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- W2594365593 abstract "Walsh functions form an orthonormal basis set consisting of square waves. Square waves make the system well suited for detecting and representing functions with discontinuities. Given a uniform distribution of 2p cells on a one-dimensional element, it is proved that the inner product of the Walsh Root function for group p with every polynomial of degree (p1) across the element is identically zero. It is also proved that the magnitude and location of a discontinuous jump, as represented by a Heaviside function, are explicitly identified by its Fast Walsh Transform (FWT) coefficients. These two proofs enable an algorithm that quickly provides a Weighted Least Squares fit to distributions across the element that include a discontinuity. It is shown that flux reconstruction relative to the FWT fit in partial differential equations provides improved accuracy. The detection of a discontinuity further enables analytic relations to locally describe its evolution and provide increased accuracy. Examples are provided for time-accurate advection, Burgers' equation, and quasi-one-dimensional nozzle flow." @default.
- W2594365593 created "2017-03-16" @default.
- W2594365593 creator A5089169844 @default.
- W2594365593 date "2017-06-01" @default.
- W2594365593 modified "2023-09-24" @default.
- W2594365593 title "Solutions of nonlinear differential equations with feature detection using fast Walsh transforms" @default.
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- W2594365593 doi "https://doi.org/10.1016/j.jcp.2017.03.016" @default.
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