WAVES 2017: 13TH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND NUMERICAL ASPECTS OF WAVE PROPAGATION
PROGRAM FOR WEDNESDAY, MAY 17TH
Days:
previous day
next day
all days

View: session overviewtalk overview

08:30-09:30 Session 13: Surface Water Waves over Bathymetry

Plenary Lecture

Location: Coffman Theater
08:30
Surface Water Waves over Bathymetry

ABSTRACT. We examine the effect of a periodic bottom on the free surface of a fluid linearized near the stationary state, and we develop a Bloch theory for the linearized water wave system. This analysis takes the form of a spectral problem for the Dirichlet – Neumann operator of the fluid domain with periodic bathymetry.

10:00-12:00 Session 14A: Nonlinear Waves in Mechanical Metamaterials and Phononic Crystals

Minisymposium

Location: Mississippi Room
10:00
Adiabatically propagating phase boundaries in non-linear chains with twist and stretch

ABSTRACT. Mass-spring chains with only extensional degrees of freedom have for long provided insights into the behavior of crystalline solids. Here we add rotational degrees of freedom to the masses in a chain and study the dynamics of phase boundaries across which both twist and stretch can jump. Surprisingly, for some combinations of parameters characterizing the energy landscape of our springs we find propagating phase boundaries for which the rate of dissipation, as calculated using isothermal expressions for the driving force, is negative. This suggests that we cannot neglect the energy stored in the oscillations of the masses in the interpretation of the dynamics of mass-spring chains. Thus, we define a local temperature of our chain and show that it jumps across phase boundaries, but not across sonic waves. Hence, impact problems in our mass-spring chains are analogous to those on continuum thermoelastic bars with Mie-Gruneisen type constitutive laws.

10:30
Nonlinear hysteretic propagation of torsional waves in a granular chain

ABSTRACT. The propagation of torsional waves in a 1D granular chain made of self-hanged magnetic beads is considered in this work. Due to the torsional coupling between beads, the propagation medium is purely nonlinear hysteretic, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. Specifically, we consider the propagation of large amplitude signals, reaching a strongly nonlinear regime, beyond the limits of the quadratic hysteretic approximation. In this regime, total torsional sliding at the contacts may be observed and strong saturation effects are expected. These results could be of fundamental interest but may also find potential applications in nonlinear wave control devices.

11:00
Wave Stability and Invariance in Nonlinear Periodic Media
SPEAKER: Matthew Fronk

ABSTRACT. This paper presents higher-order, multiple scales perturbation analyses of nonlinear periodic systems with the goal of predicting invariant, multi-harmonic waveforms of infinite extent. The multiple scales analysis is also used to study waveform stability, which is shown to be amplitude-dependent. Using example quadratic and cubic chains characterized by dimensionless parameters described herein, numerical studies confirm both amplitude-dependent stability and less temporal growth/decay in spectral content of the predicted waveforms as higher-order approximations are employed. Considering the invariance and stability behavior of the predicted waves, the study results suggest that higher-order multiple scales perturbation analysis captures long-term, non-localized invariant waves, which have the potential for propagating coherent information over long distances.

11:30
Resonant activation of Optoacoustic Functionalities in Phononic Crystals

ABSTRACT. We present a strategy to adaptively manipulate the spatial characteristics of propagating elastic waves in nonlinear phononic crystals. Our approach exploits the interplay of dispersion and nonlinearity to reversibly activate modal characteristics corresponding to higher frequencies even while operating in low-frequency acoustic regimes. This effect, studied here using the well-known nonlinear three-wave resonance mechanism, is demonstrated via numerical simulations for a broad class of phononic crystal architectures exhibiting a wide spectrum of functionality tuning capabilities.

10:00-12:00 Session 14B: Contributed Talks
Location: President's Room
10:00
Faraday cages, homogenized boundary conditions and resonance effects
SPEAKER: David Hewett

ABSTRACT. We study electromagnetic shielding by a cage of perfectly conducting wires - the `Faraday cage effect'. In the limit as the number of wires tends to infinity we derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. For wires of sufficiently large radius there are resonance effects: at wavenumbers close to the natural resonances of the equivalent solid shell, the cage actually amplifies the incident field, rather than shielding it. By modifying the continuum model we can calculate the wavenumbers giving the largest response, along with the associated peak amplitudes.

10:30
Acoustic scattering by inhomogeneous media with piecewise smooth material properties

ABSTRACT. We provide a generalization, in both two and three dimensions, of the volume-surface integral equation formulation given in [SIAM J. Appl. Math., 297-308, 2003], for acoustic scattering by inhomogeneous media to the case where the material properties have jump discontinuities within the scattering inhomogeneity. We also discuss a Nyström numerical solution methodology that relies on analytic resolution of singularities to achieve rapidly convergent integration scheme while employing an FFT based interpolation strategy for accurate approximations of differential operators.

11:00
Scattering from a row of aligned cylinders of arbitrary cross-section; tail-end asymptotics for efficient evaluation of the periodic Green's function

ABSTRACT. The problem of wave scattering from a periodic row of parallel cylinders, of arbitrary cross-section is studied via the boundary element method (BEM). The standard procedure of introducing the periodic Green's function is followed to give rise to a simplified integral equation. However, in general this requires the computation of an infinite sum that is slow to converge. Here a novel method is presented in order to approximate this infinite sum via a finite sum and asymptotic corrections; the scheme is rapidly convergent and straightforward to implement for cylinders of arbitrary cross-section. Numerical results for the transmission and reflection coefficients from arrays with different cross sections are obtained.

11:30
Acoustic Scattering by Spheres and Spheroids in the Time Domain
SPEAKER: Paul Martin

ABSTRACT. The title problems are treated using Laplace transforms and separation of variables. This approach has been used for spheres since the 1950s. When applied to spheroids, we encounter new questions, such as how do spheroidal wavefunctions behave for complex parameters? We describe our recent work in this direction.

10:00-12:00 Session 14C: Contributed Talks
Location: Room 324
10:00
A mixed quasi-reversibility approach to identify obstacles in an acoustic waveguide

ABSTRACT. We consider an inverse obstacle problem in an acoustic waveguide using a single incident wave, which we solve with the help of an ``exterior approach" coupling a mixed formulation of quasi-reversibility and a simple level set method.

10:30
Imaging defects in an elastic waveguide using time-dependent surface data

ABSTRACT. We are interested here in using the Linear Sampling Method in its modal form to image defects in an elastic waveguide by using realistic scattering data, that is data coming from sources and receivers on the surface of the waveguide in the time domain, as it has already been done in the acoustic case.

11:00
Time dependent inverse scattering in a waveguide
SPEAKER: Peter Monk

ABSTRACT. We study the inverse problem of determining the shape of sound soft inclusions in a sound hard waveguide using time domain data. We prove existence and uniqueness for the forward problem, and derive a numerical method using time domain integral equations. For the in- verse problem we suggest to use a time domain version of the Linear Sampling Method. After analysis of the time domain inversion scheme, we provide numerical examples.

11:30
Efficient Forward and Inverse Algorithms for Guided Wave Inversion
SPEAKER: Ali Vaziri

ABSTRACT. Guided waves are widely utilized for estimating the medium properties through inversion of the dispersion curves. This work presents improved methodologies for computing both dispersion curves and their derivatives, the two main ingredients of guided wave inversion. Specifically, a novel discretization approach, named complex-length finite element method (CFEM), is developed for the computation of dispersion curves, which requires much fewer elements than existing methods. Similarly, a new formulation is developed to compute the derivatives of the dispersion curves without resorting to finite difference approximation, leading to better accuracy and efficiency. As confirmed by synthetic and real-life inversion examples, these algorithms result in more accurate estimates of the medium characteristics than the traditional methods, at a small fraction of computational effort.

10:00-12:00 Session 14D: Contributed Talks
Location: Room 325
10:00
On the Local Approximate Rank of Helmholtz Green’s Kernel

ABSTRACT. The boundary elements method (BEM) leads to dense linear systems whose size grows rapidly in practice; hence the need for fast methods. The H-matrix method has been introduced and justified for asymptotically smooth kernels. However, it leads to results above expectations for relatively high-frequency wave problems.

A H-matrix is a compressed tree-based hierarchical representation of the data associated with an admissibility criterion to separate the near and far fields. An admissible block reads then as a $UV^T$ rank deficient matrix.

An original frequency-dependent criterion based on the Fresnel diffraction area is presented for wave problems and a sharp estimate of the rank of a high-frequency Fresnel-admissible block is derived from the band-limited functions theory.

The rank of a Fresnel-admissible block is eventually shown to be at most linear with the frequency for any prescribed accuracy.

10:30
Eigenvalue analysis with the boundary element method and the contour integral method for periodic boundary value problems for Helmholtz’ equation in 3D
SPEAKER: Kazuki Niino

ABSTRACT. An eigenvalue analysis of periodic boundary value problems for Helmholtz’ equation in 3D with the boundary element method (BEM) and the Sakurai-Sugiura method (SSM) is proposed. The SSM is one of numerical methods for non-linear eigenvalue problems. This method obtains eigen- values inside a fixed contour in the complex plane by calculating an integral along the con- tour. In this paper, we extend integral opera- tors in the BEM to complex phase factor in or- der to calculate the contour integral. With this calculation, we develop an eigenvalue analysis for Helmholtz’ equation in 3D with the BEM and the SSM.

11:00
Transparent Boundary Conditions for the Wave Propagation in Fractal Trees
SPEAKER: Patrick Joly

ABSTRACT. This work is dedicated to an efficient resolution of the wave equation in self-similar trees (e.g. wave propagation in a human lung). In this case it is possible to avoid computing the solution at deeper levels of the tree by using the transparent boundary conditions. The corresponding DtN operator is defined by a functional equation in the frequency domain. In this work we propose and compare two approaches to the discretization of this operator in the time domain. The first one is based on the multistep convolution quadrature, while the second one stems from the rational approximations.

11:30
On the efficiency of an ADI splitting combined with a discontinuous Galerkin discretization
SPEAKER: Jonas Köhler

ABSTRACT. We consider the alternating direction implicit (ADI) method for the time-integration of Maxwell's equations with linear, isotropic material properties on a cuboid. The main advantage of this method is unconditional stability, while only being of linear complexity if combined with finite differences on a Yee grid.

In this paper we combine the ADI method with a discontinuous Galerkin (dG) discretization in space. We show that for regular meshes consisting of cuboids the method can be implemented with optimal (linear) complexity. Our work in progress consists of proving error bounds which are uniform in the mesh discretization parameter.

10:00-12:00 Session 14E: Contributed Talks
Location: Room 326
10:00
Elastic waves in a soft electrically conducting solid in a strong magnetic field
SPEAKER: Paul Barbone

ABSTRACT. Shear wave motion of a soft, electrically-conducting solid in the presence of a strong magnetic field excites eddy currents in the solid. These, in turn, give rise to Lorentz forces that resist the wave motion. We derive a mathematical model for linear elastic wave propagation in a soft elec- trically conducting solid in the presence of a strong magnetic field. The model reduces to an effective anisotropic dissipation term resem- bling an anisotropic viscous foundation. The application to magnetic resonance elastography, which uses strong magnetic fields to measure shear wave speed in soft tissues for diagnostic purposes, is considered.

10:30
Minnaert Resonances for Acoustic Waves in Bubbly Media

ABSTRACT. Through the application of layer potential techniques and Gohberg-Sigal theory we derive an original formula for the Minnaert resonance frequencies of arbitrarily shaped bubbles along with providing a mathematical justification for the monopole approximation of scattering of acoustic waves by bubbles at their Minnaert resonant frequency. Our results are complemented by several numerical examples which serve to validate our formula in two dimensions.

11:00
Shear waves in prestrained poroelastic media
SPEAKER: Paul Barbone

ABSTRACT. Shear wave elastography measures shear wave speed in soft tissues for diagnostic purposes. In [1,2], shear wave speed was shown to depend on prestrain, but not necessarily prestress, in a perfused canine liver. We model this phe- nomenon by examining incremental waves in a pressurized poroelastic medium with incom- pressible phases. The analysis suggests novel restrictions on the strain energy functions for soft tissues.

11:30
Semidiscrete evolution of elastic waves in a piezoelectric solid
SPEAKER: Thomas Brown

ABSTRACT. We consider a model problem of the propagation of elastic waves which are coupled with an electric field inside a piezoelectic solid as well as the discretization of this problem in space. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing electric field. The system is closed using Gauss's law for the associated electric displacement. We use a first order in time and space differential system to study the well-posedness of both problems. This requires the use of an elliptic lifting operator. In the semidiscrete case we formulate the problem corresponding to an abstract Finite Element discretization in the electric and elastic fields.

13:30-14:30 Session 15: BVP and BIE Formulations for Scattering by Fractal Screens

Plenary Lecture

Location: Coffman Theater
13:30
BVP and BIE Formulations for Scattering by Fractal Screens

ABSTRACT. There are various formulations as BVPs or BIEs (boundary integral equations) for screen scattering problems in acoustics, all equivalent when the screen occupies a bounded open Lipschitz subset of the plane. Motivated by applications in electromagnetics and ultrasonics we explore what happens when the screen is less regular, in particular fractal or with fractal boundary. The standard formulations divide into an infinite family of well-posed BVP and equivalent BIE formulations, with infinitely many distinct solutions. We use ``limiting geometry'' arguments to select physically appropriate solutions, and illustrate numerically the surprising new effects that arise.

15:00-16:30 Session 16A: Nonlinear Waves in Mechanical Metamaterials and Phononic Crystals

Minisymposium

Location: Mississippi Room
15:00
Breathers and Passive Wave Redirection in Forced Ordered Granular Networks

ABSTRACT. We study passive pulse redirection in a granular network of two semi-infinite, ordered homogeneous granular chains mounted on linear elastic foundations and coupled by weak linear stiffnesses. A series of repetitive half-sine pulses is applied to an “excited chain”, whereas the “absorbing” chain is initially at rest. Passive pulse redirection from the excited to the absorbing chain can be achieved by macro-scale realization of the Landau-Zener quantum tunneling effect, induced by a stratification of the elastic foundation of the excited chain. Irreversible wave redirection in the forced network happens through sustained 1:1 resonance capture, whereas recurring nonlinear beats between the two chains occur in the absence of resonance capture.

15:30
Localized time-periodic solutions of nonlinear wave equations

ABSTRACT. We collect some results obtained recently for time-periodic solutions of nonlinear wave equations. The model problem arises from Maxwell's equations in the presence of nonlinear material responses. The emphasis will be on the aspect of localization, i.e., the effect of having solutions that decay to zero in the (unbounded) spatial directions.

16:00
Analytic solutions to the extended Korteweg – de Vries equation

ABSTRACT. Over the last few decades, the KdV equation has been extended to include higher order effects. Although this equation has only one conservation law, exact periodic and solitonic solutions are shown to exist.

15:00-16:30 Session 16B: Contributed Talks
Location: President's Room
15:00
Quasi-Stable Dynamics of a Mode-Locked Laser
SPEAKER: Yiming Yu

ABSTRACT. We study the quasi-stable dynamics of a mode-locked laser with active feedback and noise due to amplified spontaneous emission. We show that, in a distinguished small-noise limit, an effective boundary can be drawn in parameter space for quasi-stability that is distinct from the deterministic stability boundary. We consider the probability that a mode-locked laser with active feedback will experience a transition between stable equilibria in a potential well when subjected to amplified spontaneous emission noise generated by the gain medium. To investigate the influence of noise on quasi-stability, we reduce the infinite-dimensional model to a finite-dimensional system of stochastic ordinary differential equations and compute the quasi-stable state by evaluating the action functional via the geometric minimum action method. This computation shows how and to what extent noise effectively destabilizes the system, and producing a region of quasi-stability in its parameter space that is smaller than that of the deterministic system.

15:30
DPG Methodology for Wave Phenomena in Optical Fibers

ABSTRACT. The DPG methodology with its attractive properties of uniform mesh independent stability, automatic adaptivity and parallelizability is studied in the context of wave propagation in optical fibers. In this application, we are interested in pulse propagation and laser amplification. Both these tasks present mathematical and numerical challenges: stability of the variational formulation, interaction with heating effects and transverse mode instability. We show how the DPG methodology offers an effective solution strategy to address these issues.

16:00
Spectral analysis of cavities partially filled with a negative-index material

ABSTRACT. The purpose of this talk is to investigate the spectral effects of an interface between a usual dielectric and a negative-index material (NIM), that is, a dispersive material whose electric permittivity and magnetic permeability become negative in some frequency range. We consider here an elementary situation, namely, 1) the simplest existing model of NIM : the Drude model (for which negativity occurs at low frequencies); 2) a two-dimensional scalar model derived from the complete Maxwell's equations; 3) the case of a simple bounded cavity: a camembert-like domain partially filled with a portion of non dissipative Drude material. Because of the frequency dispersion (the permittivity and permeability depend on the frequency), the spectral analysis of such a cavity is unusual since it yields a nonlinear eigenvalue problem. Thanks to the use of an additional unknown, we show how to linearize the problem and we present a complete description of the spectrum.

15:00-16:30 Session 16C: Contributed Talks
Location: Room 324
15:00
Transparent boundary conditions for general waveguide problems
SPEAKER: Sonia Fliss

ABSTRACT. In this work, we propose a construction of transparent boundary conditions which can be used for quite general waveguide problems. Classical Dirichlet-to-Neumann maps used for homogeneous acoustic waveguides can be constructed using separation of variables and the orthogonality of the modes on one transverse section. These properties are also important for the mathematical and numerical analysis of problems involving DtN maps. However this framework does not extend directly to stratified, anisotropic or periodic waveguides and for Maxwell's or elastic equations. The difficulties are that (1) the separation of variables is not always possible and (2) the modes of the waveguides are not necessarily orthogonal on the transverse section. We propose an alternative to the DtN maps which uses two artificial boundaries and is constructed using a general orthogonality property.

15:30
Formulation of invisibility in waveguides as an eigenvalue problem

ABSTRACT. A scatterer placed in an infinite waveguide may be invisible at particular discrete frequencies. We consider two different definitions of invisibility: no reflection (but possible conversion or phase shift in transmission) or perfect invisibility (the scattered field is exponentially decaying at infinity). Our objective is to show that the invisibility frequencies can be characterized as eigenvalues of some spectral problems. Two different approaches will be used for the two different definitions of invisibility, leading to non-selfadjoint eigenvalue problems. Concerning the non-reflection case, our approach based on an original use of PMLs allows to extend to higher dimension and to complex eigenvalues the results obtained by Hernandez-Coronado et al on a 1D model problem.

16:00
Complete radiation boundary conditions for the Helmholtz equation in waveguides
SPEAKER: Seungil Kim

ABSTRACT. We introduce a high-order absorbing boundary condition, called a complete radiation boundary condition (CRBC), for numerical computation of radiating solutions to the Helmholtz equation in waveguides. The CRBC is defined on an artificial boundary resulting from domain truncation by a certain recursive formula of auxiliary variables involving damping parameters, which can be tuned to minimize reflected waves from the fictitious boundary. We show that the solution to the problem supplemented with the CRBC converges exponentially to the exact radiating solution and present numerical experiments illustrating the convergence theory.

15:00-16:30 Session 16D: Contributed Talks
Location: Room 325
15:00
A study of the numerical robustness of single-layer method with Fourier basis for multiple obstacle scattering in homogeneous media
SPEAKER: Ha Pham

ABSTRACT. We investigate efficient methods to simulate multiple scattering (MS) of obstacles in homogeneous media. With a large number of small obstacles, optimized softwares based on Finite Element Method (FEM) lose their robustness. As an alternative, we work with an integral equation method, which uses single-layer potentials and truncation of Fourier series to describe the scattered field. We limit our numerical experiments to disc-shaped obstacles. We first compare our method with Montjoie (a FEM-based software); secondly, we investigate the efficiency of different solver types (direct and iterative) in solving the dense linear system generated by the method. We observe that the optimal choice depends on the distance between obstacles, their size and number, and applications.

15:30
Performances of the boundary integral equations for transmission problems and the distributions of the complex fictitious eigenvalues

ABSTRACT. Boundary Integral Equations (BIEs) for scattering problems are usually designed not to have real fictitious eigenvalues. However, they may still have complex fictitious eigenvalues with small imaginary parts which may cause inaccurate solutions. This paper discusses the performances of BIEs for transmission problems based on the distributions of complex fictitious eigenvalues. Numerical examples suggest that a properly formulated Single Integral Equation (SIE) has fictitious eigenvalues with larger imaginary parts and are more accurate than other BIEs tested.

16:00
BEM with variable time step size for absorbing boundary conditions
SPEAKER: Martin Schanz

ABSTRACT. In room acoustics, sound absorbing materials are often used. The mathematical description is done with the wave equation and absorbing boundary conditions. The numerical treatment can be done with Boundary Element methods, where the absorbing boundary results in a Robin boundary condition. This boundary condition connects the Neumann trace with the Dirichlet trace of the time derivative.

Here, an indirect formulation in combination with the generalized convolution quadrature method is applied. This allows, first, to have a simple formulation of the Robin boundary condition in the Laplace domain and, second, to have a variable time step size. The latter allows to discretise right hand sides with a non-smooth behavior. Convergence studies of a pure time dependent problem show the expected rates. The computation of the sound pressure level in a staircase of the University of Zurich, show the suitability of this approach in determining the indoor acoustics.

16:45-18:15 Session 17A: Contributed Talks
Location: Mississippi Room
16:45
An energy based discontinuous Galerkin method for acoustic-elastic waves
SPEAKER: Siyang Wang

ABSTRACT. We consider wave propagation in a media with both fluid and solid. In the fluid, the problem is modeled by the acoustic wave equation in terms of a velocity potential. In the solid, the elastic wave equation in displacement form is used. To couple the two regions, suitable physical conditions are imposed on the interface. We are interested in the numerical treatment of those interface conditions. The equations are discretized directly in second-order form by a discontinuous Galerkin method. We derive stable energy-conserving and upwind discretizations. The talk will present numerical experiments illustrating the accuracy and robustness of the proposed method.

17:15
Normal modes and internal wave attractors
SPEAKER: Will Booker

ABSTRACT. Confined internal gravity wave systems in asymmetric domains can lead to the evolution of a spatial singularity called a wave attractor. The existence of this singularity is the result of wave energy focusing, that is wave energy becomes localised on small spatial scales. It has been observed that ocean ridges, such as the Luzon strait, can support such energy localisation and a study of this mechanism will lead to a better understanding of ocean mixing in these areas. Simulations of wave attractors have been shown to match laboratory observations, despite being derived from an inviscid, ideal fluid model. We utilise a non-dissipative discontinuous finite element method that preserves the Hamiltonian structure of internal wave systems. By conserving discrete energy our numerical method allows for accurate long time modelling of wave attractors. We extend previous work by considering body forces in our numerical model to allow closer comparison to experimental results.

17:45
Solving the Homogeneous Isotropic Linear Elastodynamics Equations Using Potentials. The Case of the Free Surface Boundary Condition.

ABSTRACT. We consider the numerical solution of 2D elastodynamics isotropic equations using the decomposition of the displacement fields into potentials. This appears as a challenge for finite element methods. We address here the particular question of free boundary conditions. A stable (mixed) variational formulation of the evolution problem is proposed based on a clever choice of Lagrange multipliers.

16:45-18:15 Session 17B: Contributed Talks
Location: President's Room
16:45
A Dispersion Optimized Mimetic Finite Difference Method for Maxwell's Equations in Metamaterials

ABSTRACT. We present a numerical method for a Drude metamaterial model in two dimensions that is discretized using a mimetic finite difference (MFD) method in space and exponential time discretization (ETD). The MFD spatial discretization produces a three parameter family of mimetic schemes. By optimizing over the fully discrete family of schemes for optimal numerical dispersion error we produce an optimal ET-MFD method with fourth order dispersion error.

17:15
Optoelectronic finite-element simulations of thin-film solar cells
SPEAKER: Tom Anderson

ABSTRACT. A two-dimensional COMSOL model was developed to simulate the optoelectronic properties of amorphous silicon, thin-film, p-i-n junction, solar cells.

The i-layers were periodically nonhomogeneous in the thickness direction, while the p-layer was backed by a periodically corrugated metallic back reflector. The charge carrier generation rate was calculated using the frequency-domain Maxwell postulates. The steady-state drift-diffusion equations were solved to calculate the current density-voltage curve.

Use of a periodically-corrugated back reflector and the inclusion of a periodic bandgap profile increased total efficiency by up to 17% compared to solar cell without these features.

16:45-18:15 Session 17C: Contributed Talks
Location: Room 324
16:45
Measuring Electromagnetic Chirality
SPEAKER: Tilo Arens

ABSTRACT. We present a novel definition of chirality for electromagnetic wave scattering problems. We show that this definition captures both geometric aspects of chirality as well as those caused by optical activity. The definition also makes it possible to define a measure of chirality. Scatterers of relative maximal measure of chirality are those invisible to fields of one helicity.

17:15
Solution of the focusing Davey-Stewartson equations and the reconstruction of complex-valued conductivities

ABSTRACT. We will solve the Cauchy problem for the focusing Davey-Stewartson II equations (that model the shallow-water limit of evolution of weakly nonlinear water waves) in the presence of exceptional points (and/or curves). We also provide a method of reconstruction of complex-valued once differentiable conductivities in the inverse impedance tomography problem. Both results are based on the inverse scattering problem for the Dirac equation, which is solved without restrictions that guarantee the absence of exceptional points.

17:45
Two scale Hardy space infinite elements
SPEAKER: Lothar Nannen

ABSTRACT. This paper deals with the efficient numerical simulation of time-harmonic scattering and resonance problems in open systems, which exhibit wavenumbers on different scales. One example are waves for which the geometry causes a dispersion effect, i.e. waves can propagate with different speed levels. In order to overcome the performance issues of standard non-modal methods, we present a two scale variant of the Hardy space method. It allows to optimize the method to two different wavenumbers on different scales.

16:45-18:15 Session 17D: Contributed Talks
Location: Room 325
16:45
High Order DG Overlapping Solution FEM for the Helmholtz Equation
SPEAKER: Joe Coyle

ABSTRACT. The overlapping solution finite element method relies on an integral representation of the scattered field as part of the boundary conditions. In particular, the variational form and modified integral representation of the scattered field on the artificial boundary are given in the context of a discontinuous Galerkin method. Numerical evidence of convergence is presented for uniform high order $L^2$-conforming basis functions.

17:15
An Efficient Flux-Lumped Discontinuous Galerkin Scheme for the 3D Maxwell Equations on Nonconforming Grids

ABSTRACT. Discontinuous Galerkin in Time Domain Method (DGTD) is one of the most promising methods to simulate multiscale phenomena. It combines high order precision (p) with flexible geometries (h) resulting in inhomogeneous hp-approximation spaces. In a cartesian framework we show that some parts of the numerical scheme, namely heterogeneous flux terms, can lead to an outburst of computational cost on nonconforming meshes. A new scheme devoid of this bottleneck and proved to be stable is presented along with numerical results.

17:45
Minimum-Uncertainty Squeezed States for the Simple Harmonic Oscillator

ABSTRACT. We elaborate on a missing class of solutions to the time-dependent Schrodinger equation for the simple harmonic oscillator in one dimension. They are derived by the action of the corresponding maximal kinematical invariance group on the standard ground state solution. We show that the product of the variances attains the required minimum value only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. The generalized coherent states are explicitly constructed and their Wigner function is studied. The overlap coefficients between the squeezed, or generalized harmonic, and the Fock states are explicitly evaluated in terms of hypergeometric functions and the corresponding photon statistics are discussed. Some applications to quantum optics, cavity quantum electrodynamics and superfocusing in channelling scattering are mentioned. Explicit solutions of the Heisenberg equations for radiation field operators with squeezing are found.

16:45-18:15 Session 17E: Contributed Talks
Location: Room 326
16:45
A new discontinuous Galerkin spectral element method for elastic waves with physically motivated numerical fluxes
SPEAKER: Kenneth Duru

ABSTRACT. The discontinuous Galerkin spectral element method (DGSEM) is now an established method for computing approximate solutions of partial differential equations in many applications. In DGSEM, numerical fluxes are used to enforce internal and external physical boundary conditions. This has been successful for many problems. However, for certain problems such as elastic wave propagation in complex media, where several wave types and wave speeds are simultaneously present, a numerical flux may not be compatible with physical boundary conditions. For example if surface or interface waves are present, this incompatibility can lead to numerical instabilities. We present a provably stable and arbitrary order accurate DGSEM for elastic waves with physically motivated numerical fluxes. Our numerical flux is compatible with all well-posed physical boundary conditions, and linear and nonlinear friction laws. By construction our choice of penalty parameters yield an upwind scheme and a discrete energy estimate analogous to the continuous energy estimate.

17:15
High Frequency Acoustic Scattering in Isogeometric Analysis
SPEAKER: Tahsin Khajah

ABSTRACT. There is an emerging need to perform high frequency scattering analysis on high-fidelity models. Conventional Finite Element analysis suffers from irretrievable loss of the boundary accuracy as well as pollution error. Man-made geometries can be represented exactly in Isogeometric Analysis (IGA) with no geometrical loss even with very coarse mesh. The aim of this paper is to analyze the accuracy of IGA for exterior acoustic scattering problems. The numerical results show extremely low pollution error even for very high frequencies.

17:45
Reliable and efficient a posteriori error estimate for EFIE in electromagnetism

ABSTRACT. We construct a new reliable, efficient and local a posteriori error estimate for the Electric Field Integral Equation (EFIE). It is based on a new localization technique depending on the choice of a generic operator which is used to transport the residual into L2 -type space. Under appropriate conditions on the construction of this operator, we show that it is asymptotically exact with respect to an energy norm of the error.