We explore algebraic strategies for numerically solving linear elliptic partial differential equations in polygonal domains. To discretize the polygon by means of structured meshes, we employ Schwarz-Christoffel conformal mappings, leading to a multiterm linear equation possibly including Hadamard products of some of the terms. This new algebraic formulation allows us to clearly distinguish between the role of the discretized operators and that of the domain meshing. Various algebraic strategies are discussed for the solution of the resulting matrix equation.

中文翻译：

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使用保形映射求解多边形域中PDE的矩阵方程

我们探索了在多边形域中数值求解线性椭圆型偏微分方程的代数策略。为了通过结构化网格离散化多边形，我们使用Schwarz-Christoffel共形映射，得到一个可能包含某些项的Hadamard乘积的多项线性方程。这种新的代数形式使我们能够清楚地区分离散化算子的作用和域网格化的作用。讨论了各种代数策略，以解决由此产生的矩阵方程。