Stability of a modified Peaceman-Rachford method for the paraxial Helmholtz equation on adaptive grids

DOI10.1016/j.jcp.2016.08.040zbMath1375.78021OpenAlexW2508064088MaRDI QIDQ1685106

Qin Sheng, Hai-Wei Sun

Publication date: 13 December 2017

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2016.08.040

zbMATH Keywords

asymptotic stabilitysplitting methodsadaptive gridshigh oscillationseikonal transformationparaxial wave approximations

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Waves and radiation in optics and electromagnetic theory (78A40)

Related Items (2)

Nonlinear Riemann type problems associated to Hermitian Helmholtz equations ⋮ A preservative splitting approximation of the solution of a variable coefficient quenching problem

Cites Work

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• An exponential transformation based splitting method for fast computations of highly oscillatory solutions
• A numerical coordinate transformation for efficient evaluation of oscillatory integrals over wave boundary integrals
• An effective \(z\)-stretching method for paraxial light beam propagation simulations
• Exponential splitting for \(n\)-dimensional paraxial Helmholtz equation with high wavenumbers
• On classification of symmetry reductions for the eikonal equation
• Encyclopedia of Applied and Computational Mathematics
• Highly Oscillatory Diffusion-Type Equations
• On highly oscillatory problems arising in electronic engineering
• A continuing exploration of a decomposed compact method for highly oscillatory wave problems

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