求解多维对流扩散反应方程的小波-傅里叶CORSING方法
Wavelet-Fourier CORSING techniques for multi-dimensional advection-diffusion-reaction equations
摘要：
基于CORSING（COmpRessed SolvING）范式，我们提出并分析了一种新的小波-傅立叶技术用于多维对流-扩散-反应方程的数值处理。将Petrov-Galerkin技术与压缩感知方法相结合，该方法能够逼近双正交小波基的解的最大系数。也就是说，我们组装一个压缩离散化的基础上随机抽样的傅立叶测试空间，我们采用稀疏恢复技术近似的解决方案的PDE。在本文中，我们提供了第一个严格的恢复误差界和有效的食谱，在多维设置的CORSING技术的实施。我们的理论分析依赖于新的估计的本地a-相干性，测量小波和傅立叶基函数之间的干扰相对于由PDE算子引起的度量。所提出的计划的稳定性和鲁棒性所示的数值例子中的一个，两个，和三维的情况下。
英文摘要：
We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection-diffusion-reaction equations based on the CORSING (COmpRessed SolvING) paradigm. Combining the Petrov-Galerkin technique with the compressed sensing approach, the proposed method is able to approximate the largest coefficients of the solution with respect to a biorthogonal wavelet basis. Namely, we assemble a compressed discretization based on randomized subsampling of the Fourier test space and we employ sparse recovery techniques to approximate the solution to the PDE. In this paper, we provide the first rigorous recovery error bounds and effective recipes for the implementation of the CORSING technique in the multi-dimensional setting. Our theoretical analysis relies on new estimates for the local a-coherence, which measures interferences between wavelet and Fourier basis functions with respect to the metric induced by the PDE operator. The stability and robustness of the proposed scheme is shown by numerical illustrations in the one-, two-, and three-dimensional case.
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。
