講座題目：Discontinuous Galerkin method for nonlinear Maxwell equations
主講人： 呂茂輝 北京郵電大學(xué) 特聘副研究員
講座時(shí)間： 2024年6月28日 (星期五) 14:00-15:30
講座地點(diǎn)：清水河校區(qū)六號(hào)科研樓A344
主講人簡(jiǎn)介： 呂茂輝, 北京郵電大學(xué)副研究員，碩士生導(dǎo)師。重慶大學(xué)理學(xué)博士學(xué)位，2018年-2019年受國家留學(xué)基金委資助訪問美國倫斯勒理工學(xué)院數(shù)學(xué)科學(xué)系，2020年-2023年在中科院計(jì)算數(shù)學(xué)與科學(xué)工程計(jì)算研究所從事博士后工作。主持中國博士后科學(xué)基金特別資助項(xiàng)目、國家自然科學(xué)基金青年基金項(xiàng)目等。研究方向包括電磁波傳播問題的高階間斷伽遼金方法和有限元方法、界面問題的高階數(shù)值方法等。主要成果發(fā)表于Journal of Computational Physics, SIAM Journal on Applied Mathematics和Journal of Scientific Computing等期刊上。
講座內(nèi)容：In this talk, we consider the time domain Maxwell equations that augmented with a class of nonlinear constitutive polarization laws in high dimensions. The nontrivial discrete temporal treatment of the nonlinearity in the ordinary differential equations that encode the Kerr and Raman effects (Bokil et al. 2017), is first generalized to higher spatial dimensions. To further improve the computational efficiency in dealing with the nonlinearity, we apply nodal DG methods in space. Energy stability is proved for the semi-discrete in time and in space schemes as well as for the fully-discrete schemes. Under some assumptions on the strength of nonlinearity, error estimates are established for the semi-discrete in space methods, and, in particular, optimal accuracy is achieved for the methods on Cartesian meshes with Qk-type elements and alternating fluxes. Attention is paid to the role of the nodal form of the DG discretizations in the analysis. We will also present a second order linear scheme for the nonlinear Maxwell equations. Numerical examples are presented to validate the accuracy, energy stability, and computational efficiency of the proposed schemes. We further illustrate the performance of the methods through physically relevant experiments involving spatial soliton propagation and airhole scattering in realistic glasses.
