Parallelization of Robust Multigrid Methods: ILU Factorization and Frequency Decomposition Method

1991 ◽  
Vol 12 (6) ◽  
pp. 1457-1470 ◽  
Author(s):  
Peter Bastian ◽  
Graham Horton
Keyword(s):  
Decomposition Method ◽  
Multigrid Methods ◽  
Frequency Decomposition ◽  
Robust Multigrid ◽  
Ilu Factorization

Complementary ensemble local means decomposition method and its application to rolling element bearings fault diagnosis

2019 ◽  
Vol 233 (5) ◽  
pp. 868-880 ◽  
Author(s):  
Yao Cheng ◽  
Dong Zou
Keyword(s):  
Decomposition Method ◽  
Signal Reconstruction ◽  
Outer Race ◽  
Time Frequency ◽  
Frequency Decomposition ◽  
Local Means ◽  
Residual Noise ◽  
Rolling Element ◽  
Noisy Signals ◽  
Mode Mixing

Local means decomposition is an adaptive and nonparametric time–frequency decomposition method for nonstationary and nonlinear signals. However, in practice, local means decomposition is susceptible to mode mixing phenomena and produces different scale oscillations in one mode or similar scale oscillations in different modes, rendering the decomposition results difficult to interpret in terms of physical meansing. The noise-assisted ensemble local means decomposition method not only effectively resolved mode mixing but also generated a new problem, which tolerates residual noise in signal reconstruction. Targeting these shortcomings, this article proposes complementary ensemble local means decomposition, a novel noise-assisted time–frequency analysis method. First, an ensemble of white noise is added to the original signal via complementary positive and negative pairs. Second, local means decomposition is applied to decompose the noisy signals into a series of product functions, and the final results are obtained by averaging. The simulation results confirm that complementary ensemble local means decomposition offers an innovative improvement over ensemble local means decomposition in terms of eliminating residual noise. The superiority of the proposed method was further validated on fault signals obtained from faulty railway bearings (rolling element and outer race fault signals).

Potentialities of the Robust Multigrid Technique

2010 ◽  
Vol 10 (1) ◽  
pp. 87-94 ◽  
Author(s):  
S.I. Martynenko
Keyword(s):  
Load Balance ◽  
Unstructured Grids ◽  
Multigrid Methods ◽  
Structured Grids ◽  
Minimum Speed ◽  
Speed Up ◽  
Coarse Grids ◽  
Robust Multigrid ◽  
Geometric Nature

AbstractThe present paper discusses the parallelization of the robust multigrid technique (RMT) and the possible way of applying this to unstructured grids. As opposed to the classical multigrid methods, the RMT is a trivial method of parallelization on coarse grids independent of the smoothing iterations. Estimates of the minimum speed-up and parallelism efficiency are given. An almost perfect load balance is demonstrated in a 3D illustrative test. To overcome the geometric nature of the technique, the RMT is used as a preconditioner in solving PDEs on unstructured grids. The procedure of auxiliary structured grids generation is considered in details.

A formalism for designing robust multigrid methods for Helmholtz-like problems

2013 ◽  
Vol 37 (2) ◽  
pp. 230-236
Author(s):  
Thomas K. Huckle ◽  
Christos D. Kravvaritis
Keyword(s):  
Multigrid Methods ◽  
Robust Multigrid

Wavelet frequency decomposition method

1994 ◽  
Author(s):  
Andreas Rieder ◽  
Raymond O. Wells, Jr. ◽  
Xiaodong Zhou
Keyword(s):  
Decomposition Method ◽  
Frequency Decomposition
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