超几何偏微分方程模型降阶的传输反转
Transport reversal for model reduction of hyperbolic partial differential equations
AI总结：
本文提出一种迭代算法，通过分解快照矩阵为多个移位剖面，解决超几何偏微分方程快照矩阵奇异值缓慢衰减的问题，并给出几何解释。
摘要：
由超几何偏微分方程解构建的快照矩阵表现出奇异值缓慢衰减，而快速衰减对基于投影的模型降阶方法至关重要。本文基于对称降阶方法，提出一种迭代算法，将快照矩阵分解为多个具有相应速度的移位剖面。通过数值示例展示了该方法在典型超几何问题中的适用性，并考虑了其他自然扩展，修改移位算子。最后，给出了该算法的几何解释。
英文摘要：
Snapshot matrices built from solutions to hyperbolic partial differential equations exhibit slow decay in singular values, whereas fast decay is crucial for the success of projection- based model reduction methods. To overcome this problem, we build on previous work in symmetry reduction [Rowley and Marsden, Physica D (2000), pp. 1-19] and propose an iterative algorithm that decomposes the snapshot matrix into multiple shifting profiles, each with a corresponding speed. Its applicability to typical hyperbolic problems is demonstrated through numerical examples, and other natural extensions that modify the shift operator are considered. Finally, we give a geometric interpretation of the algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
