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Full-Text Articles in Physical Sciences and Mathematics
Analysis And Application Of Perfectly Matched Layer Absorbing Boundary Conditions For Computational Aeroacoustics, Sarah Anne Parrish
Analysis And Application Of Perfectly Matched Layer Absorbing Boundary Conditions For Computational Aeroacoustics, Sarah Anne Parrish
Mathematics & Statistics Theses & Dissertations
The Perfectly Matched Layer (PML) was originally proposed by Berenger as an absorbing boundary condition for Maxwell's equations in 1994 and is still used extensively in the field of electromagnetics. The idea was extended to Computational Aeroacoustics in 1996, when Hu applied the method to Euler's equations. Since that time much of the work done on PML in the field of acoustics has been specific to the case where mean flow is perpendicular to a boundary, with an emphasis on Cartesian coordinates. The goal of this work is to further extend the PML methodology in a two-fold manner: First, to …
Dgm-Fd: A Finite Difference Scheme Based On The Discontinuous Galerkin Method, Anne Marguerite Fernando
Dgm-Fd: A Finite Difference Scheme Based On The Discontinuous Galerkin Method, Anne Marguerite Fernando
Mathematics & Statistics Theses & Dissertations
Accurate and efficient numerical wave propagation is important in many areas of study such as computational aero-acoustics (CAA). While dissipation and dispersion errors influence the accuracy of a method, efficiency can be assessed by convergence rates and effective adaptability to different mesh structures. Finite difference and finite element methods are commonly used numerical schemes in CAA. Finite difference methods have the advantages of ease of use as well as high order convergence, but often require a uniform grid, and stable boundary closure can be non-trivial. Finite element methods adapt well to different mesh structures but can become difficult to implement …
Improved Constrained Global Optimization For Estimating Molecular Structure From Atomic Distances, Terri Marie Grant
Improved Constrained Global Optimization For Estimating Molecular Structure From Atomic Distances, Terri Marie Grant
Mathematics & Statistics Theses & Dissertations
Determination of molecular structure is commonly posed as a nonlinear optimization problem. The objective functions rely on a vast amount of structural data. As a result, the objective functions are most often nonconvex, nonsmooth, and possess many local minima. Furthermore, introduction of additional structural data into the objective function creates barriers in finding the global minimum, causes additional computational issues associated with evaluating the function, and makes physical constraint enforcement intractable. To combat the computational problems associated with standard nonlinear optimization formulations, Williams et al. (2001) proposed an atom-based optimization, referred to as GNOMAD, which complements a simple interatomic distance …