arXiv subjects

Maohui Lyu

Publications and source records attributed to Maohui Lyu.

3 recordsLinked to original sources

arXiv2023

A high order unfitted finite element method for time-Harmonic Maxwell interface problems

We propose a high order unfitted finite element method for solving timeharmonic Maxwell interface problems. The unfitted finite element method is based on a mixed formulation in the discontinuous Galerkin framework on a Cartesian mesh with possible hanging nodes. The $H^2$ regularity of the solution to Maxwell interface problems with $C^2$ interfaces in each subdomain is proved. Practical interface-resolving mesh conditions are introduced under which the hp inverse estimates on three-dimensional curved domains are proved. Stability and hp a priori error estimate of the unfitted finite element method are proved. Numerical results are included to illustrate the performance of the method.

math.NA↗

arXiv2022

A PML method for signal-propagation problems in axon

This work is focused on the modelling of signal propagations in myelinated axons to characterize the functions of the myelin sheath in the neural structure. Based on reasonable assumptions on the medium properties, we derive a two-dimensional neural-signaling model in cylindrical coordinates from the time-harmonic Maxwell's equations. The well-posedness of model is established upon Dirichlet boundary conditions at the two ends of the neural structure and the radiative condition in the radial direction of the structure. Using the perfectly matched layer (PML) method, we truncate the unbounded background medium and propose an approximate problem on the truncated domain. The well-posedness of the PML problem and the exponential convergence of the approximate solution to the exact solution are established. Numerical experiments based on finite element discretization are presented to demonstrate the theoretical results and the efficiency of our methods to simulate the signal propagation in axons.

math.NA↗

arXiv2019

Numerical simulation of a coupled system of Maxwell equations and a gas dynamic model

It is known that both linear and nonlinear optical phenomena can be produced when the plasmon in metallic nanostructures are excited by the external electromagnetic waves. In this work, a coupled system of Maxwell equations and a gas dynamic model including a quantum pressure term is employed to simulate the plasmon dynamics of free electron fluid in different metallic nanostructures using a discontinuous Galerkin method in two dimensions. Numerical benchmarks demonstrate that the proposed numerical method can simulate both the high order harmonic generation and the nonlocal effect from metallic nanostructures. Based on the switch-on-and-off investigation, we can conclude that the quantum pressure term in gas dynamics is responsible for the bulk plasmon resonance. In addition, for the dielectric-filled nano-cavity, a coupled effective polarization model is further adopted to investigate the optical behavior of bound electrons. Concerning the numerical setting in this work, a strengthened influence of bound electrons on the generation of high order harmonic waves has been observed.

physics.comp-ph↗