Fast and Accurate Solutions of Steady Stokes Flows Using Multilevel Boundary Element Methods

[+] Author and Article Information
G. F. Dargush

Department of Civil Engineering, State University of New York at Buffalo, Amherst, New York 14260 USA

M. M. Grigoriev

Department of Civil Engineering, State University of New York at Buffalo, Amherst, New York 14260 USAmmg3@eng.buffalo.edu

J. Fluids Eng 127(4), 640-646 (Feb 23, 2005) (7 pages) doi:10.1115/1.1949648 History: Received August 29, 2004; Revised February 23, 2005

Most recently, we have developed a novel multilevel boundary element method (MLBEM) for steady Stokes flows in irregular two-dimensional domains (Grigoriev, M.M., and Dargush, G.F., Comput. Methods. Appl. Mech. Eng., 2005). The multilevel algorithm permitted boundary element solutions with slightly over 16,000 degrees of freedom, for which approximately 40-fold speedups were demonstrated for the fast MLBEM algorithm compared to a conventional Gauss elimination approach. Meanwhile, the sevenfold memory savings were attained for the fast algorithm. This paper extends the MLBEM methodology to dramatically improve the performance of the original multilevel formulation for the steady Stokes flows. For a model problem in an irregular pentagon, we demonstrate that the new MLBEM formulation reduces the CPU times by a factor of nearly 700,000. Meanwhile, the memory requirements are reduced more than 16,000 times. These superior run-time and memory reductions compared to regular boundary element methods are achieved while preserving the accuracy of the boundary element solution.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Problem definition for the irregular pentagon domain

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Figure 2

Convergence of the numerical errors for the conventional and fast boundary element methods with the boundary mesh refinement

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Figure 3

MLMI errors with respect to the number of singular zone points

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Figure 4

The number of singular zone points m needed to retain a desired level of accuracy

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Figure 5

Convergence history for mesh of Np=16,384 boundary elements for various number of multi-grid levels

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Figure 6

The number of iterations on the finest level mesh to achieve convergence; One-level multi-grid versus no multi-grid

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Figure 7

Comparisons of the CPU requirements for the conventional BEM and MLBEM algorithms

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Figure 8

Comparisons of the memory requirements for the conventional BEM and MLBEM algorithms



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