鲁汪涛 - 浙江大学 - 数学科学学院

个人简介

2007年中国科学技术大学学士，2012年中国科学技术大学博士，并于同年获得香港城市大学联合培养博士学位，导师陆雅言教授，陈发来教授。2017年8月回浙大工作至今。教学与课程浙江大学： 2018年冬学期数值计算方法 2018年春夏学期微积分（II) 甲 Michigan State University: 2015年秋季学期， MTH234, 微积分III 2014年秋季学期， MTH132, 微积分I 科研研究正反散射问题，光子学中的数学建模和科学计算方法，以及高频电磁波传播问题，成果如下：首次将边界积分方程法和完美匹配层（PML）方法结合起来求解分层介质中分界面具有局部扰动的波散射问题。由此开发的数值方法在具有高精度且无需计算背景空间的Green函数，因此计算复杂度比以往的高精度数值算法低。开发了一种利用边界积分方程法计算光波导中导模的高精度计算方法。对于具有光波导该方法可非常有效处理光（电磁）波在角点处的奇异行结构的光波导。首次提出了针对向量化点源Maxwell方程在非均匀介质中的Green函数的高频率下的解形式。同时提出了解形式中未知量在点源附近的渐进形式，即源处边界条件，并开发了高阶的格式去计算解形式中的未知量。招生信息课题组长期招收优秀硕士、博士研究生。对本方向感兴趣学生请准备成绩单和1页CV，发送至本人邮箱。

研究领域

正反散射问题光学、电磁学数学建模和数值计算高频电磁波传播

近期论文

查看导师最新文章（温馨提示：请注意重名现象，建议点开原文通过作者单位确认）

Wangtao Lu*, Mathematical analysis of wave radiation by a step-like surface, SIAM J. Applied Math., to appear, 2021. Jianliang Qian, Jian Song, Wangtao Lu and Rober Burridge, Hadamard-Babich ansatz for point-source elastic wave equations in variable media at high frequencies, SIAM Multlscale Modeling and Simulations, 19(1), 46–86, 2021. https://doi.org/10.1137/20M1322224 Jiaxin Zhou and Wangtao Lu*, Resonance Frequencies of a Slab with Subwavelength Slits: a Fourier-transformation Approach, submitted, arXiv preprint arXiv:2012.13691, 2020. Wangtao Lu, Jun Lai and Haijun Wu, On Wellposedness and Convergence of UPML method for analyzing wave scattering in layered media, submitted, arXiv preprint arXiv:1910.13932, 2020. Wangtao Lu and Guanghui Hu, Time-harmonic acoustic scattering from a non-locally perturbed trapezoidal surface, SIAM J. Sci. Comp., 41(3), B522-B544, 2019. https://doi.org/10.1137/18M1216195 Wangtao Lu*, Ya Yan Lu and Dawei Song, A numerical mode matching method for wave scattering in a layered medium with a stratified inhomogeneity, SIAM J. Sci. Comput., 41(2), B274–B294, 2019. https://doi.org/10.1137/18M1182693 Wangtao Lu, Jianliang Qian and Robert Burridge, Extending Babich's ansatz for point-source Maxwell's equations using Hadamard's method, SIAM Multlscale Modeling and Simulations, 16(2), 727–751, 2018. https://doi.org/10.1137/17M1130381 Wangtao Lu*, Ya Yan Lu and Jianliang Qian, Perfectly-matched-layer boundary integral equation method for wave scattering in a layered medium, SIAM J. Applied Math., 2018, 78(1), 246-265. https://doi.org/10.1137/17M1112510. Wenbin Li, Wangtao Lu, Jianliang Qian and Yaoguo Li, A multiple level set method for three-dimensional inversion of magnetic data, Geophysics, 2017, 82(5), J61-J81.https://doi.org/10.1190/geo2016-0530.1. Wangtao Lu, Jianliang Qian and Robert Burridge, Babich-like ansatz for three-dimensional point-source Maxwell's equations in an inhomogeneous medium at high frequencies, SIAM Multiscale Modeling and Simulation, vol. 14, No. 3, 2016. https://doi.org/10.1137/15M1052469. Jianliang Qian, Wangtao Lu, Lijun Yuan, Songtin Luo and Robert Burridge, Eulerian geometrical optics and fast Huygens sweeping methods for three-dimensional time-harmonic high-frequency Maxwell's equations in inhomogeneous media, SIAM Multiscale Modeling and Simulation, vol. 14, No. 2, 2016. https://doi.org/10.1137/15M1013158. Wangtao Lu, Jianliang Qian and Robert Burridge, Babich's expansion and the fast Huygens sweeping method for the Helmholtz wave equation at high frequencies, Journal of Computational Physics, vol. 313, 478-510, 2016. https://doi.org/10.1016/j.jcp.2016.02.048. Wenbin Li, Wangtao Lu and Jianliang Qian, A level set method for imaging salt structure using gravity data, Geophysics, 81(2), G27-G40, 2015. https://doi.org/10.1190/geo2015-0295.1. Wangtao Lu, Shingyu Leung, and Jianliang Qian, An improved fast local level set method for three-dimensional inverse gravimetry, Inverse Problem and Imaging, 9(2), 479-509, 2015. https://doi.org/10.3934/ipi.2015.9.479 Wangtao Lu and Jianliang Qian, A local level set method for three-dimensional inversion of gravity gradient data, Geophysics, 80, G35-G51, 2015. https://doi.org/10.1190/geo2014-0188.1 Wangtao Lu and Ya Yan Lu, Efficient high order waveguide mode solvers based on boundary integral equations, Journal of Computational Physics, 272, 507-525, 2014. https://doi.org/10.1016/j.jcp.2014.04.028 Wangtao Lu and Ya Yan Lu, Efficient boundary integral equation method for photonic crystal fibers, Journal of Lightwave Technology, 20(11), 1610-1616, 2012. https://doi.org/10.1109/JLT.2012.2189355 Wangtao Lu and Ya Yan Lu, High order integral equation method for diffraction gratings, Journal of the Optical Society of America A, 29(5), 734-740, 2012. https://doi.org/10.1364/JOSAA.29.000734 Wangtao Lu and Ya Yan Lu, Waveguide mode solver based on Neumann-to-Dirichlet operators and boundary integral equations, Journal of Computational Physics, 231(4), 1360-1371, 2012. https://doi.org/10.1016/j.jcp.2011.10.016 Huan Xie, Wangtao Lu and Ya Yan Lu, Complex modes and instability of full-vectorial beam propagation methods, Optics Letters, 36, 2474-2476, 2011. https://doi.org/10.1364/OL.36.002474