Speaker: Dr. Xiaoyu Dong (董晓宇博士)

Time: 12:10-13:10, 8 September 2022 (Thursday) (Beijing time)

Tencent Meeting ID: 858-618-627

Venue: C404, Lijiao Building

Record: https://meeting.tencent.com/v2/cloud-record/share?id=d980c5de-4ee3-4eb6-99c5-d2e4c1eb793e&from=3

Abstract

Langevin method is an important method to calculate path integrals in quantum chromodynamics, which requires to solve the Langevin equations on the special unitary group SU(n) or the special linear group SL(n, C). Since the  Langevin equations are nonlinear stochastic differential equations, we focus on the research of numerical methods to solve them. With the Ito-Taylor expansions of the equations, the truncated Taylor schemes do not guarantee that the solutions are on SU(n) or SL(n, C).

Based on the exponential expansions, the new high-order numerical schemes are presented through introducing the correction matrices, which overcomes the shortcoming of the truncated Taylor schemes successfully. In order to improve the efficiency, we also construct the Runge-Kutta schemes with the approximations of the derivatives. The numerical experiments show all of the schemes reach the theoretical convergence order.

About Dr. Dong

董晓宇，2022年毕业于中国科学院数学与系统科学研究院，获理学博士学位，即将赴新加坡国立大学从事博士后研究。研究方向主要为量子场论中的随机算法。