Efficient and Robust Shadowing Determination for Mesh-Based Physical Optics Analysis

Abstract

Visibility status determination for every mesh element/edge with respect to an illuminating source is routinely required in mesh-based physical optics (PO) methods, where the scatterer is represented by subwavelength sized elements. This article presents an optimally efficient shadowing determination algorithm for both plane wave and point source (Hertzian dipole) illumination of large-scale triangle meshes. It is based on a recursive multilevel field-of-view (image space) subdivision buffer approach, whereby a point’s status is determined by only checking against a small subset of elements. It is error-free and formulated to maintain efficiency for inhomogeneous meshes and grazing incidence, which result in concentration of projected elements in small areas of the buffer plane. A key step is to separate the grazing and nongrazing parts of the mesh. Very challenging test cases affirm the algorithm’s expected optimal and robust linear computational cost scaling of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {O}(N)$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> denotes the number of mesh elements. For fixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> , almost constant runtimes under extreme illumination and mesh variations, further demonstrate robustness.