Results 31 to 40 of about 411 (241)

Iterative realization of finite difference schemes in the fictitious domain method for elliptic problems with mixed derivatives

Журнал Белорусского государственного университета: Математика, информатика, 2019
Development of efficient finite difference schemes and iterative methods for solving anisotropic diffusion problems in an arbitrary geometry domain is considered.
Vasily M. Volkov, Alena V. Prakonina
doaj   +1 more source

A Robust Approximation of the Schur Complement Preconditioner for an Efficient Numerical Solution of the Elliptic Optimal Control Problems

Computation, 2020
In this paper, we consider the numerical solution of the optimal control problems of the elliptic partial differential equation. Numerically tackling these problems using the finite element method produces a large block coupled algebraic system of ...
Kizito Muzhinji, Stanford Shateyi
doaj   +1 more source

A comparison theorem for the iterative method with the preconditioner (I+Smax)

Journal of Computational and Applied Mathematics, 2002
The authors propose the preconditioner \(P_m=I+S_{\max}\) where \(S_{\max}\) is contructed by using only the largest element of each row of the upper triangular part of the nonsingular diagonally dominant \(\mathbb Z\)-matrix \(A\), that is, \(S_{\max}=(s_{ij}^m)=-a_{ik_i}\) for \(i=1,2,\ldots,n-1\), \(j>i\), and \(0\) otherwise, where \(k_i=\min j\in\{
Kotakemori, Hisashi, Harada, Kyouji, Morimoto, Munenori, Niki, Hiroshi   +3 more
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An Optimal Block Iterative Method and Preconditioner for Banded Matrices with Applications to PDEs on Irregular Domains [PDF]

SIAM Journal on Matrix Analysis and Applications, 2012
Classical Schwarz methods and preconditioners subdivide the domain of a PDE into subdomains and use Dirichlet transmission conditions at the artificial interfaces. Optimized Schwarz methods use Robin (or higher order) transmission conditions instead, and the Robin parameter can be optimized so that the resulting iterative method has an optimized ...
Gander Martin J., Loisel Sebastien, Szyld Daniel   +2 more
openaire   +4 more sources

Preconditioned Dirichlet-Dirichlet Methods for Optimal Control of Elliptic PDE

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018
The discretization of optimal control of elliptic partial differential equations problems yields optimality conditions in the form of large sparse linear systems with block structure. Correspondingly, when the solution method is a Dirichlet-Dirichlet non-
Loghin Daniel
doaj   +1 more source

A New Hybrid Preconditioner for the Interior Point Method

Trends in Computational and Applied Mathematics, 2019
This study aims to improve the computation of the search direction in the primal-dual Interior Point Method through preconditioned iterative methods. It is about a hybrid approach that combines the Controlled Cholesky Factorization preconditioner and ...
Manolo Rodriguez Heredia, Cecilia Orellana Castro, Aurélio Ribeiro Leitte Oliveira   +2 more
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A Survey of Low-Rank Updates of Preconditioners for Sequences of Symmetric Linear Systems

Algorithms, 2020
The aim of this survey is to review some recent developments in devising efficient preconditioners for sequences of symmetric positive definite (SPD) linear systems A k x k = b k , k = 1 , … arising in many scientific applications, such as ...
Luca Bergamaschi
doaj   +1 more source

Krylov Subspace Solvers and Preconditioners

ESAIM: Proceedings and Surveys, 2018
In these lecture notes an introduction to Krylov subspace solvers and preconditioners is presented. After a discretization of partial differential equations large, sparse systems of linear equations have to be solved.
Vuik C.
doaj   +1 more source

On a computer implementation of the block Gauss-Seidel method for normal systems of equations

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2016
This article focuses on the modification of the block option Gauss-Seidel method for normal systems of equations, which is a sufficiently effective method of solving generally overdetermined, systems of linear algebraic equations of high dimensionality ...
Alexander I Bogdanova, Ekaterina Yu Bogdanova   +1 more
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A parallelizable preconditioner for the iterative solution of implicit Runge–Kutta-type methods

Journal of Computational and Applied Mathematics, 1999
This article is concerned with the implementation of implicit Runge-Kutta (RK) methods such as those based on Gauss, Radon and Lobatto points applied to (stiff) ordinary differential equations. The use of a preconditioner, whose decomposition cost for parallel implementation is equivalent to the cost for the implicit-Euler method, is proposed.
Jay, Laurent O., Braconnier, Thierry
openaire   +2 more sources