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Pruning Wiener–Hopf Equations: From Pole Removal to Branch Removal

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If you have a question about this talk, please contact Mungo G. Aitken.

Pole removal is a common tool to help solve Wiener—Hopf problems involving meromorphic functions, allowing a full matrix factorization to be avoided at the expense of solving a linear system matching removed singularities. In this talk we show that this approach can be effectively extended to functions with branch cut singularities, without recourse to rational approximation, in certain cases. Using a weighted polynomial basis approximation for the jump across each cut, the associated linear system may be explicitly constructed and solved. The method is demonstrated for scattering a plane wave by a finite plate. This setting tightens the relationship between pole removal and the iterative approach to solving a class of Wiener—Hopf problems proposed by Kisil.

This talk is part of the Waves Group (DAMTP) series.

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