Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier B.V. All rights reserved.

A combined wavelet-element free Galerkin method for numerical calculations of electromagnetic fields

A combined wavelet-element free Galerkin (EFG) method is proposed for solving electromagnetic EM) field problems. The bridging scales are used to preserve the consistency and linear independence properties of the entire bases. A detailed description of the development of the discrete model and its numerical implementations is given to facilitate the reader to. understand the proposed algorithm. A numerical example to validate the proposed method is also reported.

The wavelet method as an alternative for reducing ionospheric effects from single-frequency GPS receivers

The ionospheric effect is one of the major errors in GPS data processing over long baselines. As a dispersive medium, it is possible to compute its influence on the GPS signal with the ionosphere-free linear combination of L1 and L2 observables, requiring dual-frequency receivers. In the case of single-frequency receivers, ionospheric effects are either neglected or reduced by using a model. In this paper, an alternative for single-frequency users is proposed. It involves multiresolution analysis (MRA) using a wavelet analysis of the double-difference observations to remove the short- and medium-scale ionosphere variations and disturbances, as well as some minor tropospheric effects. Experiments were carried out over three baseline lengths from 50 to 450 km, and the results provided by the proposed method were better than those from dual-frequency receivers. The horizontal root mean square was of about 0.28 m (1 sigma).

Wavelet shrinkage: High frequency multipath reduction from GPS relative positioning

The wavelet transform is used to reduce the high frequency multipath of pseudorange and carrier phase GPS double differences (DDs). This transform decomposes the DD signal, thus separating the high frequencies due to multipath effects. After the decomposition, the wavelet shrinkage is performed by thresholding to eliminate the high frequency component. Then the signal can be reconstructed without the high frequency component. We show how to choose the best threshold. Although the high frequency multipath is not the main multipath error component, its correction provides improvements of about 30% in pseudorange average residuals and 24% in carrier phases. The results also show that the ambiguity solutions become more reliable after correcting the high frequency multipath.

Sparse 1D discrete Dirac operators I: Quantum transport

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Sparse one-dimensional discrete Dirac operators II: Spectral properties

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)