Integral Equation Methods for Stokes Flow and Isotropic Elasticity in the Plane

✍ Scribed by Leslie Greengard; Mary Catherine Kropinski; Anita Mayo

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 408 KB
• Volume: 125
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0102

✦ Synopsis

flow. With N points in the discretization of the boundary, direct inversion of the resulting linear systems requires

We present a class of integral equation methods for the solution of biharmonic boundary value problems, with applications to two-O(N 3 ) operations. Most iterative methods, on the other dimensional Stokes flow and isotropic elasticity. The domains may hand, require only O(N 2 ) work and do not require storage be multiply-connected and finite, infinite or semi-infinite in extent. of a dense matrix [13,18,22,23]. Our algorithms are also Our analytic formulation is based on complex variables, and our based on iteration, but require only O(N ) operations, since fast multipole-based iterative solution procedure requires O(N) opthey use a version of the fast multipole method [1, 5, 6,23] erations, where N is the number of nodes in the discretization of to compute matrix-vector products. Earlier fast multipolethe boundary. The performance of the methods is illustrated with several large-scale numerical examples.