Research on the Charge Simulation Method and the Numerical Conformal Mapping

利用电荷模拟方法，给出了无界多连通域到以下正则狭缝域的数值共形映射方法：（a）平行狭缝域和共线狭缝域，（B）线性狭缝域，（c）圆形狭缝域和径向狭缝域，并证明了方法的有效性.研究了电荷模拟方法的性质，提出了求解周期Stokes流问题的基本解方法。这些在科学和工程应用中很重要。与本课题密切相关的奇异积分方程和病态线性方程的数值方法的基础研究也在不断的发展。

Using the charge simulation method, we proposed the method of numerical conformal mappings of unbounded multiply connected domains onto the following canonical slit domains: (a) the parallel and the colinear slit domains, (b) the linear slit domain and (c) the circular and radial slit domain; and showed the effectiveness of our method. We studied the property of the charge simulation method, and proposed a fundamental solution method for periodic Stokes flow problems. These are important in scientific and engineering applications. Basic studies on numerical methods for singular integral equations and ill-conditioned linear equations are progressed, which are closely related to the subject of this study.