摘要
非线性偏微分方程的建模、分析、计算已成为计算数学中最为活跃的研究领域之一.本文旨在回顾评述厦门大学计算数学相关团队在非线性偏微分方程高效算法研究方面取得的成果.我们重点关注几类在复杂流体、计算材料等领域有重要应用的非线性方程或方程组,以及针对这些方程发展的传统(如差分、有限元、谱方法)和非传统算法(如神经网络)等方面取得的进展.
The modeling,analysis,and computation of nonlinear partial differential equations(PDEs)have become one of most active research areas in computational mathematics.This work aims to review and summarize achievements of the relevant team in computational mathematics at Xiamen University in the research of efficient algorithms for nonlinear PDEs.Particularly,we focus on several classes of nonlinear PDEs that secure important applications in fields such as complex fluids and computational materials.We also highlight the progress made in the development of both classical methods(such as finite difference methods,finite element methods,and spectral methods)and non-classical algorithms(such as neural network-based methods)developed for these equations.
作者
陈黄鑫
毛志平
许传炬
CHEN Huangxin;MAO Zhiping;XU Chuanju(School of Mathematical Sciences,Xiamen University,Xiamen 361005,China)
出处
《厦门大学学报（自然科学版）》
CAS
CSCD
北大核心
2023年第6期991-1011,共21页
Journal of Xiamen University：Natural Science
基金
国家自然科学基金(12122115,11771363,12171404)
中央高校研发基金(20720210037)。
