Superalgebraically convergent smoothly windowed lattice sums for doubly periodic Green functions in three-dimensional space
Abstract
This work, part I in a two-part series, presents: (i) a simple and highly efficient algorithm for evaluation of quasi-periodic Green functions, as well as (ii) an associated boundary-integral equation method for the numerical solution of problems of scattering of waves by doubly periodic arrays of scatterers in three-dimensional space. Except for certain ‘Wood frequencies’ at which the quasi-periodic Green function ceases to exist, the proposed approach, which is based on smooth windowing functions, gives rise to tapered lattice sums which converge superalgebraically fast to the Green function—that is, faster than any power of the number of terms used. This is in sharp contrast to the extremely slow convergence exhibited by the lattice sums in the absence of smooth windowing. (The Wood-frequency problem is treated in part II.) This paper establishes rigorously the superalgebraic convergence of the windowed lattice sums. A variety of numerical results demonstrate the practical efficiency of the proposed approach.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 01, 2016
- Source ID
- 10.1098/rspa.2016.0255
Entities
People
- Catalin Turc
- Oscar P. Bruno
- Stephanos Venakides
- Stephen Shipman
Organizations
- Air Force Office of Scientific Research
- California Institute of Technology
- Duke University
- Louisiana State University
- National Science Foundation Division of Mathematical Sciences
- New Jersey Institute of Technology