Applying an iterative method numerically to solve n × n matrix Wiener–Hopf equations with exponential factors
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This paper presents a generalization of a recent iterative approach to solving a class of 2 × 2 matrix Wiener–Hopf equations involving exponential factors. We extend the method to square matrices of arbitrary dimension n, as arise in mixed boundary value problems with n junctions. To demonstrate the method, we consider the classical problem of scattering a plane wave by a set of collinear plates. The results are compared to other known methods. We describe an effective implementation using a spectral method to compute the required Cauchy transforms. The approach is ideally suited to obtaining far-field directivity patterns of utility to applications. Convergence in iteration is fastest for large wavenumbers, but remains practical at modest wavenumbers to achieve a high degree of accuracy.
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1471-2962
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Engineering and Physical Sciences Research Council (EP/R014604/1)
Engineering and Physical Sciences Research Council (EP/P015980/1)
Engineering and Physical Sciences Research Council (EP/N509620/1)
EPSRC (1936262)