Robust model reduction by L^1 -norm minimization and approximation via dictionaries: application to nonlinear hyperbolic problems
Adv. Model. and Simul. in Eng. Sciences(2016)
摘要
We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online L^1 - norm minimization of the residual. It is shown why this is a natural framework for hyperbolic problems and tested on nonlinear problems such as Burgers’ equation and the one-dimensional Euler equations involving shocks and discontinuities. Efficient algorithms are presented for the computation of the L^1 -norm minimizer, both in the cases of linear and nonlinear residuals. Results indicate that the method has the potential of being accurate when involving only very few modes, generating physically acceptable, oscillation-free, solutions.
更多查看译文
关键词
Model reduction,Dictionaries,$$L^{1}$$L1-norm residual minimization
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要