A new wavelet method for solving the Helmholtz equation with complex solution

DOI10.1002/num.22022zbMath1350.65125OpenAlexW2170267205WikidataQ115398118 ScholiaQ115398118MaRDI QIDQ2808860

F. M. Maalek Ghaini, M. H. Memarian, Reza Dehghan, Mohammad Fatehi Marji, Mohammad Reza Hooshmandasl, Mohammad Heydari

Publication date: 25 May 2016

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.22022

zbMATH Keywords

convergencenumerical exampleLegendre waveletscomplex Helmholtz equationpropagation of plane wavesderivative operational matrixintegration operational matrixmixed boundary conditions of Dirichlet and Robin type

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical methods for wavelets (65T60) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (5)

A hybrid approach based on Legendre wavelet for numerical simulation of Helmholtz equation with complex solution ⋮ Legendre wavelets Galerkin method for solving nonlinear stochastic integral equations ⋮ Legendre wavelets optimization method for variable-order fractional Poisson equation ⋮ ON LEGENDRE WAVELETS FOR POISSON EQUATION IN THE FRAME OF COMPLEX SOLUTION ⋮ A new operational matrix of fractional order integration for the Chebyshev wavelets and its application for nonlinear fractional van der Pol oscillator equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional
• A robust multilevel method for hybridizable discontinuous Galerkin method for the Helmholtz equation
• Wavelet collocation method for solving multiorder fractional differential equations
• Legendre wavelets method for solving fractional population growth model in a closed system
• Solving PDEs with the aid of two-dimensional Haar wavelets
• A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations
• Kronecker operational matrices for fractional calculus and some applications
• Nonlinear approximation schemes associated with nonseparable wavelet bi-frames
• Solution of 3D-Laplace and Helmholtz equations in exterior domains using \(hp\)-infinite elements
• A numerical assessment of parabolic partial differential equations using Haar and Legendre wavelets
• A meshless Galerkin least-square method for the Helmholtz equation
• An accelerated alternating procedure for the Cauchy problem for the Helmholtz equation
• A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution
• A survey of finite element methods for time-harmonic acoustics
• The wavelet methods to linear and nonlinear reaction-diffusion model arising in mathematical chemistry
• Two-dimensional Legendre wavelets for solving fractional Poisson equation with Dirichlet boundary conditions
• Adaptive Wavelet Schemes for Elliptic Problems---Implementation and Numerical Experiments
• The Legendre wavelets operational matrix of integration
• Legendre wavelet method for numerical solutions of partial differential equations
• Residual-free bubbles for the Helmholtz equation

This page was built for publication: A new wavelet method for solving the Helmholtz equation with complex solution