Multiple 1-D Fundamental ADI-FDTD Method for Coupled Transmission Lines on Mobile Devices

Abstract

This article presents the multiple one-dimensional (M1-D) fundamental alternating direction implicit (FADI) finite-difference time-domain (FDTD) method for coupled transmission lines on mobile devices. The method is aptly called the M1-D FADI coupled line (CL)-FDTD method. It is based on the fundamental implicit scheme, which features matrix-operator-free right-hand sides (RHS). The formulations of the M1-D FADI CL-FDTD method and update equations are provided. Various sets of split matrices, including those with self-symmetry, mutual symmetry, and self-mutual separation, are proposed and discussed. Their stability analyses are performed using the Fourier amplification matrix formulated in fundamental form, which is simpler with only one inverse term each without RHS operator. It is found that the sets of split matrices with self-symmetry are unconditionally stable, while those with mutual symmetry and self-mutual separation are not. Using two auxiliary quadratic polynomials along with single necessary and sufficient condition, the analytical proof of unconditional stability is made more convenient and concise. The efficiency of both stable sets of split matrices with self-symmetry is discussed based on the number of RHS terms and floating-point operations count. Numerical results are presented to validate the accuracy of the proposed method at time step larger than the stability limit. Several electromagnetic (EM) simulations of coupled line structures are demonstrated on mobile devices. The CPU time incurred on various platforms is provided for the M1-D FADI CL-FDTD method using both sets of split matrices with self-symmetry. Using mobile devices, the EM simulations can be performed efficiently and ubiquitously anytime, anywhere.