arXiv subjects

Younghoon Jung

Publications and source records attributed to Younghoon Jung.

3 recordsLinked to original sources

arXiv2022

Spectral analysis of the Neumann--Poincaré operator on the crescent-shaped domain and touching disks and analysis of plasmon resonance

We consider the Neumann--Poincaré operator on a planar domain enclosed by two touching circular boundaries. This domain, which is a crescent-shaped domain or touching disks, has a cusp at the touching point of two circles. We analyze the operator via the Fourier transform on the boundary circles of the domain. In particular, we define a Hilbert space on which the operator is bounded, self-adjoint. We then obtain the complete spectral resolution of the Neumann--Poincaré operator. On both the crescent-shaped domain and touching disks, the Neumann--Poincaré operator has only absolutely continuous spectrum on the closed interval $[-1/2,1/2]$. As an application, we analyze the plasmon resonance on the crescent-shaped domain and touching disks.

math.AP↗

arXiv2018

A decay estimate for the eigenvalues of the Neumann-Poincaré operator in two dimensions using the Grunsky coefficients

We investigate the decay property of the eigenvalues of the Neumann-Poincaré operator in two dimensions. As is well-known, this operator admits only a sequence of eigenvalues that accumulates to zero as its spectrum for a bounded domain having $C^{1,α}$ boundary with $α\in (0,1)$. In this paper, we show that the eigenvalue $λ_k$'s of the Neumann-Poincaré operator ordered by size satisfy that $|λ_k| = O(k^{-p-α+1/2})$ for an arbitrary simply connected domain having $C^{1+p,α}$ boundary with $p\geq 0,~ α\in(0,1)$ and $p+α>\frac{1}{2}$.

math.SP↗

arXiv2017

A Joint Sparse Recovery Framework for Accurate Reconstruction of Inclusions in Elastic Media

A robust algorithm is proposed to reconstruct the spatial support and the Lamé parameters of multiple inclusions in a homogeneous background elastic material using a few measurements of the displacement field over a finite collection of boundary points. The algorithm does not require any linearization or iterative update of Green's function but still allows very accurate reconstruction. The breakthrough comes from a novel interpretation of Lippmann-Schwinger type integral representation of the displacement field in terms of unknown densities having common sparse support on the location of inclusions. Accordingly, the proposed algorithm consists of a two-step approach. First, the localization problem is recast as a joint sparse recovery problem that renders the densities and the inclusion support simultaneously. Then, a noise robust constrained optimization problem is formulated for the reconstruction of elastic parameters. An efficient algorithm is designed for numerical implementation using the Multiple Sparse Bayesian Learning (M-SBL) for joint sparse recovery problem and the Constrained Split Augmented Lagrangian Shrinkage Algorithm (C-SALSA) for the constrained optimization problem. The efficacy of the proposed framework is manifested through extensive numerical simulations. To the best of our knowledge, this is the first algorithm tailored for parameter reconstruction problems in elastic media using highly under-sampled data in the sense of Nyquist rate.

math.NA↗