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Full-Text Articles in Physical Sciences and Mathematics
Adaptive Wavelet Discretization Of Tensor Products In H-Tucker Format, Mazen Ali
Adaptive Wavelet Discretization Of Tensor Products In H-Tucker Format, Mazen Ali
Masters Theses
"In previous work, the solution to a system of coupled parabolic PDEs, modeling the price of a CDO, was approximated numerically. Due to the nature of the problem, the system involved a large number of equations such that the parameters cannot be stored explicitly. The authors combined the data sparse H-Tucker storage format with the Galerkin method to approximate the solution, using wavelets for the space discretization together with time stepping (Method of Lines). The aforementioned approximation is of the linear kind, i.e., using a nonadaptive method. In this work, three methods for solving such systems adaptively are presented, together …
An Iterative Algorithm For Variational Data Assimilation Problems, Xin Shen
An Iterative Algorithm For Variational Data Assimilation Problems, Xin Shen
Masters Theses
"Data assimilation is a very powerful and efficient tool to use collected raw data for improving model prediction in numerical weather forecasting, hydrology, and many other areas of geosciences. In this thesis, an iterative algorithm [23] of variational data assimilation with finite element method is utilized to study different models. One motivation for this fundamental mathematical study is to provide a potential tool for simulation of CO2 sequestration by extending it to more realistic and sophisticated models in the future. The basic idea of variational data assimilation is to utilize the framework of optimal control problems. We apply the …