The construction of preconditioners for elliptic problems by substructuring. I

JH Bramble, JE Pasciak, AH Schatz - Mathematics of computation, 1986 - ams.org
elliptic boundary value problems on general domains in R2 and R3. In particular, we shall be
concerned with constructing easily invertible and "effective" preconditionersproblems in R2…

The construction of preconditioners for elliptic problems by substructuring. II

JH Bramble, JE Pasciak, AH Schatz - Mathematics of Computation, 1987 - ams.org
… be concerned with constructing easily invertible and "effective" preconditioners for the …
problem for a second-order uniformly elliptic equation we shall consider the Dirichlet problem

The construction of preconditioners for elliptic problems by substructuring. III

JH Bramble, JE Pasciak, AH Schatz - Mathematics of Computation, 1988 - ams.org
… , we constructed preconditioners for the discrete systems of equations arising from the numerical
approximation of elliptic boundary value problems. … even more efficient preconditioners. …

Multilevel preconditioners for elliptic problems by substructuring

PS Vassilevski - Applied mathematics and computation, 1991 - Elsevier
… We consider the construction of preconditioners for reduced Schur problems for solving
finite… The preconditioners are based on approximations of the considered elliptic problem on a …

The construction of preconditioners for elliptic problems by substructuring. IV

JH Bramble, JE Pasciak, AH Schatz - Mathematics of Computation, 1989 - ams.org
… of elliptic boundary value problems defined on three… preconditioners for such systems based
on substructuring … In Section 3, we show how the construction of the preconditioner B can be …

Iterative substructuring methods: Algorithms and theory for elliptic problems in the plane

OB Widlund - … Symposium on Domain Decomposition Methods for …, 1988 - books.google.com
… and the second standard preconditioner, which we will now … for elliptic problems on regions
partitioned into substructures, … , The construction of preconditioners for elliptic problems by …

Substructuring preconditioners for nonconforming finite element approximations of second-order elliptic problems with anisotropy

YA Kuznetsov, SY Maliassov - 1995 - degruyter.com
substructuring preconditioner is considered for nonconforming finite element approximations
of second-order elliptic problems … analyse a method of constructing the preconditioner for (…

[PDF][PDF] Substructuring preconditioning for finite element approximations of second order elliptic problems. II. Mixed method for an elliptic operator with scalar tensor

S Maliassov - 1994 - conservancy.umn.edu
… of constructing algebraic multilevel preconditioners for mixed finite element methods for second
order elliptic problems … Algebraic multilevel preconditioners are then constructed for this …

Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions

M Dryja, BF Smith, OB Widlund - SIAM journal on numerical analysis, 1994 - SIAM
… For the construction of the preconditioner, we assume that the set of elements is … substructures
j. For many of the algorithms considered in this paper,the shapes of the substructures can …

Iterative substructuring methods for spectral element discretizations of elliptic systems in three dimensions

LF Pavarino, OB Widlund - Parallel Solution of Partial Differential …, 2000 - Springer
… In this section, we describe our wire basket preconditioner for linear elasticity problems in …
We note that the construction of these iterative substructuring algorithms is a very modular …