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Full-Text Articles in Engineering
On Analytic Nonlinear Input-Output Systems: Expanded Global Convergence And System Interconnections, Irina M. Winter Arboleda
On Analytic Nonlinear Input-Output Systems: Expanded Global Convergence And System Interconnections, Irina M. Winter Arboleda
Electrical & Computer Engineering Theses & Dissertations
Functional series representations of nonlinear systems first appeared in engineering in the early 1950’s. One common representation of a nonlinear input-output system are Chen-Fliess series or Fliess operators. Such operators are described by functional series indexed by words over a noncommutative alphabet. They can be viewed as a noncommutative generalization of a Taylor series. A Fliess operator is said to be globally convergent when its radius of convergence is infinite, in other words, when there is no a priori upper bound on both the L1-norm of an admissible input and the length of time over which the corresponding output is …
On Hybrid Temporal Basis Functions For Stable Numerical Solution Of Time Domain Boundary Integral Equations, Fang Q. Hu
On Hybrid Temporal Basis Functions For Stable Numerical Solution Of Time Domain Boundary Integral Equations, Fang Q. Hu
Mathematics & Statistics Faculty Publications
Problems in unsteady aerodynamics and aeroacoustics can sometimes be formulated as integral equations, such as the boundary integral equations. Numerical discretization of integral equations in the time domain often leads to so-called March-On-in-Time (MOT) schemes. In the literature, the temporal basis functions used in MOT schemes have been largely limited to low-order shifted Lagrange basis functions. In order to evaluate the accuracy and effectiveness of the temporal basis functions, a Fourier analysis of the temporal interpolation schemes is carried out. Based on the Fourier analysis, the spectral resolutions of various temporal basis functions are quantified. It is argued that hybrid …