Electromagnetic theory and computation: a topological approach

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Meanwhile, the exponential growth of computational power, the invention and improvement of numerical tools for accurately simulating wave phenomena along with the invention of efficient mathematical optimization methods over the last decades have enabled the development of powerful design tools with unprecedented capabilities.

Density based topology optimization is one such tool having recently been proven capable of solving design problems with a billion design variables, translating to virtually unlimited design freedom.

ISBN 13: 9780521801607

This talk will focus on recent research into the development and application of density based topology optimization to the design of structures and metamaterials achieving a high degree of control of various wave phenomena. This includes metamaterials with exotic properties and passive structures designed for wave propagation control. Initially a brief introduction to the method is provided, taking offset in a static mechanical engineering example, followed by examples of recent applications of the method across different areas of physics.

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My PhD-fellowship was focussed on the development, application and experimental validation of topology optimization based methods for solving wave propagation based design problems in acoustics and optics. The SunTune project is centered at Aarhus University and concerns the design of passive solar cell components aimed at increasing their operating efficiency.

A Topological Approach

This includes the design of metallic nanoparticles for localized electromagnetic field enhancement. The NATEC project is centered at the Department of Photonics at DTU and is focussed on the design of active and passive photonic structures for applications in optical data processing and terabit communication.

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Johnson's group on Raman scattering problems and optical metasurfaces. NATEC: Active materials quantum wells and quantum dots , designing photonic structures with applications in optical data processing and terabit communication.

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Unveiling the topological nature of electromagnetic surface waves – Physics World

Although topology was recognized by Gauss and Maxwell to play a pivotal role in the formulation of electromagnetic boundary value problems, it is a largely unexploited tool for field computation. The development of algebraic topology since Maxwell provides a framework for linking data structures, algorithms, and computation to topological aspects of three-dimensional electromagnetic boundary value problems.

This book attempts to expose the link between Maxwell and a modern approach to algorithms.

http://taylor.evolt.org/fexoz-aiara-ligar.php The first chapters lay out the relevant facts about homology and cohomology, stressing their interpretations in electromagnetism. These topological structures are subsequently tied to variational formulations in electromagnetics, the finite element method, algorithms, and certain aspects of numerical linear algebra.