Stability and accuracy of Engquist–Majda absorbing boundary condition for pseudo spectral time domain method

Abstract

Lagrange polynomials based Chebyshev Pseudo Spectral Time Domain (L-CPSTD) method is an accurate time domain solver for electromagnetic problems. It utilizes the Lagrange interpolation polynomials to expand electromagnetic fields. This global interpolation, which uses all field values on all of the grid points to calculate the value at a single point, provides spectral accuracy. However, absorbing boundary conditions (ABCs) must be applied for open space problems. Engquist-Majda ABC is an important one due to its simplicity. Characteristic variables (CVs) can be used to implement the ABCs. In this article, for the first time, stability and accuracy of the Engquist-Majda ABC are proved by using the CVs in the L-CPSTD solution of Maxwell's equations. The theoretical findings are verified by using the matrix eigenvalue method and the reflection coefficient in one and two dimensional open space examples. The numerical result is also validated by an analytical and an FDTD solution of a parallel-plate waveguide problem. The efficiency of the proposed ABC is clearly shown.