Optrans: a parallel software library for optimal transport. In recent years, optimal transport has become a highly active and wide area of research, thanks to the discovery of a number of important theoretical results and the development of an array of new applications in various fields ranging from cosmology, geophysics, oceanography, meteorology and fluid mechanics to optics, image processing and pattern recognition. Despite this ample field of applications, there is a serious lack of numerical optimal transport softwares available to the research and academic community. To remedy to this shortage, this paper introduces Optrans, a parallel library for solving time-dependent optimal transport problems in free and convexly constrained forms. Optrans is designed following an object oriented approach and exploits the capabilities of C++, the implementation language, to offer an easy-to-use programming interface and ensure easy-extendability. The library uses MPI for communication and synchronization, allowing it to run on a variety of architectures. In addition to the software related aspects of the library, a number of implemented numerical techniques are presented, for instance, solving transport problems on domains with null Neumann boundary conditions and using a smoothing term to transport densities that approach zero. Numerical experiments are presented to demonstrate the capabilities of the library and the implemented techniques.

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  1. Kerrache, Said; Nakauchi, Yasushi: Optrans: a parallel software library for optimal transport (2010)