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Full-Text Articles in Physical Sciences and Mathematics
A Stable Algorithm For Divergence-Free And Curl-Free Radial Basis Functions In The Flat Limit, Kathryn Primrose Drake
A Stable Algorithm For Divergence-Free And Curl-Free Radial Basis Functions In The Flat Limit, Kathryn Primrose Drake
Boise State University Theses and Dissertations
Radial basis functions (RBFs) were originally developed in the 1970s for interpolating scattered topographic data. Since then they have become increasingly popular for other applications involving the approximation of scattered, scalar-valued data in two and higher dimensions, especially data collected on the surface of a sphere. In the late 2000s, matrix-valued RBFs were introduced for approximating divergence-free and curl-free vector fields on the surface of a sphere from scattered samples, which arise naturally in atmospheric and oceanic sciences. The intriguing property of these RBFs is that the resulting vector-valued approximations analytically preserve the divergence-free or curl-free properties of the field. …
Joint Inversion Of Compact Operators, James Ford
Joint Inversion Of Compact Operators, James Ford
Boise State University Theses and Dissertations
The first mention of joint inversion came in [22], where the authors used the singular value decomposition to determine the degree of ill-conditioning in inverse problems. The authors demonstrated in several examples that combining two models in a joint inversion, and effectively stacking discrete linear models, improved the conditioning of the problem. This thesis extends the notion of using the singular value decomposition to determine the conditioning of discrete joint inversion to using the singular value expansion to determine the well-posedness of joint linear operators. We focus on compact linear operators related to geophysical, electromagnetic subsurface imaging.
The operators are …
Multi-Rate Runge-Kutta-Chebyshev Time Stepping For Parabolic Equations On Adaptively Refined Meshes, Talin Mirzakhanian
Multi-Rate Runge-Kutta-Chebyshev Time Stepping For Parabolic Equations On Adaptively Refined Meshes, Talin Mirzakhanian
Boise State University Theses and Dissertations
In this thesis, we develop an explicit multi-rate time stepping method for solving parabolic equations on a one dimensional adaptively refined mesh. Parabolic equations are characterized by their stiffness and as a result are usually solved using implicit time stepping schemes [16]. However, implicit schemes have the disadvantage that they can be expensive in higher dimensions or complicated to implement on adaptive or otherwise non-uniform meshes. Moreover, for coupled systems of parabolic equations, it can be difficult to achieve the expected order of accuracy without using sophisticated operator splitting techniques. For these reasons, we seek to exploit the properties of …