Iterative approach for the numerical simulation of scattering from one- and two-dimensional rough surfaces

Area of Science:

• Computational physics
• Electromagnetics
• Wave scattering theory

Background:

• Integral equations model wave scattering from rough surfaces.
• Exact solutions are computationally intensive.
• Direct inversion methods can be inefficient.

Purpose of the Study:

• To evaluate iterative techniques for solving integral equations in scalar wave scattering.
• To assess the efficiency and applicability of these techniques for randomly rough surfaces.
• To compare iterative methods with direct inversion and analyze convergence behavior.

Main Methods:

• Application of iterative techniques to solve integral equations for wave scattering.
• Treatment of surfaces with one or two dimensions and Dirichlet boundary conditions.
• Preconditioning strategies to enhance iterative method efficiency.
• Monitoring of residuals to detect convergence or failure.

Main Results:

• Iterative techniques, especially with preconditioning, are significantly more efficient than direct inversion.
• Convergence is achieved for root-mean-square (rms) roughness up to approximately 1.
• The methods converge to the exact solution, except in cases of extremely large-scaled rms surface heights.
• Residual monitoring effectively indicates the performance and potential failure of iterative techniques.

Conclusions:

• Iterative techniques provide an efficient and accurate approach for scalar wave scattering from randomly rough surfaces.
• These methods are applicable across a wide parameter range of surface roughness.
• The ability to monitor residuals enhances the reliability and diagnostic capability of the iterative solutions.