Overlapping Schwarz for Nonlinear Problems. An Element Agglomeration Nonlinear Additive Schwarz Preconditioned Newton Method for Unstructured Finite Element Problems
This paper extends previous results on nonlinear Schwarz preconditioning ([4]) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The non-local finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in [8]. Then, the algebraic construction from [9] of the corresponding non-linear finite element subproblems is applied to generate the subspace based nonlinear preconditioner. The overall nonlinearly preconditioned problem is solved by an inexact Newton method. Numerical illustration is also provided.
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 936450
- Report Number(s):
- UCRL-JRNL-209688
- Journal Information:
- Application of Mathematics, vol. 50, no. 3, July 12, 2005, pp. 247-275, Journal Name: Application of Mathematics, vol. 50, no. 3, July 12, 2005, pp. 247-275 Journal Issue: 3 Vol. 50
- Country of Publication:
- United States
- Language:
- English
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