A fast direct solver for scattering from periodic structures with multiple material interfaces in two dimensions

DOI10.1016/j.jcp.2013.11.011zbMath1349.74353arXiv1307.7496OpenAlexW2112939584MaRDI QIDQ348640

Kenneth L. Ho, June-Yub Lee, Leslie F. Greengard

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.7496

zbMATH Keywords

acoustic scatteringboundary integral equationselectromagnetic scatteringtriple junctionsfast direct solversmultiple material interfaces

Mathematics Subject Classification ID

Related Items (9)

Fast solver for quasi-periodic 2D-Helmholtz scattering in layered media ⋮ A fast and robust solver for the scattering from a layered periodic structure containing multi-particle inclusions ⋮ A fast direct solver for two dimensional quasi-periodic multilayered media scattering problems ⋮ A volume integral equation method for periodic scattering problems for anisotropic Maxwell's equations ⋮ Robust integral formulations for electromagnetic scattering from three-dimensional cavities ⋮ Multitrace/singletrace formulations and domain decomposition methods for the solution of Helmholtz transmission problems for bounded composite scatterers ⋮ A tensor product finite element method for the diffraction grating problem with transparent boundary conditions ⋮ A new hybrid integral representation for frequency domain scattering in layered media ⋮ An isogeometric boundary element method for three-dimensional doubly-periodic layered structures in electromagnetics

Uses Software

• UMFPACK
• mctoolbox

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A fast direct solver for quasi-periodic scattering problems
• Quadrature by expansion: a new method for the evaluation of layer potentials
• Stable and accurate integral equation methods for scattering problems with multiple material interfaces in two dimensions
• A new integral representation for quasi-periodic scattering problems in two dimensions
• Universal quadratures for boundary integral equations on two-dimensional domains with corners
• On the Nyström discretization of integral equations on planar curves with corners
• Resonant effects in scattering by periodic arrays
• A direct solver with \(O(N)\) complexity for integral equations on one-dimensional domains
• Multiple traces boundary integral formulation for Helmholtz transmission problems
• Boundary integral equations in time-harmonic acoustic scattering
• A periodic FMM for Maxwell's equations in 3D and its applications to problems related to photonic crystals
• Corner singularities for elliptic problems: Integral equations, graded meshes, quadrature, and compressed inverse preconditioning
• A higher order numerical method for 3-D double periodic electromagnetic scattering problems
• Integral equation methods for elliptic problems with boundary conditions of mixed type
• Solution of acoustic scattering problems by means of second kind integral equations
• The Green's function for the two-dimensional Helmholtz equation in periodic domains
• A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
• A fast direct solver for boundary integral equations in two dimensions
• Data-sparse approximation by adaptive \({\mathcal H}^2\)-matrices
• A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems
• Lattice sums for gratings and arrays
• Lattice sums and the two-dimensional, periodic Green's function for the Helmholtz equation
• A fast summation method for oscillatory lattice sums
• A Nonlinear Optimization Procedure for Generalized Gaussian Quadratures
• Lattice Sums for the Helmholtz Equation
• An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization
• Boundary-Integral Calculations of Two-Dimensional Electromagnetic Scattering in Infinite Photonic Crystal Slabs: Channel Defects and Resonances
• An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons
• Superfast Multifrontal Method for Large Structured Linear Systems of Equations
• Fast direct solvers for integral equations in complex three-dimensional domains
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Transmission problems for the Helmholtz equation
• Integral Equation Methods in a Quasi-Periodic Diffraction Problem for the Time-Harmonic Maxwell’s Equations
• Hybrid Gauss-Trapezoidal Quadrature Rules
• Guided waves by electromagnetic gratings and non‐uniqueness examples for the diffraction problem
• Boundary Integral Calculations of Two-Dimensional Electromagnetic Scattering by Photonic Crystal Fabry--Perot Structures
• Accuracy and Stability of Numerical Algorithms
• A Fast Direct Solver for Structured Linear Systems by Recursive Skeletonization
• A Fast $ULV$ Decomposition Solver for Hierarchically Semiseparable Representations
• On the Compression of Low Rank Matrices
• A Fast Solver for HSS Representations via Sparse Matrices
• Algorithm 832
• Acoustic and electromagnetic equations. Integral representations for harmonic problems

This page was built for publication: A fast direct solver for scattering from periodic structures with multiple material interfaces in two dimensions