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Compact Support (compact + support)

Distribution by Scientific Domains
Mathematics and Statistics57%

Selected Abstracts

Implicit Surface Modelling with a Globally Regularised Basis of Compact Support

COMPUTER GRAPHICS FORUM, Issue 3 2006
C. Walder
We consider the problem of constructing a globally smooth analytic function that represents a surface implicitly by way of its zero set, given sample points with surface normal vectors. The contributions of the paper include a novel means of regularising multi-scale compactly supported basis functions that leads to the desirable interpolation properties previously only associated with fully supported bases. We also provide a regularisation framework for simpler and more direct treatment of surface normals, along with a corresponding generalisation of the representer theorem lying at the core of kernel-based machine learning methods. We demonstrate the techniques on 3D problems of up to 14 million data points, as well as 4D time series data and four-dimensional interpolation between three-dimensional shapes. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations [source]

Explicit calculation of smoothed sensitivity coefficients for linear problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003
R. A. Bia, ecki
Abstract A technique of explicit calculation of sensitivity coefficients based on the approximation of the retrieved function by a linear combination of trial functions of compact support is presented. The method is applicable to steady state and transient linear inverse problems where unknown distributions of boundary fluxes, temperatures, initial conditions or source terms are retrieved. The sensitivity coefficients are obtained by solving a sequence of boundary value problems with boundary conditions and source term being homogeneous except for one term. This inhomogeneous term is taken as subsequent trial functions. Depending on the type of the retrieved function, it may appear on boundary conditions (Dirichlet or Neumann), initial conditions or the source term. Commercial software and analytic techniques can be used to solve this sequence of boundary value problems producing the required sensitivity coefficients. The choice of the approximating functions guarantees a filtration of the high frequency errors. Several numerical examples are included where the sensitivity coefficients are used to retrieve the unknown values of boundary fluxes in transient state and volumetric sources. Analytic, boundary-element and finite-element techniques are employed in the study. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Boundary value problem for the N -dimensional time periodic Vlasov,Poisson system

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2006
M. Bostan
Abstract In this work, we study the existence of time periodic weak solution for the N -dimensional Vlasov,Poisson system with boundary conditions. We start by constructing time periodic solutions with compact support in momentum and bounded electric field for a regularized system. Then, the a priori estimates follow by computations involving the conservation laws of mass, momentum and energy. One of the key point is to impose a geometric hypothesis on the domain: we suppose that its boundary is strictly star-shaped with respect to some point of the domain. These results apply for both classical or relativistic case and for systems with several species of particles. Copyright © 2006 John Wiley & Sons, Ltd. [source]

On the absence of eigenvalues of Maxwell and Lamé systems in exterior domains

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2004
Sebastian Bauer
Abstract The arguments showing non-existence of eigensolutions to exterior-boundary value problems associated with systems,such as the Maxwell and Lamé system,rely on showing that such solutions would have to have compact support and therefore,by a unique continuation property,cannot be non-trivial. Here we will focus on the first part of the argument. For a class of second order elliptic systems it will be shown that L2 -solutions in exterior domains must have compact support. Both the asymptotically isotropic Maxwell system and the Lamé system with asymptotically decaying perturbations can be reduced to this class of elliptic systems. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Stability of quantization dimension and quantization for homogeneous Cantor measures

MATHEMATISCHE NACHRICHTEN, Issue 8 2007
Marc Kesseböhmer
Abstract We effect a stabilization formalism for dimensions of measures and discuss the stability of upper and lower quantization dimension. For instance, we show for a Borel probability measure with compact support that its stabilized upper quantization dimension coincides with its packing dimension and that the upper quantization dimension is finitely stable but not countably stable. Also, under suitable conditions explicit dimension formulae for the quantization dimension of homogeneous Cantor measures are provided. This allows us to construct examples showing that the lower quantization dimension is not even finitely stable. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

A finite-element scheme for the vertical discretization of the semi-Lagrangian version of the ECMWF forecast model

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 599 2004
A. Untch
Abstract A vertical finite-element (FE) discretization designed for the European Centre for Medium-Range Weather Forecasts (ECMWF) model with semi-Lagrangian advection is described. Only non-local operations are evaluated in FE representation, while products of variables are evaluated in physical space. With semi-Lagrangian advection the only non-local vertical operations to be evaluated are vertical integrals. An integral operator is derived based on the Galerkin method using B-splines as basis functions with compact support. Two versions have been implemented, one using piecewise linear basis functions (hat functions) and the other using cubic B-splines. No staggering of dependent variables is employed in physical space, making the method well suited for use with semi-Lagrangian advection. The two versions of the FE scheme are compared to finite-difference (FD) schemes in both the Lorenz and the Charney,Phillips staggering of the dependent variables for the linearized model. The FE schemes give more accurate results than the two FD schemes for the phase speeds of most of the linear gravity waves. Evidence is shown that the FE schemes suffer less from the computational mode than the FD scheme with Lorenz staggering, although temperature and geopotential are held at the same set of levels in the FE scheme too. As a result, the FE schemes reduce the level of vertical noise in forecasts with the full model. They also reduce by about 50% a persistent cold bias in the lower stratosphere present with the FD scheme in Lorenz staggering (i.e. the operational scheme at ECMWF before its replacement by the cubic version of the FE scheme described here) and improve the transport in the stratosphere. Copyright © 2004 Royal Meteorological Society [source]

Exponential growth for the wave equation with compact time-periodic positive potential

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 4 2009
Ferruccio Colombini
We prove the existence of smooth positive potentials V(t, x), periodic in time and with compact support in x, for which the Cauchy problem for the wave equation utt , ,xu + V(t, x)u = 0 has solutions with exponentially growing global and local energy. Moreover, we show that there are resonances, z , ,, |z| > 1, associated to V(t, x). © 2008 Wiley Periodicals, Inc. [source]