An efficient adaptive mesh redistribution method for a nonlinear Dirac equation

DOI10.1016/j.jcp.2006.07.011zbMath1110.65085OpenAlexW2037728558WikidataQ104006857 ScholiaQ104006857MaRDI QIDQ870608

Han Wang, Hua-Zhong Tang

Publication date: 13 March 2007

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2006.07.011

zbMATH Keywords

algorithmconvergencenumerical experimentssolitary waveshock-capturing methodhigh resolution schemelocal uniform refinementthe Dirac equation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) PDEs in connection with quantum mechanics (35Q40) Computational methods for problems pertaining to quantum theory (81-08) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (16)

High-order conservative schemes for the nonlinear Dirac equation ⋮ Uniformly Accurate Nested Picard Iterative Integrators for the Nonlinear Dirac Equation in the Nonrelativistic Regime ⋮ Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime ⋮ Numerical methods for nonlinear Dirac equation ⋮ A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in \((1+1)\)D ⋮ Numerical simulations of time-dependent partial differential equations ⋮ Finite difference time domain methods for the Dirac equation coupled with the Chern-Simons gauge field ⋮ A Splitting Spectral Method for the Nonlinear Dirac-Poisson Equations ⋮ High-order compact methods for the nonlinear Dirac equation ⋮ Nonlinear spin and pseudo-spin symmetric Dirac equations ⋮ Structure-Preserving Wavelet Algorithms for the Nonlinear Dirac Model ⋮ Three Discontinuous Galerkin Methods for One- and Two-Dimensional Nonlinear Dirac Equations with a Scalar Self-Interaction ⋮ An integrating factor for nonlinear Dirac equations ⋮ Compact implicit integration factor method for the nonlinear Dirac equation ⋮ A uniformly accurate (UA) multiscale time integrator pseudospectral method for the nonlinear Dirac equation in the nonrelativistic limit regime ⋮ A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Dirac Equation in the Nonrelativistic Limit Regime

Uses Software

• CLAWPACK

Cites Work

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