Energy Optimization of Algebraic Multigrid Bases

被引：0

作者：

J. Mandel

M. Brezina

P. Vaněk

机构：

[1] Department of Mathematics,

[2] University of Colorado at Denver,undefined

[3] Denver,undefined

[4] CO 80217-3364,undefined

[5] USA,undefined

[6] e-mail: jmandel@math.cudenver.edu ,undefined

[7] Department of Applied Mathematics,undefined

[8] University of Colorado at Boulder,undefined

[9] Boulder,undefined

[10] CO 80309-0526,undefined

[11] USA,undefined

[12] e-mail: Marian.Brezina@colorado.edu ,undefined

[13] Department of Mathematics,undefined

[14] University of California at Los Angeles,undefined

[15] Los Angeles,undefined

[16] CA 90095-1555,undefined

[17] USA,undefined

[18] e-mail: vanek@math.ucla.edu. (On leave from University of West Bohemia,undefined

[19] Plzeň,undefined

[20] Czech Republic) ,undefined

来源：

Computing | 1999年 / 62卷

关键词：

AMS Subject Classifications:65N55, 65F10.; Key words.Algebraic multigrid, constrained optimization.;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We propose a fast iterative method to optimize coarse basis functions in algebraic multigrid by minimizing the sum of their energies, subject to the condition that linear combinations of the basis functions equal to given zero energy modes, and subject to restrictions on the supports of the coarse basis functions. For a particular selection of the supports, the first iteration gives exactly the same basis functions as our earlier method using smoothed aggregation. The convergence rate of the minimization algorithm is bounded independently of the mesh size under usual assumptions on finite elements. The construction is presented for scalar problems as well as for linear elasticity. Computational results on difficult industrial problems demonstrate that the use of energy minimal basis functions improves algebraic multigrid performance and yields a more robust multigrid algorithm than smoothed aggregation.

引用

页码：205 / 228

页数：23