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Computational aspects of harmonic wavelet Galerkin methods and an application to a precipitation front propagation model

机译:谐波小波Galerkin方法的计算方面及其在降水前传播模型中的应用

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This article is dedicated to harmonic wavelet Galerkin methods for the solution of partial differential equations. Several variants of the method are proposed and analyzed, using the Burgers equation as a test model. The computational complexity can be reduced when the localization properties of the wavelets and restricted interactions between different scales are exploited. The resulting variants of the method have computational complexities ranging from O(N~3) to O(N) (N being the space dimension) per time step. A pseudo-spectral wavelet scheme is also described and compared to the methods based on connection coefficients. The harmonic wavelet Calerkin scheme is applied to a nonlinear model for the propagation of precipitation fronts, with the front locations being exposed in the sizes of the localized wavelet coefficients.
机译:本文致力于谐波小波Galerkin方法的偏微分方程解。使用Burgers方程作为测试模型,提出并分析了该方法的几种变体。当利用小波的定位特性和不同尺度之间的受限相互作用时,可以降低计算复杂度。该方法的结果变体具有每时间步长从O(N〜3)到O(N)(N是空间维)的计算复杂度。还描述了伪谱小波方案,并将其与基于连接系数的方法进行了比较。谐波小波Calerkin方案应用于降水锋面传播的非线性模型,其中锋面的位置暴露在局部小波系数的大小中。

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