Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  is devoted to the efficient computation of the time dependent Schrodinger equation for quantum particles subject to intense electromagnetic fields including ionization and recombination of electrons with their parent ion. The proposed approach is based on a domain decomposition technique, allowing a fine computation of the wavefunction in the vicinity of the nuclei located in a domain $$\Omega _1$$Ω1 and a fast computation in a roughly meshed domain $$\Omega _2$$Ω2 far from the nuclei where the electrons are assumed free. The key ingredients in the method are (i) ll designed transmission boundary conditions on $$\partial \Omega _1$$?Ω1 (resp. $$\partial \Omega _2$$?Ω2) in order to estimate the part of the wavefunction "leaving" Domain $$\Omega _1$$Ω1 (resp. $$\Omega _2$$Ω2), (ii) a Schwarz waveform relaxation algorithm to accurately reconstruct the solution. The developed method makes it possible for electrons to travel from one domain to another without loosing accuracy, when the frontier or the overlapping region beten two domains is crossed by the wavefunction.
['Xavier Antoine', 'Emmanuel Lorin', 'André D. Bandrauk']
I am writing a research paper on a idea Domain Decomposition Method and High-Order Absorbing Boundary Conditions for the Numerical Simulation of the Time Dependent Schrödinger Equation with Ionization and Recombination by Intense Electric Field
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