Alternative numerical methods, such as finite element or boundary element methods, can also be applied to scattering problems and offer distinct advantages compared to the Nyström method.
Finite Element Method (FEM): FEM is well-suited for handling complex geometries and irregular boundaries. It can efficiently model wave propagation in heterogeneous media and adapt to varying mesh resolutions. FEM is particularly useful when dealing with large-scale problems or when detailed spatial variations are present in the domain.
Boundary Element Method (BEM): BEM excels in problems with infinite domains or unbounded regions, making it suitable for exterior wave propagation analyses. By discretizing only the boundary of the domain, BEM can reduce the computational burden compared to volumetric meshing in FEM. It is advantageous for problems where the boundary conditions dominate the physics of the system.
Performance Comparison: The choice between Nyström, FEM, and BEM depends on the specific characteristics of the scattering problem. While Nyström method is efficient for problems with smooth boundaries and moderate property contrasts, FEM and BEM offer more versatility in handling complex geometries and diverse boundary conditions. Performance comparisons should consider factors like accuracy, computational cost, scalability, and ease of implementation to determine the most suitable method for a given scenario.