Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

A Scalable Substructuring Method by Lagrange Multipliers for Plate Bending Problems

Jan Mandel, Radek Tezaur and Charbel Farhat
SIAM Journal on Numerical Analysis
Vol. 36, No. 5 (1999), pp. 1370-1391
Stable URL: http://www.jstor.org/stable/2587162
Page Count: 22
  • Subscribe ($19.50)
  • Cite this Item
A Scalable Substructuring Method by Lagrange Multipliers for Plate Bending Problems
Preview not available

Abstract

We present a new Lagrange multiplier-based domain decomposition method for solving iteratively systems of equations arising from the finite element discretization of plate bending problems. The proposed method is essentially an extension of the finite element tearing and interconnecting substructuring algorithm to the biharmonic equation. The main idea is to enforce continuity of the transversal displacement field at the subdomain crosspoints throughout the preconditioned conjugate gradient iterations. The resulting method is proved to have a condition number that does not grow with the number of subdomains but rather grows at most polylogarithmically with the number of elements per subdomain. These optimal properties hold for numerous plate bending elements that are used in practice including the Hsieh-Clough-Tocher element, the discrete Kirchhoff triangle, and a class of nonlocking elements for the Reissner-Mindlin plate models. Computational experiments are reported and shown to confirm the theoretical optimal convergence properties of the new domain decomposition method. Computational efficiency is also demonstrated with the numerical solution in 45 iterations and 105 seconds on a 64-processor IBM SP2 of a plate bending problem with almost one million degrees of freedom.

Page Thumbnails

  • Thumbnail: Page 
1370
    1370
  • Thumbnail: Page 
1371
    1371
  • Thumbnail: Page 
1372
    1372
  • Thumbnail: Page 
1373
    1373
  • Thumbnail: Page 
1374
    1374
  • Thumbnail: Page 
1375
    1375
  • Thumbnail: Page 
1376
    1376
  • Thumbnail: Page 
1377
    1377
  • Thumbnail: Page 
1378
    1378
  • Thumbnail: Page 
1379
    1379
  • Thumbnail: Page 
1380
    1380
  • Thumbnail: Page 
1381
    1381
  • Thumbnail: Page 
1382
    1382
  • Thumbnail: Page 
1383
    1383
  • Thumbnail: Page 
1384
    1384
  • Thumbnail: Page 
1385
    1385
  • Thumbnail: Page 
1386
    1386
  • Thumbnail: Page 
1387
    1387
  • Thumbnail: Page 
1388
    1388
  • Thumbnail: Page 
1389
    1389
  • Thumbnail: Page 
1390
    1390
  • Thumbnail: Page 
1391
    1391