zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A new class of iterative methods for nonselfadjoint or indefinite problems. (English) Zbl 0756.65050
A new iterative technique for solving nonsymmetric or indefinite (NSPD) systems is proposed and analyzed. The iterations of the basic algorithm consist of two steps: first, the original NSPD operator is solved exactly in a subspace (coarser grid space) and then the equation with the SPD part of the NSPD operator is solved approximately by a suitable inner iterative method. In both steps the corresponding residual serves as the right hand side. The algorithm is applied to the solution of finite element systems arising from second-order elliptic boundary value problems with first- order derivatives. It is shown that the convergence factor of the new method is a sum of two items: the first item is given by the convergence factor of the inner iterative method, the second item is given by the approximation properties of the coarser grid space. For properly choosen coarse grid space the rate of convergence of the new method is close to the rate of convergence of the inner iterative method. For uniformly convergent inner iterations, the new method is also uniformly convergent. The special choices of the inner iterative method are discussed as e.g. multiplicative domain decomposition or multigrid methods and some modifications of the basic algorithm suitable for these choices are described.

65F10Iterative methods for linear systems
65N55Multigrid methods; domain decomposition (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
35J25Second order elliptic equations, boundary value problems
Full Text: DOI