ABOUT SOME BOUNDARY INTEGRAL OPERATORS ON THE UNIT DISK RELATED TO THE LAPLACE EQUATION

作者：Ramaciotti Pedro^*; Nedelec Jean Claude

来源：SIAM Journal on Numerical Analysis, 2017, 55(4): 1892-1914.

DOI：10.1137/15M1033721

• open surface problem
• boundary integral operators
• boundary element methods
• preconditioners for iterative methods

We introduce four integral operators related to the Laplace equation in three dimensions on the circular unit disk. Two of them are related to the weakly singular operator and the other two are related to the hypersingular operator. We provide series expressions for their kernels using proposed bases for the Sobolev trace spaces involved in the symmetric Dirichlet and antisymmetric Neumann Laplace screen problems on the disk. We then provide explicit and closed variational forms suitable for boundary element computations. We develop numerical computation schemes for the associated Galerkin matrices and test their use as preconditioners for the matrices arising from the integral equations associated with the solution of the mentioned screen problems.

• 出版日期2017