A heterogeneous FMM for layered media Helmholtz equation. I: Two layers in \(\mathbb{R}^2\)

DOI10.1016/j.jcp.2018.05.007zbMath1392.78018arXiv1703.09136OpenAlexW2799865484MaRDI QIDQ725487

Dangxing Chen, Jingfang Huang, Wei Cai, Min-Hyung Cho

Publication date: 1 August 2018

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

Full work available at URL: https://arxiv.org/abs/1703.09136

zbMATH Keywords

Helmholtz equationhierarchical modelfast multipole methodimpedance boundary conditionlow-rank representationmultilayered media

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Composite media; random media in optics and electromagnetic theory (78A48) Multipole methods applied to problems in optics and electromagnetic theory (78M16)

Related Items (7)

Adapting free-space fast multipole method for layered media Green's function: algorithm and analysis ⋮ A hybrid stochastic interpolation and compression method for kernel matrices ⋮ Exponential Convergence for Multipole and Local Expansions and Their Translations for Sources in Layered Media: Two-Dimensional Acoustic Wave ⋮ Spectrally-accurate numerical method for acoustic scattering from doubly-periodic 3D multilayered media ⋮ An \(O(N \log N)\) hierarchical random compression method for kernel matrices by sampling partial matrix entries ⋮ Taylor expansion based fast multipole method for 3-d Helmholtz equations in layered media ⋮ A new numerical approach to the solution of the 2-D Helmholtz equation with optimal accuracy on irregular domains and Cartesian meshes

Uses Software

• Cilk
• 2D-WFMM
• DASHMM

Cites Work

• Unnamed Item
• Quadrature by expansion: a new method for the evaluation of layer potentials
• A parallel fast algorithm for computing the Helmholtz integral operator in 3-D layered media
• A wideband fast multipole method for the two-dimensional complex Helmholtz equation
• Extending the fast multipole method to charges inside or outside a dielectric sphere
• Rapid solution of integral equations of scattering theory in two dimensions
• A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
• On the efficient representation of the half-space impedance Green's function for the Helmholtz equation
• A sparse \({\mathcal H}\)-matrix arithmetic. II: Application to multi-dimensional problems
• Efficient and accurate computation of electric field dyadic Green's function in layered media
• A wideband fast multipole method for the Helmholtz equation in three dimensions
• Windowed Green Function Method for Layered-Media Scattering
• Fast direct solvers for integral equations in complex three-dimensional domains
• Multi-Level Adaptive Solutions to Boundary-Value Problems
• Hybrid Gauss-Trapezoidal Quadrature Rules
• High-Order Corrected Trapezoidal Quadrature Rules for Singular Functions
• Accurate and Efficient Nyström Volume Integral Equation Method for Electromagnetic Scattering of 3-D Metamaterials in Layered Media
• A Fast Direct Solver for Structured Linear Systems by Recursive Skeletonization
• Preface
• An Algorithm for the Machine Calculation of Complex Fourier Series
• A fast volume integral equation solver for electromagnetic scattering from large inhomogeneous objects in planarly layered media
• Computational Software: Simple FMM Libraries for Electrostatics, Slow Viscous Flow, and Frequency-Domain Wave Propagation
• <scp>REC</scp>FMM: Recursive Parallelization of the Adaptive Fast Multipole Method for Coulomb and Screened Coulomb Interactions
• DASHMM: Dynamic Adaptive System for Hierarchical Multipole Methods
• Integral Equation Methods in Scattering Theory
• Linear integral equations

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