domain a refinement strategy is developed First the parameter is calculated over the problem domain Then some new nodes are added at the location with maximums error The number of the additional nodes is based the percentage of error which is defined by the user In this dissertation this percentage of error is defined based on the proposed error indicator Refinement of the problem domain is done until the error values become lesser than the desired values The spatial structure of nodes is updated in each refinement stage but the parameter remains constant Therefore refinement can

محمود فرزين، حميد هاشم الحسيني

حسين ديباجيان

بيژن برومند، محمد مشايخي