Search results for "Interpolation"
showing 10 items of 331 documents
Numerical Approximation of Elliptic Variational Problems
2003
This chapter is dedicated to the study of Elliptic Variational Inequalities (EVI). Different forms of such an EVI are considered. The Ritz—Galerkin discretization method is introduced, and methods to approximate the solution of an EVI are presented. The finite dimensional subspaces are built by use of the Finite Element Method. The discretized problems are solved using variants of the Successive OverRelaxation (SOR) method. The algorithms are tested on a typical example. The way to develop computer programs is carefully analysed.
Approximate survival probability determination of hysteretic systems with fractional derivative elements
2018
Abstract A Galerkin scheme-based approach is developed for determining the survival probability and first-passage probability of a randomly excited hysteretic systems endowed with fractional derivative elements. Specifically, by employing a combination of statistical linearization and of stochastic averaging, the amplitude of the system response is modeled as one-dimensional Markovian Process. In this manner the corresponding backward Kolmogorov equation which governs the evolution of the survival probability of the system is determined. An approximate solution of this equation is sought by employing a Galerkin scheme in which a convenient set of confluent hypergeometric functions is used a…
Error bounds for a convexity-preserving interpolation and its limit function
2008
AbstractError bounds between a nonlinear interpolation and the limit function of its associated subdivision scheme are estimated. The bounds can be evaluated without recursive subdivision. We show that this interpolation is convexity preserving, as its associated subdivision scheme. Finally, some numerical experiments are presented.
Comparison of continuous and discontinuous Galerkin approaches for variable-viscosity Stokes flow
2015
We describe a Discontinuous Galerkin (DG) scheme for variable-viscosity Stokes flow which is a crucial aspect of many geophysical modelling applications and conduct numerical experiments with different elements comparing the DG approach to the standard Finite Element Method (FEM). We compare the divergence-conforming lowest-order Raviart-Thomas (RT0P0) and Brezzi-Douglas-Marini (BDM1P0) element in the DG scheme with the bilinear Q1P0 and biquadratic Q2P1 elements for velocity and their matching piecewise constant/linear elements for pressure in the standard continuous Galerkin (CG) scheme with respect to accuracy and memory usage in 2D benchmark setups. We find that for the chosen geodynami…
Physics Contributions Evaluation of interpolation methods for TG-43 dosimetric parameters based on comparison with Monte Carlo data for high-energy b…
2010
Purpose: The aim of this work was to determine dose distributions for high-energy brachytherapy sources at spa- tial locations not included in the radial dose function gL(r) and 2D anisotropy function F(r,θ) table entries for radial dis- tance r and polar angle θ. The objectives of this study are as follows: 1) to evaluate interpolation methods in order to accurately derive gL(r) and F(r,θ) from the reported data; 2) to determine the minimum number of entries in gL(r) and F(r,θ) that allow reproduction of dose distributions with sufficient accuracy. Material and methods: Four high-energy photon-emitting brachytherapy sources were studied: 60Co model Co0.A86, 137Cs model CSM-3, 192Ir model I…
The Bishop–Phelps–Bollobás point property
2016
Abstract In this article, we study a version of the Bishop–Phelps–Bollobas property. We investigate a pair of Banach spaces ( X , Y ) such that every operator from X into Y is approximated by operators which attain their norm at the same point where the original operator almost attains its norm. In this case, we say that such a pair has the Bishop–Phelps–Bollobas point property (BPBpp). We characterize uniform smoothness in terms of BPBpp and we give some examples of pairs ( X , Y ) which have and fail this property. Some stability results are obtained about l 1 and l ∞ sums of Banach spaces and we also study this property for bilinear mappings.
A fully adaptive multiresolution scheme for image processing
2007
A nonlinear multiresolution scheme within Harten's framework [A. Harten, Discrete multiresolution analysis and generalized wavelets, J. Appl. Numer. Math. 12 (1993) 153-192; A. Harten, Multiresolution representation of data II, SIAM J. Numer. Anal. 33 (3) (1996) 1205-1256] is presented. It is based on a centered piecewise polynomial interpolation fully adapted to discontinuities. Compression properties of the multiresolution scheme are studied on various numerical experiments on images.
Mapping properties for the Bargmann transform on modulation spaces
2010
We investigate mapping properties for the Bargmann transform and prove that this transform is isometric and bijective from modulation spaces to convenient Banach spaces of analytic functions.
Discrete Maximum Principle for Galerkin Finite Element Solutions to Parabolic Problems on Rectangular Meshes
2004
One of the most important problems in numerical simulation is the preservation of qualitative properties of solutions of mathematical models. For problems of parabolic type, one of such properties is the maximum principle. In [5], Fujii analyzed the discrete analogue of the (continuous) maximum principle for the linear parabolic problems, and derived sufficient conditions guaranteeing its validity for the Galerkin finite element approximations built on simplicial meshes. In our paper, we present the sufficient conditions for the validity of the discrete maximum principle for the case of bilinear finite element space approximations on rectangular meshes.
Identification of linear parameter varying models
2002
We consider identification of a certain class of discrete-time nonlinear systems known as linear parameter varying system. We assume that inputs, outputs and the scheduling parameters are directly measured, and a form of the functional dependence of the system coefficients on the parameters is known. We show how this identification problem can be reduced to a linear regression, and provide compact formulae for the corresponding least mean square and recursive least-squares algorithms. We derive conditions on persistency of excitation in terms of the inputs and scheduling parameter trajectories when the functional dependence is of polynomial type. These conditions have a natural polynomial i…