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Application of harmonic coordinates to 2D interface problems on regular grids
Finite difference and finite element methods exhibit first order convergence when applied to static interface problems where the grid and interface are not aligned. Although modified and unstructured grid methods would ...
Nonlinear model reduction via discrete empirical interpolation
This thesis proposes a model reduction technique for nonlinear dynamical systems based upon combining Proper Orthogonal Decomposition (POD) and a new method, called the Discrete Empirical Interpolation Method (DEIM). The ...
Ritz values and Arnoldi convergence for non-Hermitian matrices
This thesis develops ways of localizing the Ritz values of non-Hermitian matrices. The restarted Arnoldi method with exact shifts, useful for determining a few desired eigenvalues of a matrix, employs Ritz values to refine ...
Compressive Sensing for 3D Data Processing Tasks: Applications, Models and Algorithms
Compressive sensing (CS) is a novel sampling methodology representing a paradigm shift from conventional data acquisition schemes. The theory of compressive sensing ensures that under suitable conditions compressible signals ...