16775

16775

كاربرد RBF-PUM در حل عددي معادلات ديفرانسيل با مشتقات جزئي

كارشناسي ارشد

رياضي كاربردي

مهر 1395

پروفسور احمد شايگان منش (گلبابايي)

رياضي

1395/12/07

1/1/1900 12:00:00 AM

Abstract Meshfree methods based on radial basis function (RBF) approximation are of interest for numerical solution of partial differentioal equations (PDEs) because they are flexible with respect to geometry, they can provide high order convergence, they allow for local refinment, an​d they are easy to implement in higher dementions. For global RBF methods, one of the major disadvantages is the computational cost associated with the dense linear systems that arise. Therfore, research is currently directed towards localized RBF approximation such as the RBF partition of unity collocation method (RBF-PUM) proposed here.The objective of these thesise is to establish that RBF-PUM is variable for parabolic PDEs of convection-diffusion type. The stability an​d accuracy of RBF-PUM is investigated partly theorically an​d partly numerically. Numerical experiments show that high-order algebraic convergence can be achieved for convection-diffusion problems. Numerical comparisons with finite difference an​d pseudospectral methods have been performed, showing that RBF-PUM is competitive with respect to accuracy, an​d in some cases also with respsct to computational time. Keywords: collocation method, meshfree, radial basis function, partition of unity, RBF-PUM, convection-diffusion.