Optimal shape parameter in the MQ-RBF by minimizing an energy gap functional

DOI10.1016/j.aml.2018.06.031zbMath1411.35085OpenAlexW2810993265MaRDI QIDQ1726449

Dongjie Liu, Chein-Shan Liu

Publication date: 20 February 2019

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2018.06.031

zbMATH Keywords

Cauchy problemLaplace equationoptimal shape parameterenergy gap functionalminimizing energy gap functional

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for partial differential equations, boundary value problems (65N99)

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Cites Work

• On the increasingly flat radial basis function and optimal shape parameter for the solution of elliptic PDEs
• Multiquadric and its shape parameter -- a numerical investigation of error estimate, condition number, and round-off error by arbitrary precision computation
• Optimal constant shape parameter for multiquadric based RBF-FD method
• A multiple-scale MQ-RBF for solving the inverse Cauchy problems in arbitrary plane domain
• Doubly stochastic radial basis function methods
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method
• An algorithm for selecting a good value for the parameter \(c\) in radial basis function interpolation
• The sample solution approach for determination of the optimal shape parameter in the multiquadric function of the Kansa method

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