Domain decomposition PCG methods for serial and parallel processing

  • M. Papadrakakis National Technical University oj Athens
  • S. Bitzarakis National Technical University oj Athens

Abstract

In this paper two domain decomposition formulations are presented in conjunction with the preconditioned conjugate gradient method (PCG) for the solution of large-scale problems in solid and structural mechanics. In the first approach the PCG method is applied to the global coefficient matrix, while in the second approach it is applied to the interface problem after eliminating the internal d.o.f. For both implementations a Subdomain-by-Subdomain (SBS) polynomial pre conditioner is employed based on local information of each sub domain. The approximate inverse of the global coefficient matrix or the Schur complement matrix, which acts as the preconditioner, is expressed by a truncated Neumann series resulting in an additive type local preconditioner. Block type preconditioning, where full elimination is performer inside each block, is also studied and compared with the proposed polynomial preconditioning.

Keywords

References

[1] R.L. Fox, E.L. Stanton. Developments in structural analysis by direct energy minimization. AIAA J., 6: 1036- 1042, 1968.
[2] I. Fried. More on gradient iterative methods in finite element analysis. AIAA J ., 7: 565-567, 1969.
[3] T.J.R. Hughes, J. Winget, I. Levit, T. Tezduyar. New alternating direction procedures in finite element analysis based upon EBE approximate factorizations. In: S.N. Atluri, N. Perrone, eds., Computer Methods in Nonlinear Solids and Structural Mechanics, AMD Vol. 4, 75- 109. ASME, New York, 1983.
[4] B. Nour-Omid, B. N. Parlett. Element preconditioning using splitting techniques. SIAM J. Sci. Stat. Comput. , 6: 761-770, 1985.
[5] M. Papadrakakis, Solving large-scale linear problems in solid and structural mechanics. In: M. Papadrakakis, ed., Solving Large Problems in Mechanics, pp. 1- 37. J. Wiley, 1993.
Published
Jun 26, 2023
How to Cite
PAPADRAKAKIS, M.; BITZARAKIS, S.. Domain decomposition PCG methods for serial and parallel processing. Computer Assisted Methods in Engineering and Science, [S.l.], v. 4, n. 1, p. 69-93, june 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1414>. Date accessed: 13 nov. 2024.
Section
Articles