A simple and accurate mixed \(P^{0}-Q^{1}\) solver for the Maxwell-Dirac equations

DOI10.1016/j.nonrwa.2010.06.007zbMath1202.35014OpenAlexW1490137490MaRDI QIDQ611231

Emmanuel Lorin, André D. Bandrauk

Publication date: 14 December 2010

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2010.06.007

zbMATH Keywords

finite element methodhyperbolic systemsrelativistic particlesexternal ultrashort pulselaser-gas interaction

Mathematics Subject Classification ID

Theoretical approximation in context of PDEs (35A35) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Maxwell equations (35Q61) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (14)

Stationary state computation for nonlinear Dirac operators ⋮ Error Estimate of a New Conservative Finite Difference Scheme for the Klein-Gordon-Dirac System ⋮ Avoiding the Coordinate Singularity Problem in the Numerical Solution of the Dirac Equation in Cylindrical Coordinates ⋮ A split-step numerical method for the time-dependent Dirac equation in 3-D axisymmetric geometry ⋮ Absorbing boundary conditions for relativistic quantum mechanics equations ⋮ Vortices and vortex sources of multiple vortex interaction systems ⋮ Conservative second-order accurate finite-difference scheme for the coupled Maxwell-Dirac equations ⋮ Numerical solution of the time-dependent Dirac equation in coordinate space without fermion-doubling ⋮ High-order compact methods for the nonlinear Dirac equation ⋮ A simple pseudospectral method for the computation of the time-dependent Dirac equation with perfectly matched layers ⋮ Computational performance of simple and efficient sequential and parallel Dirac equation solvers ⋮ Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis ⋮ Frozen Gaussian Approximation for the Dirac Equation in Semiclassical Regime ⋮ Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces

Uses Software

• Dirac++

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multiresolution scheme for time-dependent Schrödinger equation
• A numerical Maxwell-Schrödinger model for intense laser-matter interaction and propagation
• FFT-split-operator code for solving the Dirac equation in \(2+1\) dimensions
• Numerical approximation of hyperbolic systems of conservation laws
• Quantum dynamics of relativistic electrons
• An efficient and stable numerical method for the Maxwell--Dirac system
• A time-splitting spectral scheme for the Maxwell-Dirac system
• Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension
• Convergence of the Dirac–Maxwell System to the Vlasov–Poisson System
• Footbridge between finite volumes and finite elements with applications to CFD
• Asymptotic completeness, global existence and the infrared problem for the Maxwell-Dirac equations
• ON THE ASYMPTOTIC ANALYSIS OF THE DIRAC–MAXWELL SYSTEM IN THE NONRELATIVISTIC LIMIT
• Local existence for the maxwell-dirac equations in three space dimensions
• The cauchy problem for the coupled maxwell and dirac equations
• Éléments finis: théorie, applications, mise en œuvre.

This page was built for publication: A simple and accurate mixed \(P^{0}-Q^{1}\) solver for the Maxwell-Dirac equations