TY  - EJOU
AU  - Yang, Miaomiao 
AU  - Ma, Wentao 
AU  - Ge, Yongbin 

TI  - A Meshless Collocation Method with Barycentric Lagrange Interpolation for Solving the Helmholtz Equation
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2021
VL  - 126
IS  - 1
SN  - 1526-1506

AB  - In this paper, Chebyshev interpolation nodes and barycentric Lagrange interpolation basis function are used to
deduce the scheme for solving the Helmholtz equation. First of all, the interpolation basis function is applied to
treat the spatial variables and their partial derivatives, and the collocation method for solving the second order
differential equations is established. Secondly, the differential equations on a given test node. Finally, based on three kinds of test nodes, numerical experiments show that
the present scheme can not only calculate the high wave numbers problems, but also calculate the variable wave
numbers problems. In addition, the algorithm has the advantages of high calculation accuracy, good numerical
stability and less time consuming.
KW  - Helmholtz equation; Chebyshev interpolation nodes; Barycentric Lagrange interpolation; meshless collocation method; high wave number; variable wave number

DO  - 10.32604/cmes.2021.012575