Markov Chain Monte Carlo Solution of Laplace’s Equation in Axisymmetric Homogeneous Domain

Abstract

With increasing complexity of today's electromagnetic problems, the need and opportunity to reduce domain sizes, memory requirement, computational time and possibility of errors abound for symmetric domains. With several competing computational methods in recent times, methods with little or no iterations are generally preferred as they tend to consume less computer memory resources and time. This paper presents the application of simple and efficient Markov Chain Monte Carlo (MCMC) method to the Laplace's equation in axisymmetric homogeneous domains. Two cases of axisymmetric homogeneous problems are considered. Simulation results for analytical, finite difference and MCMC solutions are reported. The results obtained from the MCMC method agree with analytical and finite difference solutions. However, the MCMC method has the advantage that its implementation is simple and fast.

FDTD Modeling of Au/Ag Nanoparticles Incorporated Au/Ag Photonic Crystal for Seeking the Maximal Localized Electric Field

“…To fulfill the requirements of large-scale simulations, take solving electromagnetic problems of complex structures as an example, many numerical approaches are available, such as finite difference time domain (FDTD), the finite element methods, Monte Carlo, Harrington method of moment, boundary-integral equations, Fourier expansion, and so on. [29,30] Among these approaches, FDTD is widely used in computational electromagnetic models because of its high precision in the description of geometry and material, easy accessibility, low computational costs, and free divergence nature. [31] Furthermore, FDTD is also suitable for solving the scattering problem of periodic dielectric structures.…”