平面电阻抗方程数值解的研究：Dirichlet边值问题的拟解析法
Study of the numerical solutions for the Electrical Impedance Equation in the plane: A pseudoanalytic approach of the forward Dirichlet boundary value problem
摘要：
采用一个极限情况下的猜想，用于构建分段可分离变量函数，伪解析函数理论的元素被用于数值逼近的解决方案的前狄利克雷边值问题，对应于在平面上的电阻抗方程，当电导率是一个任意的非零函数，完全定义在一个有界域。新方法的研究考虑了各种例子时，有界域与单位圆重合，它也包括一个描述其行为在非光滑域，选择特殊情况下，不需要额外的正则化技术，在非光滑区域的收敛性的方法，当某些要求得到满足。
英文摘要：
Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value problem, corresponding to the Electrical Impedance Equation in the plane, when the electrical conductivity is an arbitrary non-vanishing function, fully defined within a bounded domain. The new method is studied considering a variety of examples when the bounded domain coincides with the unit circle, and it is also included a description of its behaviour in non-smooth domains, selecting special cases that do not require additional regularization techniques, for warranting the convergence of the approach at the non-smooth regions, when certain requirements are fulfilled.
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