论文标题
降低了反应转化扩散问题的超定位正交分解
A reduced basis super-localized orthogonal decomposition for reaction-convection-diffusion problems
论文作者
论文摘要
本文提出了一种用参数依赖性系数的反应转化扩散问题的数值处理方法，这些系数是任意粗糙的，并且可能在非常细的范围内变化。提出的技术将简化基础（RB）框架与最近提出的超定位正交分解（Slod）结合在一起。更具体地说，RB用于加速典型的昂贵的平台基础计算，而slod则用于有效地压缩问题的解决方案运算符，仅需要粗求解。两种方法的综合优点都使人们可以应对参数异质系数引起的挑战。给定参数矢量的值，该方法输出了相应的压缩解决方案操作员，该操作员可用于同时有效地处理多个，可能是非植物的右侧，同时只需要一个右侧的一个粗解决方案。
This paper presents a method for the numerical treatment of reaction-convection-diffusion problems with parameter-dependent coefficients that are arbitrary rough and possibly varying at a very fine scale. The presented technique combines the reduced basis (RB) framework with the recently proposed super-localized orthogonal decomposition (SLOD). More specifically, the RB is used for accelerating the typically costly SLOD basis computation, while the SLOD is employed for an efficient compression of the problem's solution operator requiring coarse solves only. The combined advantages of both methods allow one to tackle the challenges arising from parametric heterogeneous coefficients. Given a value of the parameter vector, the method outputs a corresponding compressed solution operator which can be used to efficiently treat multiple, possibly non-affine, right-hand sides at the same time, requiring only one coarse solve per right-hand side.
