Weighted Radial Basis Collocation Method for the Nonlinear Inverse Helmholtz Problems

In this paper, a meshfree weighted radial basis collocation method associated with the Newton’s iteration is introduced to solve nonlinear inverse Helmholtz problems for identifying parameter. All measurement data can be included in least-squares solution, which avoid calculations comparing solutions part of Galerkin-based methods. Appropriate weights are imposed on boundary conditions and balance errors, leads high accuracy optimal convergence solving problems. Moreover, it quite easy extend solution process one-dimensional problem high-dimensional problem. Nonlinear numerical examples include one-, two- three-dimensional constant varying parameter identification regular irregular domains show exponential presented method.