Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
Finite Element Methods with B-Splines
Finite Element Methods with B-Splines
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Journal of Computational Physics
Reviving the Method of Particular Solutions
SIAM Review
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
A Boundary Integral Equation Method for Photonic Crystal Fibers
Journal of Scientific Computing
Meshfree Particle Methods
Photonic Crystals: Molding the Flow of Light
Photonic Crystals: Molding the Flow of Light
The generalized product partition of unity for the meshless methods
Journal of Computational Physics
Reproducing polynomial particle methods for boundary integral equations
Computational Mechanics
Quasi-optimal rates of convergence for the Generalized Finite Element Method in polygonal domains
Journal of Computational and Applied Mathematics
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In this paper, we study electromagnetic wave scattering from periodic structures and eigenvalue analysis of the Helmholtz equation. Boundary element method (BEM) is an effective tool to deal with Helmholtz problems on bounded as well as unbounded domains. Recently, Oh et al. (Comput. Mech. 48:27---45, 2011) developed reproducing polynomial boundary particle methods (RPBPM) that can handle effectively boundary integral equations in the framework of the collocation BEM. The reproducing polynomial particle (RPP) shape functions used in RPBPM have compact support and are not periodic. Thus it is not ideal to use these RPP shape functions as approximation functions along the boundary of a circular domain. In order to get periodic approximation functions, we consider the limit of the RPP shape function as its support is getting infinitely large. We show that the basic approximation function obtained by the limit of the RPP shape function yields accurate solutions of Helmholtz problems on circular, or annular domains as well as on the infinite domains.