Applying an iterative method numerically to solve n × n matrix Wiener-Hopf equations with exponential factors

Area of Science:

• Electromagnetics and wave propagation
• Applied mathematics
• Numerical analysis

Background:

• Matrix Wiener-Hopf equations are crucial in solving wave scattering problems.
• Existing iterative methods are limited to 2x2 matrices.
• Mixed boundary value problems with multiple junctions require higher-order matrix solutions.

Purpose of the Study:

• To generalize an iterative approach for solving matrix Wiener-Hopf equations with exponential factors.
• To extend the method to square matrices of arbitrary dimension n.
• To apply the generalized method to mixed boundary value problems, specifically scattering by collinear plates.

Main Methods:

• Generalization of a recent iterative approach for 2x2 matrix Wiener-Hopf equations.
• Extension to square matrices of arbitrary dimension n.
• Implementation using a spectral method for Cauchy transform computation.

Main Results:

• The generalized method effectively solves mixed boundary value problems with n junctions.
• Demonstrated application to plane wave scattering by collinear plates.
• Comparison with other known methods confirms accuracy and efficiency.
• Far-field directivity patterns are obtained, useful for applications.
• Iterative convergence is rapid for large wavenumbers and practical for modest ones.

Conclusions:

• The generalized iterative method provides an effective solution for n x n matrix Wiener-Hopf equations.
• The approach is suitable for analyzing scattering phenomena and obtaining directivity patterns.
• The spectral method implementation enhances computational efficiency.
• The method offers a practical and accurate tool for various applications in electromagnetics and wave physics.