论文标题
诺伊曼的问题
Neumann problem on a torus
论文作者
论文摘要
我们考虑了在圆环坐标中给出的dirichlet到neumann映射和诺伊曼的诺伊曼问题。 Dirichlet到Neumann的映射是关于环形谐波中串联膨胀的表达的，从而减少了系数的代数操纵。提出了一种计算相应Neumann问题的数值解决方案的方法，并提供了数值插图。我们将内部和外部结构域的结果结合在一起，以解决环形壳的Neumann问题。
We consider the Dirichlet-to-Neumann mapping and the Neumann problem for the Laplace operator on a torus, given in toroidal coordinates. The Dirichlet-to-Neumann mapping is expressed with respect to series expansions in toroidal harmonics and thereby reduced to algebraic manipulations on the coefficients. A method for computing the numerical solutions of the corresponding Neumann problem is presented, and numerical illustrations are provided. We combine the results for interior and exterior domains to solve the Neumann problem for a toroidal shell.
