Control Volume Isogeometric Analysis for groundwater flow modeling in heterogeneous porous media

Gotovac, Hrvoje; Malenica, Luka; Gotovac, Blaž

doi:10.1016/j.advwatres.2020.103838

Cited by 6 publications

(1 citation statement)

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“…The first monographs on the results of research were published in [ 36 , 37 ], while in [ 38 , 39 ] a detailed analysis of the current publications on ABF is provided, from the first publications until now. Furthermore, based on ABF theory, many different classes of weight functions have arisen, which are often used, especially in digital signal processing [ 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 ] and groundwater flow modeling [ 48 , 49 , 50 , 51 ]. A very interesting theory of atomic solitons is based on ABF theory that is used in new areas, like matter quantization, quantum gravity, Higgs fields, unified theory of nature, as well as in non-traditional areas, like medicine and life sciences, geology and financial markets [ 52 , 53 , 54 , 55 ].…”

Section: Introductionmentioning

confidence: 99%

Numerical Algorithms for Estimating Probability Density Function Based on the Maximum Entropy Principle and Fup Basis Functions

Kurbaša

Gotovac

Kozulić

et al. 2021

Entropy

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Estimation of the probability density function from the statistical power moments presents a challenging nonlinear numerical problem posed by unbalanced nonlinearities, numerical instability and a lack of convergence, especially for larger numbers of moments. Despite many numerical improvements over the past two decades, the classical moment problem of maximum entropy (MaxEnt) is still a very demanding numerical and statistical task. Among others, it was presented how Fup basis functions with compact support can significantly improve the convergence properties of the mentioned nonlinear algorithm, but still, there is a lot of obstacles to an efficient pdf solution in different applied examples. Therefore, besides the mentioned classical nonlinear Algorithm 1, in this paper, we present a linear approximation of the MaxEnt moment problem as Algorithm 2 using exponential Fup basis functions. Algorithm 2 solves the linear problem, satisfying only the proposed moments, using an optimal exponential tension parameter that maximizes Shannon entropy. Algorithm 2 is very efficient for larger numbers of moments and especially for skewed pdfs. Since both Algorithms have pros and cons, a hybrid strategy is proposed to combine their best approximation properties.

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