1,359,470 research outputs found
Benefits of using a Wendland Kernel for free-surface flows
No full textThe aim of this paper Is lo discuss the influence of the selection of the interpolation kernel in the accuracy of the modeling of the internal viscous dissipation in Tree surface Hows, Simulations corresponding to a standing wave* for which an analytic solution available, are presented. Wendland and renormalized Gaussian kernels are considered. The differences in the flow pattern* and Internal dissipation mechanisms are documented for a range of Reynolds numbers. It is shown that the simulations with Wendland kernels replicate the dissipation mechanisms more accurately than those with a renormalized Gaussian kernel. Although some explanations are hinted we have Tailed to clarify which the core structural reasons for Mich differences are
Wendland functions with increasing smoothness converge to a Gaussian
No full textThe Wendland functions are a class of compactly supported radial basis functions with a user-specified smoothness parameter. We prove that with an appropriate rescaling of the variables, both the original and the "missing" Wendland functions converge uniformly to a Gaussian as the smoothness parameter approaches infinity. We also explore the convergence numerically with Wendland functions of different smoothness. © 2013 Springer Science+Business Media New York
Wendland functions a C++ code to compute them
No full textIn this paper we present a code in C++ to compute Wendland functions for arbitrary smoothness parameters. Wendland functions are compactly supported Radial Basis Functions that are used for interpolation of data or solving Partial Differential Equations with mesh-free collocation. For the computations of Lyapunov functions using Wendland functions their derivatives are also needed so we include this in the code. Wendland functions with a few fixed smoothness parameters are included in some C++ libraries, but for the general case the only code freely available was implemented in MAPLE taking advantage of the computer algebra system. The aim of this contribution is to allow scientists to use Wendland functions in their C++ code without having to implement them themselves. The computed Wendland functions are polynomials and their coefficients are computed and stored in a vector, which allows for efficient computation of their values using the Horner scheme
Wendland Functions - A C++ Code to Compute Them
No full textIn this paper we present a code in C++ to compute Wendland functions for arbitrary smoothness parameters. Wendland functions are compactly supported Radial Basis Functions that are used for interpolation of data or solving Partial Differential Equations with mesh-free collocation. For the computations of Lyapunov functions using Wendland functions their derivatives are also needed so we include this in the code. Wendland functions with a few fixed smoothness parameters are included in some C++ libraries, but for the general case the only code freely available was implemented in MAPLE taking advantage of the computer algebra system. The aim of this contribution is to allow scientists to use Wendland functions in their C++ code without having to implement them themselves. The computed Wendland functions are polynomials and their coefficients are computed and stored in a vector, which allows for efficient computation of their values using the Horner scheme
The missing Wendland functions
No full textThe Wendland radial basis functions (Wendland, Adv Comput Math 4: 389-396, 1995) are piecewise polynomial compactly supported reproducing kernels in Hilbert spaces which are norm-equivalent to Sobolev spaces. But they only cover the Sobolev spaces H(d/2+ k+ 1/2)(R(d)), k is an element of N (1) and leave out the integer order spaces in even dimensions. We derive the missing Wendland functions working for half-integer k and even dimensions, reproducing integer-order Sobolev spaces in even dimensions, but they turn out to have two additional non-polynomial terms: a logarithm and a square root. To give these functions a solid mathematical foundation, a generalized version of the "dimension walk" is applied. While the classical dimension walk proceeds in steps of two space dimensions taking single derivatives, the new one proceeds in steps of single dimensions and uses "halved" derivatives of fractional calculus
Extending the generalized Wendland covariance model
No full textThe generalized Wendland covariance model is a flexible compactly supported covariance model that allows for a continuous parameterization of smoothness of the underlying Gaussian random field, and includes the celebrated Matérn as a special limit case. However, the generalized Wendland model does not cover the full range of validity of the smoothness parameter of the Matérn model. In this paper, we provide new necessary and sufficient conditions of validity of the generalized Wendland model that allows to fill this gap. The effectiveness of our proposal is illustrated through a simulation study and a re-analysis of a large geo-referenced dataset of yearly total precipitation anomalies
Closed form representations for the compactly supported radial basis functions of Buhmann, Wendland and Wu
No full textThe original compactly supported radial basis functions of Wendland and Wu have a polynomial form and are constructed using a two-step dimension walk strategy. Focussing on the Wendland functions, Schaback proposed a one-step dimension walk which is shown to recover the original Wendland functions at every second step but also introduces new examples, the so-called missing Wendland functions at the intermediate steps. In a recent paper by Huang et at., the analogue of Schaback's work is presented for the Wu functions and so deliver the so-called missing Wu functions. The original and missing Wendland functions belong to a much wider class proposed by Buhmann. The classical Buhmann functions, which are related to thin-plate spline radial basis functions, also belong to this much wider class. The theme uniting the classical Buhmann functions and the missing Wendland/Wu functions is that they are
non-polynomial and closed form expressions are not known for all of them. In this paper we revisit these functions and show how closed form representations can be given using direct techniques. The results for the classical Buhmann and Wu functions are new and the resulting expressions for the missing Wendland functions improve on those given iby the first author and so their implementation should be more straightforward
Combined resistance to Bacterial Wilt and Fusarium Wilt in common bean Genotypes derived from a segregating population.
No full textBacterial wilt (C. flaccumfaciens pv. flaccumfaciens - Cff) and Fusarium wilt (F. oxysporum f. sp. phaseoli - Fop) present similar symptoms derived from the obstruction of xylem vessels. A mapping population obtained by crossing Ouro Branco (resistant) x CNFP 10132 (susceptible), contrasting for bacterial wilt was evaluated for both diseases
The Robert Wendland case: Legal implications of the Wendland case for end-of-life decision making
No full textIn Conservatorship of Wendland, the California Supreme Court established a high standard of proof for end-of-life decision making on behalf of patients who are incompetent but conscious and have a court-appointed conservator.1 The court\u27s opinion establishes an easier standard of proof for some situations where there is no conservator, but the opinion leaves many questions unanswered. We address the implications of Wendland for health care professionals in California and, in particular, the questions of what evidence of a patient\u27s end-of-life wishes is required for physicians to withhold life-sustaining treatment and how strong that evidence must be in various situations
Wendland kernel function and its first derivative as a function.
No full textWendland kernel function and its first derivative as a function.</p
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