论文标题
多尺度多维线性传输方程
An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation
论文作者
论文摘要
我们引入了一种动态低级方法，以降低解决多尺度多维线性传输方程的计算复杂性。该方法基于方程式的宏微分解。所提出的数值方法仅用于溶液的微部分。时间和空间离散是正确完成的，以便整体方案是二阶准确且渐近可及的（AP）；也就是说，在扩散状态下，该方案成为限制扩散方程的宏观求解器，并且自动级别较低。我们通过许多二维示例证明了所提出的低级方法的准确性和效率。
We introduce a dynamical low-rank method to reduce the computational complexity for solving the multi-scale multi-dimensional linear transport equation. The method is based on a macro-micro decomposition of the equation. The proposed numerical method uses the low rank approximation only for the micro part of the solution. The time and spatial discretizations are done properly so that the overall scheme is second order accurate and asymptotic-preserving (AP); that is, in the diffusive regime, the scheme becomes a macroscopic solver for the limiting diffusion equation and is automatically low rank. We demonstrate the accuracy and efficiency of the proposed low rank method by a number of two-dimensional examples.
