A well-balanced and asymptotic-preserving scheme for the one-dimensional linear Dirac equation
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| 024 | 7 | 0 | |a 10.1007/s10543-014-0510-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10543-014-0510-4 | ||
| 100 | 1 | |a Gosse |D Laurent |u Istituto per le Applicazioni del Calcolo, Via dei Taurini, 19, 00185, Rome, Italy |4 aut | |
| 245 | 1 | 2 | |a A well-balanced and asymptotic-preserving scheme for the one-dimensional linear Dirac equation |h [Elektronische Daten] |c [Laurent Gosse] |
| 520 | 3 | |a 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 $$L^2$$ L 2 norm despite being explicit in time. This construction is well-suited for particles for which the reference velocity is of the order of $$c$$ c , the speed of light. Moreover, when $$c$$ c 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 Schrödinger equation for free particles, but it handles the more intricate case with an external potential only conditionally (the grid should be such that $$c \Delta x\rightarrow 0$$ c Δ x → 0 ). Such a stringent restriction on the computational grid can be circumvented easily in order to derive a seemingly original Schrödinger scheme still containing tiny relativistic features. Numerical tests (on both linear and nonlinear equations) are displayed. | |
| 540 | |a Springer Science+Business Media Dordrecht, 2014 | ||
| 690 | 7 | |a Dirac equation |2 nationallicence | |
| 690 | 7 | |a One-dimensional relativistic quantum mechanics |2 nationallicence | |
| 690 | 7 | |a Asymptotic-preserving and well-balanced numerical methods |2 nationallicence | |
| 773 | 0 | |t BIT Numerical Mathematics |d Springer Netherlands |g 55/2(2015-06-01), 433-458 |x 0006-3835 |q 55:2<433 |1 2015 |2 55 |o 10543 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10543-014-0510-4 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10543-014-0510-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Gosse |D Laurent |u Istituto per le Applicazioni del Calcolo, Via dei Taurini, 19, 00185, Rome, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t BIT Numerical Mathematics |d Springer Netherlands |g 55/2(2015-06-01), 433-458 |x 0006-3835 |q 55:2<433 |1 2015 |2 55 |o 10543 | ||