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A finite element approach to solve numerically the Takagi-Taupin equationsexpressed in a weak form is presented and applied to simulate X-rayreflectivity curves, spatial intensity distributions and focusing properties ofbent perfect crystals in symmetric reflection geometry. The proposed frameworkencompasses a new formulation of the Takagi-Taupin equations, which appears tobe promising in terms of robustness and stability and supports the Fresnelpropagation of the diffracted waves. The presented method is very flexible andhas the potential of dealing with dynamical X-ray or neutron diffractionproblems related to crystals of arbitrary shapes and deformations. Thereference implementation based on the commercial COMSOL Multiphysics softwarepackage is available to the relevant user community.

A finite element approach to dynamical diffraction problems