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article / document resource request "5227"
MS Classification: 65M06 (Primary), 78A45 (Secondary) 1999-01-18 arXiv:physics/arXiv:9901033,
DOI: 10.48550/arXiv.physics/9901033 19 P. January 1999 Keywords: X-ray Diffraction, Takagi Equations, PDEs, Hyperbolic Systems, Finite Differences, Scientific Computing The objective of this article is to study the behavior of electromagnetic field under
X-ray diffraction by time-dependent deformed crystals. Derived system of differential
equations looks like the Takagi equations in the case of non-stationary crystals. This is a
system of multidimensional first-order hyperbolic equations with complex time-dependent
coefficients. Efficient difference schemes based on the multicomponent modification of
the alternating direction method are proposed. The stability and convergence of devised
schemes are proved. Numerical results are shown for the case of an ideal crystal, a crystal
heated uniformly according to a linear law and a time-varying bent crystal. Detailed
numerical studies indicate the importance of consideration even small crystal changes. Download:
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