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.
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e-mail: mmg3@eng.buffalo.edu
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July 2005
Special Section On Cfd Methods
Fast and Accurate Solutions of Steady Stokes Flows Using Multilevel Boundary Element Methods
G. F. Dargush,
G. F. Dargush
Department of Civil Engineering,
State University of New York at Buffalo
, Amherst, New York 14260 USA
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M. M. Grigoriev
M. M. Grigoriev
Department of Civil Engineering,
e-mail: mmg3@eng.buffalo.edu
State University of New York at Buffalo
, Amherst, New York 14260 USA
Search for other works by this author on:
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 USAe-mail: mmg3@eng.buffalo.edu
J. Fluids Eng. Jul 2005, 127(4): 640-646 (7 pages)
Published Online: February 23, 2005
Article history
Received:
August 29, 2004
Revised:
February 23, 2005
Citation
Dargush, G. F., and Grigoriev, M. M. (February 23, 2005). "Fast and Accurate Solutions of Steady Stokes Flows Using Multilevel Boundary Element Methods." ASME. J. Fluids Eng. July 2005; 127(4): 640–646. https://doi.org/10.1115/1.1949648
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