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Full-Text Articles in Physical Sciences and Mathematics
On The Selection Of A Good Shape Parameter For Rbf Approximation And Its Application For Solving Pdes, Lei-Hsin Kuo
On The Selection Of A Good Shape Parameter For Rbf Approximation And Its Application For Solving Pdes, Lei-Hsin Kuo
Dissertations
Meshless methods utilizing Radial Basis Functions~(RBFs) are a numerical method that require no mesh connections within the computational domain. They are useful for solving numerous real-world engineering problems. Over the past decades, after the 1970s, several RBFs have been developed and successfully applied to recover unknown functions and to solve Partial Differential Equations (PDEs).
However, some RBFs, such as Multiquadratic (MQ), Gaussian (GA), and Matern functions, contain a free variable, the shape parameter, c. Because c exerts a strong influence on the accuracy of numerical solutions, much effort has been devoted to developing methods for determining shape parameters which provide …
Solution Of Nonlinear Time-Dependent Pde Through Componentwise Approximation Of Matrix Functions, Alexandru Cibotarica
Solution Of Nonlinear Time-Dependent Pde Through Componentwise Approximation Of Matrix Functions, Alexandru Cibotarica
Dissertations
Exponential propagation iterative (EPI) methods provide an efficient approach to the solution of large stiff systems of ODE, compared to standard integrators. However, the bulk of the computational effort in these methods is due to products of matrix functions and vectors, which can become very costly at high resolution due to an increase in the number of Krylov projection steps needed to maintain accuracy. In this dissertation, it is proposed to modify EPI methods by using Krylov subspace spectral (KSS) methods, instead of standard Krylov projection methods, to compute products of matrix functions and vectors. This improvement allowed the benefits …