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Kansa, E.J. and Carlson, R.E. (1992) Improved Accuracy of Multiquadric Interpolation Using Variable Shape Parameters. Computers & Mathematics with Applications, 24, 99-120.
https://doi.org/10.1016/0898-1221(92)90174-g

has been cited by the following article:

• TITLE: Numerical Simulation of Dam-Break Flows Using Radial Basis Functions: Application to Urban Flood Inundation

  AUTHORS: Abdoulhafar Halassi Bacar, Said Charriffaini Rawhoudine

  KEYWORDS: Dam-Break Flows, Numerical Simulation, Shallow Water Equations, Radial Basis Functions, Urban Flood Inundation

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.14 No.3, September 20, 2024

  ABSTRACT: Dam-break flows pose significant threats to urban areas due to their potential for causing rapid and extensive flooding. Traditional numerical methods for simulating these events struggle with complex urban landscapes. This paper presents an alternative approach using Radial Basis Functions to simulate dam-break flows and their impact on urban flood inundation. The proposed method adapts a new strategy based on Particle Swarm Optimization for variable shape parameter selection on meshfree formulation to enhance the numerical stability and convergence of the simulation. The method’s accuracy and efficiency are demonstrated through numerical experiments, including well-known partial and circular dam-break problems and an idealized city with a single building, highlighting its potential as a valuable tool for urban flood risk management.