Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
