On the block wavelet transform applied to the boundary element method

This paper follows an earlier work by Bucher et al. [1] on the application of wavelet transforms to the boundary element method, which shows how to reuse models stored in compressed form to solve new models with the same geometry but arbitrary load cases - the so-called virtual assembly technique. The extension presented in this paper involves a new computational procedure created to perform the required two-dimensional wavelet transforms by blocks, theoretically allowing the compression of matrices of arbitrary size. Details of the computer implementation that allows the use of this methodology for very large models or at high compression ratios are given. A numerical application shows a standard PC being used to solve a 131,072 DOF model, previously compressed, for 100 distinct load cases in less than 1 hour – or 33 seconds for each load case

Fast solution of problems with multiple load cases by using wavelet-compressed boundary element matrices

This paper presents a fast approach for rapidly solving problems with multiple load cases using the boundary element method (BEM). The basic idea of this approach is to assemble the BEM matrices separately and to compress them using fast wavelet transforms. Using a technique called “virtual assembly”, the matrices are then combined inside an iterative solver according to the boundary conditions of the problem, with no need for recompression each time a new load case is solved. This technique does not change the condition number of the matrices – up to a small variation introduced by compression – so that previous theoretical convergence estimates are still valid. Substantial savings in computer time are obtained with the present technique

OMAE2004-51218 DAMPING ESTIMATION OF RISERS USING TIME-FREQUENCY TRANSFORMS

ABSTRACT Offshore oil exploitation at increasing water depths has been carrying out studies focused on improving riser response prediction. In order to have a safety design of flexible risers it is necessary to evaluate its dynamic characteristics, mainly the damping factor. This parameter is obtained experimentally and the usual techniques sometimes are not appropriated. For these techniques the damping factor is considered constant, but some tests performed in COPPE's Lab showed that this is not completely true. In order to estimate the damping factors of a multi-degree of freedom system, cross-sections of Continuous Wavelet Transforms (CWT) based on the Morlet wavelet function from time-domain responses are used. The procedures are then tested on signals acquired from the lateral vibration of a flexible riser. Non-linearity analysis capabilities are also verified