A weighted stabilized lagrange interpolation collocation method for boundary condition identification in 3D electromagnetic inverse scattering

Abstract

The identification of boundary conditions in electromagnetic inverse scattering is of importance in various engineering applications, ranging from geophysical exploration to wireless communication. Conventional numerical methods solving this problem often suffer from the iterative process, leading to inefficiencies and non-convergence. This paper introduces a weighted scheme of the stabilized Lagrange interpolation collocation method (weighted SLICM) to resolve this problem. Weighted SLICM efficiently integrates governing equations, boundary conditions, and measurement conditions using a weighted least squares approach, offering a straightforward single-step solution and obviating the need for iterative processes in traditional methods like the finite element method. By incorporating regularization techniques, weighted SLICM decreases measurement errors which are unavoidable in engineering problems, thereby ensuring high efficiency and accuracy. In addition, characterized as a strong-form collocation method that relies solely on point information but not on grid connectivity, the weighted SLICM is readily extendible to complex three-dimensional applications in electromagnetic inverse scattering. Extensive simulations of benchmark problems show its ability to achieve accurate and stable results in boundary condition identification in electromagnetic inverse scattering problems including 1D, 2D, and 3D environments, highlighting the effectiveness of the weighted SLICM in navigating complex engineering challenges and substantially enriching research methodologies in this area.