Research on the Charge Simulation Method and the Numerical Conformal Mapping

利用电荷模拟方法，我们提出了无界多连通区域到以下典型狭缝区域的数值共形映射方法：(A)平行和共线狭缝区域，(B)线性狭缝区域和(C)圆形和径向狭缝区域，并证明了该方法的有效性。研究了电荷模拟方法的性质，提出了一种求解周期Stokes流问题的基本方法。这些在科学和工程应用中都很重要。与本研究主题密切相关的奇异积分方程组和病态线性方程组的数值方法的基础研究也取得了进展。

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.