Parallel Calculation of Accurate Path Lines in Virtual Environments through Exploitation of Multi-Block CFD Data Set Topology

The use of Virtual Reality (VR) techniques for the investigation of complex flow phenomena offers distinct advantages in comparison to conventional visualization techniques. Especially for unsteady flows, VR methodology provides an intuitive approach for the exploration of simulated fluid flows. However, the visualization of Computational Fluid Dynamics (CFD) data is often too time-consuming to be carried out in real-time, and thus violates essential constraints concerning real-time interaction and visualization. To overcome this obstacle, we make use of the fact that typically a multi-block approach is employed for domain decomposition, and we use the corresponding data structures for the computation of path lines and for parallelization. In this paper, we present the synthesis of fragmented multi-block data sets and our implementation of an accurate path line integration scheme in order to speed up path line computations. We report on the results of our efforts and describe a combination of this algorithm with a highly efficient visualization approach of large amounts of particle traces, thus considerably improving interactivity when exploring large scale CFD data sets.Mathematics Subject Classifications (2000) 76Mxx, 76M27, 76M28, 65M55, 65L05, 65L06, 65D05, 65Y05, 68U05.     

Quasilinear evolutionary equations and continuous interpolation spaces

In this paper we analyze the abstract parabolic evolutionary equations

     

On theorems of Gelfond and Selberg concerning integral-valued entire functions

For each sN define the constant θ_s with the following properties: if an entire function g(z) of type t(g)<θ_s satisfies then g is a polynomial; conversely, for any δ>0 there exists an entire transcendental function g(z) satisfying the display conditin and t(g)<θ_s+δ. The result θ₁=log2 is known due to Hardy and Pólya. We provide the upper bound θ_sπs/3 and improve earlier lower bounds due to Gelfond (1929) and Selberg (1941).     

The uniform closure of non-dense rational spaces on the unit interval

Let P_n denote the set of all algebraic polynomials of degree at most n with real coefficients. Associated with a set of poles a₁,a₂,…,a_n R[-1,1] we define the rational function spaces Associated with a set of poles a₁,a₂,… R[-1,1], we define the rational function spacesIt is an interesting problem to characterize sets a₁,a₂,… R[-1,1] for which P(a₁,a₂,…) is not dense in C[-1,1], where C[-1,1] denotes the space of all continuous functions equipped with the uniform norm on [-1,1]. Akhieser showed that the density of P(a₁,a₂,…) is characterized by the divergence of the series .In this paper, we show that the so-called Clarkson–Erdős–Schwartz phenomenon occurs in the non-dense case. Namely, if P(a₁,a₂,…) is not dense in C[-1,1], then it is “very much not so”. More precisely, we prove the following result.Theorem Let a₁,a₂,… R[-1,1]. Suppose P(a₁,a₂,…) is not dense in C[-1,1], that is,Then every function in the uniform closure of P(a₁,a₂,…) in C[-1,1] can be extended analytically throughout the set C -1,1,a₁,a₂,… .     

小波双线性插值搜索算法及其在光学遥感图像中的应用

详细分析了在小波双线性插值中高频外推阈值门限与峰值信噪比的变化关系,提出了基于峰值信噪比最大的小波双线性插值搜索算法。提出的算法能够自动搜索到峰值信噪比最大的高频外推最佳阈值门限,实现了在不破坏光学遥感图像原始信息的情况下,提高了图像的空间分辨率,有利于对图像的细节信息进行观察分析。实验结果表明:该算法能够得到比双线性插值和全小波插值更高的峰值信噪比、熵值和更好的图像细节效果,是一种适合提高光学遥感图像分辨率的有效算法。     

Anisotropic interpolation and quasi-Wilson element for narrow quadrilateral meshes

In this paper an anisotropic interpolation theorem is presentedthat can be easily used to check the anisotropy of an element.A kind of quasi-Wilson element is considered for second-orderproblems on narrow quadrilateral meshes for which the usualregularity condition _K/h_K c₀ > 0 is not satisfied, whereh_K is the diameter of the element K and _K is the radius of thelargest inscribed circle in K. Anisotropic error estimates ofthe interpolation error and the consistency error in the energynorm and the L²-norm are given. Furthermore, we give a Poincaréinequality on a trapezoid which improves a result of eniek.     

Uniform asymptotic stability for perturbed neutral delay differential equations

One-dimensional perturbed neutral delay differential equations of the form (x(t)−P(t,x(t−τ)))′=f(t,x_t)+g(t,x_t) are considered assuming that f satisfies −v(t)M(φ)?f(t,φ)?v(t)M(−φ), where M(φ)=max{0,max_s∈[−r,0]φ(s)}. A typical result is the following: if ‖g(t,φ)‖?w(t)‖φ‖ and , then the zero solution is uniformly asymptotically stable providing that the zero solution of the corresponding equation without perturbation (x(t)−P(t,x(t−τ)))′=f(t,x_t) is uniformly asymptotically stable. Some known results associated with this equation are extended and improved.     

Interpolation between and

We show that if is a rearrangement invariant space on that is an interpolation space between and and for which we have only a one-sided estimate of the Boyd index 1/p, 1 < p < \infty$">, then is an interpolation space between and . This gives a positive answer for a question posed by Semenov. We also present the one-sided interpolation theorem about operators of strong type and weak type .

     

Local behaviour of polynomials

In this paper we study the local behaviour of a trigonometric polynomial around any of its zeros in terms of its estimated values at an adequate number of freely chosen points in . The freedom in the choice of sample points makes our results particularly convenient for numerical calculations. Analogous results for polynomials of the form are also proved.