< 응용수학 세미나 강연 >

■ 일시: 2021년 1월 22일 (금) 오후 3시-5시

■ 연사: 최우철 교수(성균관대학교), 홍영준 교수(San Diego State University)

■  줌 연결 정보:  https://us02web.zoom.us/j/5078261756?pwd=dW1BTTJxZ1dBV09kbVRLaWE2QlN1QT09

      Meeting ID: 507 826 1756

      Passcode: 1fvgXf

■ 강연 제목 및 초록

3시~3시 50분: 최우철 교수

Title: Communication-Computation balanced distributed convex optimization

Abstract: Distributed convex optimization has received a lot of interest from many researchers since it is widely used in various applications, containing wireless network sensor and machine learning. Recently, A. S. Berahas et al (2018) introduced a variant of the distributed gradient descent called the Near DGD+ which combines nested communications and gradient descent steps. They proved that this scheme finds the optimum point using a constant step size when the target function is strongly convex and smooth function. In the first part, we show that the scheme attains O(1/t) convergence rate for convex and smooth function. In addition we obtain a convergence result of the scheme for quasi-strong convex function. In the second part, we use the idea of Near DGD+ to design a variant of the push-sum gradient method on directed graph.

4시~4시 50분: 홍영준 교수

Title: Numerical Study of Nanoplasmonics and Solar Thermophotovoltaics

Abstract: The accurate simulation of scattering of electromagnetic waves in three dimensions by a diffraction grating is crucial in many applications of engineering and scientific interest. In this lecture, we explore a novel High-Order Perturbation of Surfaces method for the numerical approximation of electromagnetic scattering by a periodic layered medium. For this we apply the method of Transformed Field Expansions which delivers a Fourier collocation, Legendre-Galerkin, Boundary Perturbation approach to solve the problem in transformed coordinates. A sequence of numerical simulations demonstrate the efficient and robust spectral convergence which can be achieved with the proposed algorithm. As an application, our approaches can be generalized to investigate periodic metal interface shapes in Solar thermophotovoltaics structures that tailor thermal emission using nanophotonic structures for increased solar energy conversion.