Search results for "Numerical"
showing 10 items of 2002 documents
Tridiagonal preconditioning for Poisson-like difference equations with flat grids: Application to incompressible atmospheric flow
2011
AbstractThe convergence of many iterative procedures, in particular that of the conjugate gradient method, strongly depends on the condition number of the linear system to be solved. In cases with a large condition number, therefore, preconditioning is often used to transform the system into an equivalent one, with a smaller condition number and therefore faster convergence. For Poisson-like difference equations with flat grids, the vertical part of the difference operator is dominant and tridiagonal and can be used for preconditioning. Such a procedure has been applied to incompressible atmospheric flows to preserve incompressibility, where a system of Poisson-like difference equations is …
Polarity-reversal subduction zone initiation triggered by buoyant plateau obstruction
2022
Abstract Oceanic lithosphere worldwide is younger than ca. 200 Myr, suggesting that it must have been globally recycled by the recurrent formation of new subduction zones since the existence of subduction on Earth. However, postulated subduction zone initiation processes remain difficult to explain in many cases, and the specific geodynamic conditions under which these might occur are still largely unknown. We here use numerical models driven by the internal force balance of a subduction system to better understand the (geo)dynamics governing (intra-oceanic) polarity-reversal subduction zone initiation. This initiation mode assumes that the birth of a new subduction zone could be triggered …
Validation of a Microscale Pollution Dispersal Model
1996
The three-dimensional numerical model MISCAM (Micro Scale Air Pollution Model) has been developed to study wind flow and pollutant dispersal in densely built-up urban areas (Eichhorn, 1989). The model has been successfully applied for planning purposes by a variety of institutions in Germany. MISCAM consists of the non-hydrostatic Eulerian equations of motion and a transport equation for pollutants. Turbulence closure is carried out by means of a k-e-model. To reduce numerical diffusion errors, Smolarkiewicz and Grabowski’s (1989) scheme may be used for the calculation of advective transport. Additionally, sedimentation and dry deposition of pollutants may be taken into account.
An Approximating-Interpolatory Subdivision Scheme.
2011
International audience; In the last decade, study and construction of quad/triangle subdivision schemes have attracted attention. The quad/triangle subdivision starts with a control mesh consisting of both quads and triangles and produces ner and ner meshes with quads and triangles (Fig. 1). Design- ers often want to model certain regions with quad meshes and others with triangle meshes to get better visual qual- ity of subdivision surfaces. Smoothness analysis tools exist for regular quad/triangle vertices. Moreover C1 and C2 quad/triangle schemes (for regular vertices) have been con- structed. But to our knowledge, there are no quad/triangle schemes that uni es approximating and interpola…
Non-separable local polynomial regression cell-average multiresolution operators. Application to compression of images
2016
Abstract Cell-average multiresolution Harten׳s algorithms have been satisfactorily used to compress data. These schemes are based on two operators: decimation and prediction. The accuracy of the method depends on the prediction operator. In order to design a precise function, local polynomial regression has been used in the last years. This paper is devoted to construct a family of non-separable two-dimensional linear prediction operators approximating the real values with this procedure. Some properties are proved as the order of the scheme and the stability. Some numerical experiments are performed comparing the new methods with the classical linear method.
Non-consistent cell-average multiresolution operators with application to image processing
2016
In recent years different techniques to process signal and image have been designed and developed. In particular, multiresolution representations of data have been studied and used successfully for several applications such as compression, denoising or inpainting. A general framework about multiresolution representation has been presented by Harten (1996) 20. Harten's schemes are based on two operators: decimation, D , and prediction, P , that satisfy the consistency property D P = I , where I is the identity operator. Recently, some new classes of multiresolution operators have been designed using learning statistical tools and weighted local polynomial regression methods obtaining filters…
On specific stability bounds for linear multiresolution schemes based on piecewise polynomial Lagrange interpolation
2009
Abstract The Deslauriers–Dubuc symmetric interpolation process can be considered as an interpolatory prediction scheme within Harten's framework. In this paper we express the Deslauriers–Dubuc prediction operator as a combination of either second order or first order differences. Through a detailed analysis of certain contractivity properties, we arrive to specific l ∞ -stability bounds for the multiresolution transform. A variety of tests indicate that these l ∞ bounds are closer to numerical estimates than those obtained with other approaches.
A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering
2021
<p style='text-indent:20px;'>Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine learning, mechanics, economics, electrodynamics and so on. Besides, special classes of functional differential equations have been investigated in many researches. In this study, a numerical investigation of retarded type of these models together with initial conditions are introduced. The technique is based on a polynomial approach along with collocation points which maintains an approximated solutions to the problem. Beside…
Analysis of negative-resistance oscillators with piecewise nonlinearity
1977
An iterative method of solution of negative-resistance oscillators with piecewise-analytical characteristics is presented. The method allows the determination of the frequency and the harmonic content of the waveform as a function of the circuit parameters and bias of the nonlinear device. An application of the method, extended to the second order, for a polynomial characteristic limited by two straight lines is also reported. The results are compared with those obtained by numerical integration.
Upper bounds for the zeros of ultraspherical polynomials
1990
AbstractFor k = 1, 2, …, [n2] let xnk(λ) denote the Kth positive zero in decreasing order of the ultraspherical polynomial Pn(λ)(x). We establish upper bounds for xnk(λ). All the bounds become exact when λ = 0 and, in some cases (see case (iii) of Theorem 3.1), also when λ = 1. As a consequence of our results, we obtain for the largest zero xn1(λ)0.. We point out that our results remain useful for large values of λ. Numerical examples show that our upper bounds are quite sharp.