TY  - CHAP
A1  - Pieronek, Lukas
A1  - Kleefeld, Andreas
ED  - Constanda, Christian
ED  - Harris, Paul
T1  - The Method of Fundamental Solutions for Computing Interior Transmission Eigenvalues of Inhomogeneous Media
T2  - Integral Methods in Science and Engineering: Analytic Treatment and Numerical Approximations
N2  - The method of fundamental solutions is applied to the approximate computation of interior transmission eigenvalues for a special class of inhomogeneous media in two dimensions. We give a short approximation analysis accompanied with numerical results that clearly prove practical convenience of our alternative approach.
Y1  - 2019
SN  - 978-3-030-16077-7
U6  - https://doi.org/10.1007/978-3-030-16077-7_28
SP  - 353
EP  - 365
PB  - Birkhäuser
CY  - Cham
ER  - 
TY  - CHAP
A1  - Abele, Daniel
A1  - Kleefeld, Andreas
ED  - Constanda, Christian
T1  - New Numerical Results for the Optimization of Neumann Eigenvalues
T2  - Computational and Analytic Methods in Science and Engineering
N2  - We present new numerical results for shape optimization problems of interior Neumann eigenvalues. This field is not well understood from a theoretical standpoint. The existence of shape maximizers is not proven beyond the first two eigenvalues, so we study the problem numerically. We describe a method to compute the eigenvalues for a given shape that combines the boundary element method with an algorithm for nonlinear eigenvalues. As numerical optimization requires many such evaluations, we put a focus on the efficiency of the method and the implemented routine. The method is well suited for parallelization. Using the resulting fast routines and a specialized parametrization of the shapes, we found improved maxima for several eigenvalues.
Y1  - 2020
SN  - 978-3-030-48185-8 (Print)
SN  - 978-3-030-48186-5 (Online)
U6  - https://doi.org/10.1007/978-3-030-48186-5_1
SP  - 1
EP  - 20
PB  - Birkhäuser
CY  - Cham
ER  -