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Modeling mixed boundary conditions in a Hilbert space with the complex variable boundary element method (CVBEM)

机译：使用复杂变量边界元方法（CVBEM）对希尔伯特空间中的混合边界条件建模

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Graphical abstract Display Omitted Abstract The Laplace equation that results from specifying either the normal or tangential force equilibrium equation in terms of the warping functions or its conjugate can be modeled as a complex variable boundary element method or CVBEM mixed boundary problem. The CVBEM is a well-known numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an approximation function that is derived from the Cauchy Integral in complex analysis. This paper highlights three customizations to the technique. ? A least squares approach to modeling the complex-valued approximation function will be compared and analyzed to determine if modeling error on the boundary can be reduced without the need to find and evaluated additional linearly independent complex functions. ? The nodal point locations will be moved outside the problem domain. ? Contour and streamline plots representing the warping function and its complementary conjugate are generated simultaneously from the complex-valued approximating function.
机译：图形摘要省略的摘要可将根据弯曲函数或其共轭指定法向力或切向力平衡方程而得出的拉普拉斯方程建模为复杂变量边界元法或CVBEM混合边界问题。 CVBEM是一种众所周知的数值技术，可以通过使用从复杂分析中的柯西积分得出的逼近函数，为二维或更多维的潜在值问题提供解决方案。本文重点介绍了该技术的三种定制。 ？将对用于对复数值逼近函数建模的最小二乘法进行比较和分析，以确定是否可以减少边界上的建模误差，而无需查找和评估其他线性独立的复函数。 ？节点位置将移至问题域之外。 ？从复数值逼近函数同时生成表示翘曲函数及其互补共轭的等高线图和流线图。

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