On integral equation methods for the first Dirichlet problem of the biharmonic and modified biharmonic equations in nonsmooth domains

Document Type

Article

Publication Date

1-1-2018

Abstract

Despite important applications in unsteady Stokes flow, a Fredholm second kind integral equation formulation modeling the first Dirichlet problem of the modified biharmonic equation in the plane has been derived only recently. Furthermore, this formulation becomes very ill-conditioned when the boundary is not smooth, say, having corners. The present work demonstrates numerically that a method called recursively compressed inverse preconditioning (RCIP) can be effective when dealing with this geometrically induced ill-conditioning in the context of Nystr\"om discretization. The RCIP method not only reduces the number of iterations needed in iterative solvers but also improves the achievable accuracy in the solution. Adaptive mesh refinement is only used in the construction of a compressed inverse preconditioner, leading to an optimal number of unknowns in the linear system in the solve phase.

Identifier

85053775840 (Scopus)

Publication Title

SIAM Journal on Scientific Computing

External Full Text Location

https://doi.org/10.1137/17M1162238

e-ISSN

10957197

ISSN

10648275

First Page

A2609

Last Page

A2630

Issue

4

Volume

40

Grant

1720405

Fund Ref

National Science Foundation

This document is currently not available here.

Share

COinS