Abstract : Wave scattering problems in acoustics, elastodynamics and electromagnetics are important in a large number of applications wherein challenging mathematical and numerical issues require sophisticated methods and techniques to resolve. The study of numerical methods for solving wave scattering problems has been heavily focused by researchers in both mathematical and engineering committees. This symposium devotes to combining experts from different countries and discussing some latest advances in computational modelling and simulation of complex wave phenomena with their application to real-world problems.
[02173] Fast butterfly compressed Hadamard-Babich integrators for Helmholtz equations
Format : Talk at Waseda University
Author(s) :
Jianliang Qian (Michigan State University)
Yang Liu (Lawrence Berkeley National Laboratory)
Abstract : We present a butterfly-compressed representation of the Hadamard-Babich (HB) ansatz for the Green's function of the high-frequency Helmholtz equation in smooth inhomogeneous media. The proposed scheme can accurately model wave propagation in 2D domains with 640 wavelengths per direction and in 3D domains with 54 wavelengths per direction {on a state-the-art supercomputer at Lawrence Berkeley National Laboratory}.
Abstract : We consider an inverse problem for imaging the support of a wave-number-dependent source function. The source function is given by the Fourier transform of some time-dependent source with a priori given radiating period. Using the multi-frequency far-field data at a fixed observation direction, we provide a necessary and sufficient criterion for characterizing the smallest strip containing the support and perpendicular to the observation direction.
[04115] The PML-method for a scattering problem for a local perturbation of an open periodic waveguide
Format : Talk at Waseda University
Author(s) :
Andreas Kirsch (Karlsruher Institut für Technologie)
Ruming Zhang (Technische Universität Berlin)
Abstract : In this talk, we study the convergence of the PML method to approximate wave propagating in an open periodic waveguide. Different from the scattering problem with periodic surfaces, the existence of propagating modes makes things challenging. We apply a complex contour integral method to deal with the difficulty. Finally an exponential convergence of the PML method is proved.
[03704] A PML method for signal-propagation problems in axon
Format : Talk at Waseda University
Author(s) :
Xue Jiang (Beijing University of Technology)
maohui lyu (Chinese Academy of Sciences)
Tao Yin (Chinese Academy of Sciences)
Weiying Zheng (Chinese Academy of Sciences)
Abstract : This talk concerns the modelling of signal propagations in myelinated axons to characterize the functions of the myelin sheath in the neural structure. 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. Using the PML method, we propose an approximate problem. The well-posedness of the PML problem and the exponential convergence of the approximate solution to the exact solution are established.
[01969] Frequency-time Green function acceleration for simulation, optimization and design
Format : Talk at Waseda University
Author(s) :
Oscar P Bruno (Caltech)
Abstract : We present a novel "Interpolated Factored Green Function" method (IFGF), including a massively parallel implementation, for the accelerated evaluation of the integral operators in scattering theory and other areas. The IFGF algorithm runs on a small memory footprint, and it is better suited than other methods for efficient distributed-memory parallelization. A variety of applications will be mentioned, including frequency- and time-domain scattering in interior and exterior domains, atmospheric propagation and metamaterial design.
[03041] Analysis of scattering matrix algorithm
Format : Talk at Waseda University
Author(s) :
Andreas Rathsfeld (Weierstrass Institute for Applied Analysis and Stochastics, Berlin)
Abstract : The scattering matrix algorithm is a popular numerical method for
the diffraction of optical waves by periodic surfaces. The computational
domain is divided into horizontal slices and, by a clever
recursion, an approximated operator, mapping incoming into outgoing waves, is
obtained. Combining this with numerical schemes inside the slices, methods
like RCWA and FMM have been designed. The key for
the analysis is the scattering problem with special radiation conditions
for inhomogeneous cover materials.
[04576] On the coupling schemes of finite element and boundary integral equation methods solving the acoustic/elastic scattering problems
Format : Talk at Waseda University
Author(s) :
Liwei Xu (University of Electronic Science and Technology of China)
Abstract : In this talk, we introduce two coupling schemes of finite element and boundary integral equation methods solving the acoustic/elastic scattering problems. The first one is the coupling of finite element and Fourier series based boundary integral solving the exterior time-harmonic elastic scattering problem. The second is the coupling of discontinuous Galerkin finite element and boundary integral equations solving the fluid-structure interaction problem. Well-posedness of the approximate problems, analysis on the accuracy and stability of numerical schemes, and numerical results will be presented.
[03004] Fast multipole method in layered media: from Helmholtz to Maxwell's equations
Format : Talk at Waseda University
Author(s) :
Bo Wang (LCSM(MOE), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, 410081, P. R. China.)
Abstract : In this talk, a fast multipole method (FMM) for the dyadic Green’s function of Maxwell’s equations in layered isotropic media is presented. As in the homogeneous media, layered dyadic Green’s function (LDGF) of Maxwell’s equation is shown closely related to the Green’s function of Helmholtz equation in layered media. Actually, there are only two essential components in the LDGF.By following the theory developed for the Green’s function of Helmholtz equation, we derive multipole expansions (MEs) and local expansions (LEs) as well as the multipole-to-local translation (M2L) operators for all the reaction field components of the LDGF. Then, the FMMs for the LDGF is implemented with the target particles and equivalent polarization sources associated with the reaction field components. Numerical results validate the fast convergence of the MEs and the O(N) complexity of the FMM for N particle problem in 3-D layered media.
[03722] Dirac points for the honeycomb lattice with impenetrable obstacles
Format : Online Talk on Zoom
Author(s) :
Junshan Lin (Auburn University)
Abstract : Dirac points are special vertices in the band structure when two bands of the spectrum for the operator touch in a linear conical fashion, and their investigations play an important role in the design of novel topological materials. In this talk, I will discuss Dirac points for the honeycomb lattice with impenetrable obstacles arranged periodically in a homogeneous medium. I will discuss both the Dirichlet and Neumann eigenvalue problems and prove the existence of Dirac points for both eigenvalue problems at crossing of the lower band surfaces as well as higher band surfaces. In addition, quantitative analysis for the eigenvalues and the slopes of two conical dispersion surfaces near each Dirac point will be presented by a combination of the layer potential technique and asymptotic analysis.
[03675] Electronic Structure of Incommensurate 2D Heterostructures with Mechanical Relaxation
Format : Online Talk on Zoom
Author(s) :
Daniel Massatt (Louisiana State University)
Abstract : Momentum space transformations for incommensurate 2D electronic structure calculations are fundamental for reducing computational cost and for representing electronic structure data in a more physically motivating format, as exemplified in the Bistritzer-MacDonald model. However, these transformations can be difficult to implement in more complex systems such as when mechanical relaxation patterns are present. In this work, we aim for two objectives. Firstly, we strive to simplify the understanding and implementation of this transformation by rigorously writing the transformations between the four relevant spaces, which we denote real space, configuration space, momentum space, and reciprocal space. This provides a straight-forward algorithm for writing the complex momentum space model from the original real space model. Secondly, we implement this for twisted bilayer graphene with mechanical relaxation affects included. We also analyze the convergence rates of the approximations, and show the tight-binding coupling range increases for smaller relative twists between layers, demonstrating that the 3-nearest neighbor coupling of the Bistritzer-MacDonald model is insufficient when mechanical relaxation is included for very small angles. We quantify this and verify with numerical simulation.
[03832] Structural Symmetry and Fabry-Perot Bound States in the Continuum: A Numerical Study
Format : Talk at Waseda University
Author(s) :
Zitao MAI (City University of Hong Kong)
Ya Yan LU (City University of Hong Kong)
Abstract : Fabry-Perot BIC is a special type of BIC occurs in systems with two parallel identical structures acting as ideal mirrors. Similar phenomena may arise in two-layer periodic dielectric structures by tuning different parameters such as the spacing between two layers. In our study, structures with different symmetry properties are used to verify the existence of Fabry-Perot BIC, and the minimum number of tuning parameters required is also examined.
