A high-efficient splitting step reduced-dimension pure meshless method for transient 2D/3D Maxwell's equations in complex irregular domain

In this work, a high-efficient and accurate pure meshless method is designated as splitting step reduced-dimension finite pointset method, which is first proposed to solve the time-dependent 2D/3D Maxwell equations in lossy medium with periodic or perfect conducting boundary condition. The proposed method is mainly motivated by following three points. (a) The coupled 2D/3D Maxwell equations are decomposed into several mutually uncoupled 1D partial differential equations through a splitting step method. (b) The space-derivatives of the above those 1D systems are discretized by the 1D finite pointset method based on the Taylor expansion and the weighted least squares method. Meanwhile, the time-derivatives are approximated by second-order scheme. (c) The local refinement technique is adopted at the selected region to improve the numerical accuracy, and the multi-CPUs parallel computing is used to enhance the computational efficiency. All the numerical results show the proposed scheme has second-order convergence rate, and which has higher computational efficiency than the traditional finite pointset method for solving the 2D/3D Maxwell equations, especially for the case of 3D problems or higher-order Taylor expansion in finite pointset method. Subsequently, the advantage of the proposed scheme applied in complex irregular domain is illustrated.