The wavelet transform for BEM computational fluid dynamics

A wavelet matrix compression technique was used to solve systems of linear equations resulting from HEM applied to fluid dynamics. The governing equations were written in velocily-vorticity formulation and solutions of the resulting systems of equations were obtained with and without wavelet matrix compression. A modification of the Haar wavelet transform, which can transform vectors of any size, is proposed. The threshold, used for making fully populated matrices sparse, was written as a product of a user defined factor K and the average value of absolute matrix elements values. Numerical tests were performed to assert, that the error caused by wavelet compression depends linearly on the factor K, while the dependence of the error on the share of thresholded elements in the system matrix is highly non-linear. The results also showed that the increasing non-linearity (higher Ra and Re number values) limits the extent of compression. On the other hand, higher mesh density enables higher compression ratios. (C) 2004 Elsevier Ltd. All rights reserved.