An Improved Collocation Meshless Method Based on the Variable Shaped Radial Basis Function for the Solution of the Interior Acoustic Problems

Table 1

Typical radial basis functions with dimensionless shape parameters.

Name	Expression	Shape parameter
Multiquadrics (MQ)	𝑅𝑖(𝑟)=(𝑟^2+(𝜀𝑙)^2)^𝑞	𝜀≥0,𝑞
Inverse multiquadrics (IMQ)	𝑅𝑖(𝑟)=(𝑟^2+(𝜀𝑙)^2)^−𝑞	𝜀≥0,𝑞
Gaussian (GA)	𝑅𝑖(𝑟)=exp[−𝜀(𝑟/𝑙)^2]	𝜀
Thin plate spline (TPS)	𝑅𝑖(𝑟)=𝑟^𝜂	𝜂

Note: 𝑙 is a characteristic length that relates to the nodal spacing in the computational domain.