Dynamical low-rank approximation for radiation transport with random input

我的项目的重点是发展一种有效的方法来计算辐射输运的不确定性。在该应用领域中，寻求依赖于具有高维度的相空间的粒子分布。这种高维相空间的数值离散化导致相当大的数值成本和传统方法中的高内存要求。特别是在我们研究的放射治疗领域，对精度的高要求和对不确定性的考虑产生了显着高维的相空间，这是常规方法无法解决的。在本项目中，我们开发了一种基于动态低秩近似的离散化方法，大大降低了内存需求和数值成本。该方法的效率基于三个要求，将在项目中进行调查和开发。这些要求包括一个问题相关的推导的演化方程，一个强大的空间离散化，并有效地实现现代计算机体系结构。

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.