Seminar on PDE and related topics in October 2018

1

Seminar for undergraduate students
Time: 12th October (Friday) 14:30 - 15:30
Speaker: Prof. Woocheol Choi (Incheon National University)
Place: #702, Natural Science Building, Hanyang University

Title: Introduction to the control theory with applications in mechanical engineerings.

Abstract:
제어이론은 수학과 공학의 접점에 있는 분야로 20세기를 거치며 광범위하게 발전해 왔다. 특히 기계공학에서의 필수적인 역할을 하고 있으며, 현대에는 에너지, 반도체 등의 기술 발전으로 드론과 다양한 로봇들이 상용화 되고 있고, 관련된 제어기술의 수요도 증가하고 있다. 이번 발표에서는 제어 이론의 몇가지 기본적인 아이디어들과 예들을 소개하고, 최근 몇가지 발전 동향을 살펴본다.

 

2

Time: 17th October (Wednesday) 16:00 - 17:00
Speaker: Seungyeon Cho (Sungkyunkwan University)
Place: #702, Natural Science Building, Hanyang University

Title: High order conservative semi-Lagrangian scheme for the BGK model of the Boltzmann equation

Abstract:
In this work, we present a conservative semi-Lagrangian finite-difference scheme for the BGK model. The classical semi-Lagrangian finite difference scheme for the BGK model performs stably for all the range of Knudsen number, but are not conservative. There are two source of such loss of the conservation property. First, the accuracy of the cancellation of the relaxation operator in the zeroth, first and second velocity moments depends heavily on the number of velocity grids and non-negligible errors may arise if the number of velocity grids is not sufficient. Secondly, since the scheme is not of the conservative form, the error may accumulate in the numerical computation of the transport term. To treat the first problem and ensure the machine precision conservation of mass, momentum and energy with a relatively small number of velocity grid points, we replace the continuous Maxwellian with the discrete Maxwellian introduced by Mieussens. The second difficulty is treated by implementing a conservative correction procedure based on the flux difference form. The effectiveness of the proposed scheme is demonstrated by extensive numerical tests.

 

3

Seminar for undergraduate students
Time: 30th October (Tuesday) 14:30 - 16:00
Speaker: Prof. Kyung Hoon Han (University of Suwon)
Place: #208, Natural Science Building, Hanyang University

Title: 인공신경망의 기초

Abstract:
인공신경망 기법은 안면인식, 기계번역, 자율주행등에 응용되며 머신러닝의 핵심기법으로 부각되고 있다. 인공신경망은 그레디언트, 연쇄법칙과 같은 다변수 미분이론이 그 기초를 이루고 있다. 본 발표에서는 인공신경망의 원리와 수학적 기초를 설명하고 파이썬을 통해 시연해본다.