Solving a one-dimensional moving boundary problem based on wave digital principles

Abstract

We report on a novel method for solving one-dimensional moving boundary problems based on wave digital principles. Here, we exploit multidimensional wave digital algorithms to derive an efficient and robust algorithm for the solution of the considered problem. Our method lets the wave digital model, on which the algorithm is based, expand according to the size of the solution domain. The expanding model introduces new dynamical elements, which must be properly initialized to obtain a calculable algorithm. To deal with this problem, we make use of linear multistep methods to extrapolate the missing values. Our results show the proposed method to indeed be capable of correctly solving a one-dimensional partial differential equation describing a growing biological axon.

Oscillator networks with N‐shaped nonlinearities: Electrical modeling and wave digital emulation

“…Second, it breaks the delay-free loop in the WD domain, yielding significant speedups in simulation time, while still correctly modeling an ideal circuit. [41][42][43] In the WD domain, a transmission line equals a delay in the path of both the incident and reflected wave as depicted in Figure 4, marked by the blue dashed box. That is equal to a 4-port circulator with two capacitors with capacitance C, dictating the port resistance R T ¼ T= 2C ½ .…”