A boundary element method for the Dirichlet eigenvalue problem of the Laplace operator

✍ Scribed by O. Steinbach; G. Unger

• Publisher: Springer-Verlag
• Year: 2009
• Tongue: English
• Weight: 256 KB
• Volume: 113
• Category: Article
• ISSN: 0029-599X
• DOI: 10.1007/s00211-009-0239-1

✦ Synopsis

The solution of eigenvalue problems for partial differential operators byusing boundary integral equation methods usually involves some Newton potentialswhich may be resolved by using a multiple reciprocity approach. Here we proposean alternative approach which is in some sense equivalent to the above. Instead of alinear eigenvalue problem for the partial differential operator we consider a nonlineareigenvalue problem for an associated boundary integral operator. This nonlineareigenvalue problem can be solved by using some appropriate iterative scheme, herewe will consider a Newton scheme.We will discuss the convergence and the boundaryelement discretization of this algorithm, and give some numerical results.