Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxll's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxll's equations with dissipation terms,  first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme.  have obtained four formal local conservation laws and three formal energy global conservation laws.  have also proved that both of our derived schemes preserve the discrete version of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxll's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme.  also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very ll even after long time propagation.
['Hongling Su', 'Shengtai Li']
I am writing a research paper on a idea Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms
[{"from": "human", "value": "I am writing a research paper on a idea Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxll's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxll's equations with dissipation terms,  first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme.  have obtained four formal local conservation laws and three formal energy global conservation laws.  have also proved that both of our derived schemes preserve the discrete version of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxll's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme.  also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show that the Birkhoffian scheme recovers the magnitude of the current source and reaction history very ll even after long time propagation."}]