Geodesic
An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems
Applications of Mathematics, Tome 50 (2005) no. 3, pp. 247-275.

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This paper extends previous results on nonlinear Schwarz preconditioning (Cai and Keyes 2002) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The nonlocal 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 Jones and Vassilevski 2001. Then, the algebraic construction from Jones, Vassilevski and Woodward 2003 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. A numerical illustration is also provided.
DOI : 10.1007/s10492-005-0016-0
Classification : 65F10, 65F35, 65N30, 65N55
Keywords: algebraic multigrid; agglomeration; non-linear elliptic problem; nonlinear preconditioning; Newton method; finite elements 
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     title = {An element agglomeration nonlinear additive {Schwarz} preconditioned {Newton} method for unstructured finite element problems},
     journal = {Applications of Mathematics},
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Cai, Xiao-Chuan; Marcinkowski, Leszek; Vassilevski, Panayot S. An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems. Applications of Mathematics, Tome 50 (2005) no. 3, pp. 247-275. doi : 10.1007/s10492-005-0016-0. http://geodesic.mathdoc.fr/articles/10.1007/s10492-005-0016-0/

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