Symplectic and multisymplectic numerical methods for Maxwell's equations
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Publication:630457
DOI10.1016/j.jcp.2010.12.006zbMath1210.78029OpenAlexW2093162681MaRDI QIDQ630457
Publication date: 17 March 2011
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2010.12.006
dispersion relationsMaxwell's equationssymplectic methodsbackward error analysisenergy-preserving methodsmultisymplectic methods
Finite difference methods applied to problems in optics and electromagnetic theory (78M20) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)
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Cites Work
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- Dispersive properties of multisymplectic integrators
- Splitting multisymplectic integrators for Maxwell's equations
- The Hamiltonian structure of the Maxwell-Vlasov equations
- Multisymplectic geometry, variational integrators, and nonlinear PDEs
- Symplectic integration of Hamiltonian wave equations
- Multisymplectic box schemes and the Korteweg-de Vries equation.
- Geometric space-time integration of ferromagnetic materials.
- Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
- The symplecticity of multi-step methods
- Quadratic invariants and multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs
- Energy-conserved splitting FDTD methods for Maxwell's equations
- Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
- New multisymplectic self-adjoint scheme and its composition scheme for the time-domain Maxwell’s equations
- Geometric Computational Electrodynamics with Variational Integrators and Discrete Differential Forms
- Numerical Methods for Evolutionary Differential Equations
- On the multisymplecticity of partitioned Runge–Kutta and splitting methods
- Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
- Group Velocity in Finite Difference Schemes
- On Krylov Subspace Approximations to the Matrix Exponential Operator
- Numerical methods for Hamiltonian PDEs
- Geometric Numerical Integration
- Linear PDEs and Numerical Methods That Preserve a Multisymplectic Conservation Law
- Computational Electromagnetics
- Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
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