科研之友
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摘要
The numerical approximation of one-dimensional relativistic Dirac wave equations is considered within the recent framework consisting in deriving local scattering matrices at each interface of the uniform Cartesian computational grid. For a Courant number equal to unity, it is rigorously shown that such a discretization preserves exactly the norm despite being explicit in time. This construction is well-suited for particles for which the reference velocity is of the order of , the speed of light. Moreover, when diverges, that is to say, for slow particles (the characteristic scale of the motion is non-relativistic), Dirac equations are naturally written so as to let a "diffusive limit" emerge numerically, like for discrete 2-velocity kinetic models. It is shown that an asymptotic-preserving scheme can be deduced from the aforementioned well-balanced one, with the following properties: it yields unconditionally a classical Schrodinger equation for free particles, but it handles the more intricate case with an external potential only conditionally (the grid should be such that ). Such a stringent restriction on the computational grid can be circumvented easily in order to derive a seemingly original Schrodinger scheme still containing tiny relativistic features. Numerical tests (on both linear and nonlinear equations) are displayed.
- 出版日期2015-6
