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1
Introduction
2
Metamaterial resonators
3
Visualisation
4
Outline
5
Notation
6
Greens Function
7
Design Variable
8
Optimization
9
Oneshot Approach
10
Spectral Characterization
11
Monotonicity
12
Boundary Integral Approach
13
Nucleation
14
Why Boundary Integral
15
Asymptotic Expansion
16
Generalized Riches Theorem
17
Generalized Argument Principle
18
Integral Operator
19
Algorithm Sketch
20
Asymptotic Formula
21
Mixed Problem
22
Kite Shaped Domain
23
Higher Frequency Domain
24
Example Problem
25
Question
Description:
Explore wave enhancement techniques through spectral optimization in this 57-minute virtual seminar presented by Nilima Nigam from Simon Fraser University. Delve into an efficient approach for optimizing transmission signals between two points in a cavity at a given frequency by altering boundary conditions from Dirichlet to Neumann. Learn about the monotonicity of eigenvalues in mixed boundary value problems and the sensitivity of Green's function to small boundary condition changes. Discover highly accurate calculation methods for mixed Dirichlet-Neumann eigenvalues using a layer potential approach. Gain insights into metamaterial resonators, visualization techniques, and the oneshot optimization approach. Examine spectral characterization, boundary integral methods, and asymptotic expansions. Explore practical applications through examples involving kite-shaped domains and higher frequency domains.

Wave Enhancement Through Spectral Optimization - 33rd IMAGINE Seminar

Society for Industrial and Applied Mathematics
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