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Cardinal interpolation with general multiquadrics: convergence rates [PDF]
Advances in Computational Mathematics, 2017 Wholesale changes from previous version; 26 pages ...
Keaton Hamm, Jeff Ledford
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Multiquadrics Collocation Method for Transient Eddy Current Problems [PDF]
IEEE Transactions on Magnetics, 2006 This paper presents the multiquadrics collocation method (MQCM) for transient eddy current problems. Both the implicit scheme and Crank-Nicolson time matching scheme are used here for time discretization. An example on analyzing transient eddy current of
K R Shao, Youguang Guo, Jianguo Zhu
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Mathematical and Computational ApplicationsThis paper aims to systematically assess the local radial basis function collocation method, structured with multiquadrics (MQs) and polyharmonic splines (PHSs), for solving steady and transient diffusion problems.
Umut Hanoglu +2 more
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Mathematics and Computers in SimulationUnisolvence of unsymmetric Kansa collocation is still a substantially open problem. We prove that Kansa matrices with MultiQuadrics and Inverse MultiQuadrics for the Dirichlet problem of the Poisson equation are almost surely nonsingular, when the collocation points are chosen by any continuous random distribution in the domain interior and arbitrarily
Roberto Cavoretto +2 more
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Solving Poisson Equations by the MN-Curve Approach
Mathematics, 2022 In this paper, we adopt the choice theory of the shape parameters contained in the smooth radial basis functions to solve Poisson equations. Luh’s choice theory, based on harmonic analysis, is mathematically complicated and applies only to function ...
Lin-Tian Luh
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Numerical Solution of the Advection-Diffusion Equation Using the Radial Basis Function
JTAM (Jurnal Teori dan Aplikasi Matematika), 2023 The advection-diffusion equation is a form of partial differential equation. This equation is also known as the transport equation. The purpose of this research is to approximatio the solution of advection-diffusion equation by numerical approach using ...
La Ode Sabran, Mohamad Syafi'i
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Cardinal interpolation with general multiquadrics [PDF]
Advances in Computational Mathematics, 2016 This paper studies the cardinal interpolation operators associated with the general multiquadrics, $ϕ_{α,c}(x) = (\|x\|^2+c^2)^α$, $x\in\mathbb{R}^d$. These operators take the form $$\mathscr{I}_{α,c}\mathbf{y}(x) = \sum_{j\in\mathbb{Z}^d}y_jL_{α,c}(x-j),\quad\mathbf{y}=(y_j)_{j\in\mathbb{Z}^d},\quad x\in\mathbb{R}^d,$$ where $L_{α,c}$ is a fundamental
Keaton Hamm, Jeff Ledford
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Numerical Simulation of Thermal Field in Mass Concrete With Pipe Water Cooling
Frontiers in Physics, 2021 Water pipe cooling is mainly used to control temperature in the construction of mass concrete structures. It is important to reveal how to accurately stimulate the temperature field of mass concrete under action of this water pipe cooling.
Fuxian Zhu +3 more
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A Direct Prediction of the Shape Parameter in the Collocation Method of Solving Poisson Equation
Mathematics, 2022 In this paper, we totally discard the traditional trial-and-error algorithms of choosing the acceptable shape parameter c in the multiquadrics −c2+∥x∥2 when dealing with differential equations, for example, the Poisson equation, with the RBF collocation ...
Lin-Tian Luh
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Journal of Approximation Theory, 1996 The authors define certain combinations of multiquadrics, denoted as \(\Psi\)-splines, and investigate their properties. In particular, the strong analogy between these \(\Psi\)-splines and the usual polynomial B-splines is pointed out at several places.
Beatson, R.K., Dyn, N.
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