Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

Please note that all times are shown in the time zone of the conference. The current conference time is: 4th Dec 2022, 08:27:47pm CET

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Session Overview
MS 6a: high-order spectral methods for plasmonics and optics
Wednesday, 14/July/2021:
4:10pm - 6:10pm

Session Chair: Youngjoon Hong
Session Chair: David Nicholls
Virtual location: Zoom 4

Session Abstract

The scattering of electromagnetic waves by irregular obstacles, periodic

gratings, and other geometrically complex structures arises in a wide array of

scientific and engineering applications. In fact, these models are at the heart

of everyday technologies such as seismic imaging, underwater acoustics, and

biological sensing. Clearly, there is a compelling need for algorithm design,

rigorous analysis, and mathematical model development from applied

mathematicians and computational scientists. Despite significant successes

along these lines, some very important challenges remain. While low-order

numerical methods play a significant role in the simulation of these devices,

High Order Spectral approaches are becoming increasingly important to

theoreticians and practitioners alike due to their superior accuracy and

reduced cost. Interestingly, many paths have been taken to achieve high

accuracy in this setting including Spectral, Integral Equation, Spectral

Element, hp Continuous and Discontinuous Galerkin, and High-Order Perturbation

of Surfaces methods. The main purpose of this minisymposium is to bring together

experts in all of these approaches with the goal of not only communicating the

state-of-the-art in these fields, but also identifying areas of future


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4:10pm - 4:40pm

A High-Order Perturbation of Envelopes (HOPE) Method for Scattering by Periodic Inhomogeneous Media

David Nicholls

University of Illinois at Chicago, United States of America

The interaction of linear waves with periodic structures arises in a

broad range of scientific and engineering applications. For such

problems it is often mandatory that numerical simulations be rapid,

robust, and highly accurate. With such qualities in mind High-Order

Spectral methods are often utilized, and in this talk we describe and

test a perturbative method which fits into this class. Here we view

the inhomogeneous (but laterally periodic) permittivity as a

perturbation of a constant value and pursue (regular) perturbation

theory. We demonstrate that not only does this lead to a fast and

accurate numerical method, but also that the expansion of the field in

this geometric parameter is valid for large deformations (up to

topological obstruction). Finally, we show that, if the permittivity

deformation is spatially analytic, then so is the field scattered by


4:40pm - 5:10pm

Planewave Density Interpolation Methods for the EFIE on Simple and Composite Surfaces

Catalin Turc

NJIT, United States of America

We present a planewave density interpolation (PWDI) method for the numerical solution of the electric field integral equation (EFIE) formulation of problems of scattering and radiation by perfect electric conducting (PEC) objects. Relying on Kirchhoff integral formula and local interpolation of surface current densities that regularize the kernel singularities, the PWDI method enables off-and on-surface EFIE operators to be re-expressed in terms of integrands that are globally bounded over the whole domain of integration. Surface integrals resulting from the application of the method-of-moments (MoM) using Rao-Wilton-Glisson (RWG) basis functions, can then be directly and easily evaluated by means of elementary quadrature rules irrespective of the singularity location. The proposed technique can be applied to simple and composite surfaces comprising two or more simply-connected overlapping components. The use of composite surfaces can significantly simplify the geometric treatment of complex structures, as the PWDI method enables the use of separate non-conformal meshes for the discretization of each of the surface components that make up the composite surface. A variety of examples, including multi-scale and intricate structures, demonstrate the effectiveness of the proposed methodology. Joint work with C. Perez-Arancibia, Luiz Faria, and C. SIderis.

5:10pm - 5:40pm

Automatic Synthesis of Low-Complexity Translation Operators for the Fast Multipole Method

Andreas Kloeckner, Isuru Fernando

University of Illinois, United States of America

Expansion and translation operators (e.g. particle-to-multipole, multipole-to-local) underpin fast algorithms such as the FMM and can be used (via quadrature by expansion and GIGAQBX) to attain high-order singular quadrature. They thus provide a complete backbone for the asymptotically fast solution of PDE boundary value problems via integral equation methods, which are themselves popular tools in photonics and optics. As a key building block, their cost is of paramount importance. To attain low complexity, translation operators can exploit the PDE obeyed by the potential. To keep computational tools broadly applicable, it is desirable for translation operators to not be specific to a PDE and kernel. In this talk, we demonstrate a combined numerical/symbolic technique for the synthesis of translation operators provided a symbolic expression for kernel and PDE. In three dimensions, the typical complexity of the synthesized operators is O(p^3).

5:40pm - 6:10pm

Simulation, optimization and design methods for electromagnetic metamaterial devices

Oscar Bruno

Caltech, United States of America

We present fast spectral electromagnetic solvers that address some of the main difficulties associated with the simulation of realistic engineering electromagnetic problems in the frequency- and time-domain. Based on the use of Green functions and fast high-order methods for evaluation of integral operators, these algorithms can solve, with high-order accuracy, problems of electromagnetic propagation and scattering for large and complex three-dimensional structures and devices -- such as silicon devices, structured lenses, and metamaterials. In particular, we will consider the important but challenging problem of the design and optimization of optical and photonic devices of large electrical sizes. A variety of applications will be presented demonstrating the significant design capabilities inherent in the new methods, as well as the improvements these algorithms can provide, over other approaches, in generality, accuracy, and speed. Time permitting, a novel class of accelerated Green function methods will be presented.

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