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Wen Chen
Summary Construction of multivariate wavelets for scattered data and meshfree computing via the fundamental and general solutions of partial differential equations.
Comments In recent years, we developed the distance function wavelets (DFW), which bases on the general solutions and the fundamental solutions of partial differential equations (PDE) and is a natural wavelet. In comparison, the Fourier analysis is actually to use the eigensolutions of the 1D Helmholtz equation, while the Laplace transform employs the eigensolutions of the 1D modified Helmholtz equation.

These distance function wavelets are quite different from the common wavelets, which has little to do with the PDE solutions. The DFW's are very easy and explicit to implement for multivariate scattered data and multiscale meshfree numerical PDE, and hold some very nice features such as the closed-form basis functions and shift and rotation invariants.

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