Research on domain decomposition methods for partial differential equations

(A) 1995年至1996年期间，我们组织了两次国际会议，会议名称如下：1.科学与工程计算的并行算法（千叶大学，1995年5月22-24日）。2.域分解方法及相关主题（京都大学数学科学研究所，1996年7月17-19日）。上述会议有效地开展了（B）我们的项目成果如下：1.最优控制问题算法的发展。我们称之为多启动FOM-MCA。2.多启动FOM-MCA算法应用于维稳定纳维-斯托克斯流的自由边界控制问题。3.3.磁场对超导体的穿透现象分析。4.倾斜海滩波浪运动的分析与模拟。

(A) We organized two international conferences in the period from 1995 to 1996. The titles of them are the followings.1.Parallel Algorithm for Scientific and Engineering Computations (Chiba University, May 22-24,1995).2.Domain Decomposition Method and Related Topics (Research Institute for Mathematical Sciences, Kyoto University, July 17-19,1996).The above conferences were effective to carry out our project.(B) Our results of project are as follows.1.Developement of algorithm in optimal control problems.We call it multi-start FOM-MCA.2.Multi-start FOM-MCA algorithm was applied to the problem on control of free boundary for steady Navier-Stokes flow in dimenssion 3.3.The analysis for penetration phenomenon of magnetic field into superconductor.4.The analysis and simulation on wave motion on sloping beach.