Dynamical low-rank approximation for radiation transport with random input

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The focus of my project is the development of an efficient method for the computation of radiation transport under uncertainties. In this application field, a partical distribution is sought that depends on a phase space with high dimension. The numerical discretization of this high-dimensional phase space leads to considerable numerical costs and high memory requirements in conventional methods. In particular, in the field of radiotherapy, which we study in this project, the high requirements for accuracy and the consideration of uncertainties yield phase spaces with significantly high dimension, which conventional methods cannot resolve.In this project, we develop a discretization method based on the dynamic low-rank approximation that greatly reduces memory requirements and numerical costs. The efficiency of this method is based on three requirements, which will be investigated and developed within the project. These equirements consist of a problem-dependent derivation of the evolution equations, a robust spatial discretization, and an efficient implementation for modern computer architecture.