A fast algorithm for particle simulations
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
A Stable High-Order Method for Two-Dimensional Bounded-Obstacle Scattering
SIAM Journal on Scientific Computing
A stable, high-order method for three-dimensional, bounded-obstacle, acoustic scattering
Journal of Computational Physics
Analysis of a Spectral-Galerkin Approximation to the Helmholtz Equation in Exterior Domains
SIAM Journal on Numerical Analysis
A Rigorous Numerical Analysis of the Transformed Field Expansion Method
SIAM Journal on Numerical Analysis
Spectral Methods: Algorithms, Analysis and Applications
Spectral Methods: Algorithms, Analysis and Applications
A Spectral-Element Method for Transmission Eigenvalue Problems
Journal of Scientific Computing
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The scattering of acoustic and electromagnetic waves by periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the stable and high-order numerical simulation of the interaction of time-harmonic electromagnetic waves incident upon a periodic doubly layered dielectric media with sharp, irregular interface. We describe a boundary perturbation method for this problem which avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of boundary integral/element methods. Additionally, it is a provably stable algorithm as opposed to other boundary perturbation approaches such as Bruno and Reitich's ''method of field expansions'' or Milder's ''method of operator expansions''. Our spectrally accurate approach is a natural extension of the ''method of transformed field expansions'' originally described by Nicholls and Reitich (and later refined to other geometries by the authors) in the single-layer case.