Preconditioning based on Calderón's formulae for periodic fast multipole methods for Helmholtz equation

DOI10.1016/j.jcp.2011.08.019zbMath1243.65141OpenAlexW1989511950MaRDI QIDQ425602

Kazuki Niino, Naoshi Nishimura

Publication date: 8 June 2012

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2011.08.019

zbMATH Keywords

performancenumerical examplesconvergence accelerationboundary element methodpreconditioningHelmholtz equationfast multipole methodCalderón's formulaeWood's anomaly

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Complexity and performance of numerical algorithms (65Y20) Boundary element methods for boundary value problems involving PDEs (65N38) Preconditioners for iterative methods (65F08)

Related Items (11)

Boundary integral formulations for acoustic modelling of high-contrast media ⋮ Stable and efficient FEM-BEM coupling with OSRC regularisation for acoustic wave transmission ⋮ Conforming boundary element methods in acoustics ⋮ Fast multipole boundary element method for the acoustic analysis of finite periodic structures ⋮ Boundary Integral Equations for Calculating Complex Eigenvalues of Transmission Problems ⋮ An FMM for waveguide problems of 2-D Helmholtz' equation and its application to eigenvalue problems ⋮ Application of the inverse fast multipole method as a preconditioner in a 3D Helmholtz boundary element method ⋮ Recent Advances in Acoustic Boundary Element Methods ⋮ An efficient preconditioner for adaptive fast multipole accelerated boundary element methods to model time-harmonic 3D wave propagation ⋮ Application of the multi-level time-harmonic fast multipole BEM to 3-D visco-elastodynamics ⋮ A level-set-based topology optimisation for acoustic-elastic coupled problems with a fast BEM-FEM solver

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A periodic FMM for Maxwell's equations in 3D and its applications to problems related to photonic crystals
• Existence of guided modes on periodic slabs
• The construction of some efficient preconditioners in the boundary element method
• A new integral representation for quasi-periodic fields and its application to two-dimensional band structure calculations
• Calderon's preconditioning for periodic fast multipole method for elastodynamics in 3D
• An integral preconditioner for solving the two-dimensional scattering transmission problem using integral equations
• An FMM for periodic boundary value problems for cracks for Helmholtz' equation in 2D
• Guided waves by electromagnetic gratings and non‐uniqueness examples for the diffraction problem
• Des préconditionneurs pour la résolution numérique des équations intégrales de frontière de l'acoustique
• A Preconditioner for the Electric Field Integral Equation Based on Calderon Formulas
• A Comparative Study of Calderón Preconditioners for PMCHWT Equations
• A Multiplicative Calderon Preconditioner for the Electric Field Integral Equation
• A dual finite element complex on the barycentric refinement

This page was built for publication: Preconditioning based on Calderón's formulae for periodic fast multipole methods for Helmholtz equation