报告题目：Compact Fourth-Order Schemes for the Acoustic Wave Equation with Variable Speed of Sound

主 讲 人：Alexander A. Zlotnik 教授（俄罗斯国立高等经济大学）

报告邀请人：李树光 副教授

报 告 时间：2025年05月06日下午13:30-15:00

报告地点：数理楼 224

报告摘要：We deal with an initial-boundary value problem for the multidimensional acoustic wave equation, with the variable speed of sound. For a three-level semi-explicit in time higher-order vector compact scheme, we prove conditional stability and derive 4th-order error bound in the enlarged energy norm. It exploits additional sought functions which approximate 2nd-order non-mixed spatial derivatives of the exact solution. At the first time level, a similar two-level in time scheme is applied, without using derivatives of the data in the problem. No iterations are required to implement the scheme. We also present results of various 3D numerical experiments. They demonstrate a very high accuracy of the scheme, for smooth data, and its advantages in the error behavior over the classical explicit 2nd-order scheme, for nonsmooth data. An example of the wave in a layered medium (with a discontinuous speed of sound) initiated by the Ricker-type wavelet source function is also included.

个人简历：Alexander A. Zlotnik是俄罗斯国立高等经济大学教授，物理数学科学大博士。Alexander A. Zlotnik教授毕业于莫斯科国立大学，历任俄罗斯科学院应用数学研究所高级研究员、莫斯科国立师范大学副教授、莫斯科动力学院副教授、教授等。主要从事计算数学和偏微分方程数值解领域的研究，包括了椭圆、抛物、双曲型方程和薛定谔方程的有限元法和有限差分法的误差估计、稳定性分析、分裂方法、紧致格式等，以及可压缩纳维-斯托克斯方程和欧拉方程组的存在性、唯一性、正则性、大时间行为的理论分析和有限差分方法等数值求解。Alexander A. Zlotnik教授先后获得了1998-2000年度和2000-2003年度的俄罗斯国家科学奖，2022年SCI期刊“Entropy”杰出评审等。目前，已发表了220余篇高水平学术文章，担任了“Mathematical Modelling and Analysis”，“Computational Methods in Applied Mathematics”，“Applicable Analysis”，“Entropy”，“Symmetry”等期刊的编委。