Barycentric rational interpolation method of the Helmholtz equation with irregular domain

Abstract

In the work, a numerical method of the 2D Helmholtz equation with meshless interpolation collocation method is developed, which is defined in arbitrary domain with irregular shape. In our numerical method, based on the Chebyshev points, the partial derivatives and the spatial variables are discretized by the barycentric rational form basis function. After that the differential equations are simplified by employing differential matrix. To verify the the accuracy, effectiveness and stability in our method, some numerical tests based on the three types of different test points are adopted. Moreover, we can also verify that present method can be applied to both variable wave number problems and high wave number problems.

Keywords

• barycentric rational interpolation
• meshless method
• irregular domain
• Helmholtz equation
• variable wave number