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

✍ Scribed by Steinbach O., Unger G.

Year: 2009
Tongue: English
Leaves: 18
Category: Library

No coin nor oath required. For personal study only.

✦ 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.

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