Simulation of Synchrotron White-Beam Topographs. An Algorithm for Parallel Processing: Application to the Study of Piezoelectric Devices

This paper presents a new algorithm for the integration of Takagi-Taupin equations taking into account the fact that X-ray diffraction is a parallel phenomenon. The diffraction equations show that the propagation of the waves is independent in each incidence plane. It is thus possible to compute in parallel the propagation of the waves in different planes. Two algorithms are presented: the first one for multiprocessor machines where the processors share a common memory, the second one for massively parallel computers. The program is written to achieve a high vectorization ratio and to make it as efficient as possible with modem superscalar and array processors. The simulation of the image of a defect has been divided into two independent parts. In the first one, one computes the derivatives of the deformation inside the crystal; in the second one, these results are used to simulate the image. This allows one rapidly to change the model for a defect, something that was not feasible in all previously written simulation programs since the computation of the deformation was part of the simulation. The study of stroboscopic images of the propagation of acoustic waves in piezoelectric devices is given as an example of the possibilities of this new program.