Iterative substructuring methods: the general elliptic case. by Olof B. Widlund

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Published by Courant Institute of Mathematical Sciences, New York University in New York .

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Pagination25 p.
Number of Pages25
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Open LibraryOL17978566M

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The elliptic problem is second-order with piecewise constant coe cients and Iterative substructuring methods: the general elliptic case. book Dirichlet boundary condition. Using the framework of the mortar method, the problem is approximated by a nite element method with piecewise linear functions on nonmatching meshes.

Our domain decomposition method is an iterative substructuring one with a new coarse. Iterative substructuring methods: the general elliptic case / 5 Finite element capacitance matrix methods / 5 Iterative substructuring methods: algorithms and theory for elliptic 4/5(5).

() A unified framework for accelerating the convergence of iterative substructuring methods with Lagrange multipliers. International Journal for Numerical Methods in Engineering() Domain decomposition method for the h-p version finite element by: A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems.

Typically, the methods considered are well suited for the kind of systems arising from the discretization of partial differential equations. In many cases, the selection of a proper preconditioner is. An illustration of an open book. Books. An illustration of two cells of a film strip.

Video. An illustration of an audio speaker. Audio. An illustration of a " floppy disk. Full text of "Iterative substructuring methods: algorithms and theory for elliptic problems in the plane".

Abstract. In this paper, certain iterative substructuring methods with Lagrange multipliers are considered for elliptic problems in three dimensions. The algorithms belong to the family of dual{ primal FETI methods which have recently been introduced and analyzed successfully for elliptic problems in the plane.

Full text of "Iterative methods for elliptic problems on regions partitioned into substructures and the biharmonic Dirichlet problem" See other formats Computer Science Depaftmen TECHNICAL REPORT ITERATIVE METHODS FOR ELLIPTIC PROBLEMS ON REGION PARTITIONED INTO SUBSTRUCTURES AND THE BIHARMONIC DIRICHLET PROBLEM By Olof B.

Widlund January. Widlund, O.B.: Iterative substructuring methods: The general elliptic case, Technical ReportComputer Science Department, Courant Institute, New York Google Scholar Download references.

The iterative substructuring methods, based on decompositions of the region into non-overlapping subregions, form one of the main families of such algorithms.

Many domain decomposition algorithms can conveniently be described and analyzed as Schwarz methods. Other papers providing iterative methods involving domain decomposition for the solution of elliptic problems have appeared in the literature [l]-[8].

The earliest papers involved splitting the domain into subdomains without interior corner points [1], [2], [4]-[6], [8]. These methods became inefficient when many long thin subdo.

A few years ago, much of the work on iterative substructuring methods was focused on elliptic problems defined on regions divided into two or a few subregions with separating curves (surfaces) which do not intersect; see e.g., Bj0rstad and Widlund and Widlund.

Summary. In this paper we consider an iterative substructuring method for solv-ing system of equations arising from mortar Morley nite element discretization of a model fourth order elliptic problem in 2D.

The parallel preconditioner for the inter-face problem is introduced using Additive Schwarz Method framework. The method. Schwarz’s method, iterative substructuring methods, domain decomposition, elliptic equations, finite elements. Robust iterative methods for solution of transport problems with flow: a block two-level preconditioned Schwarz-domain decomposition method for solution of nonlinear viscous flow problems.

Some Domain Decomposition Algorithms. A procedure to generate an initial guess for a multilevel/multigrid is shown, and an approach that relates multilevel methods to standard Jacobi and Gauss-Seidel iterative methods is presented. Chapter 4 discusses a large class of methods using nonoverlapping domains, also called substructuring methods.

The domain decomposition method is of iterative substructuring type and is described as an additive Schwarz method (ASM) using the general framework of ASMs; see [DW95, Ben95a]. It is applied to the Schur complement of our discrete problems, i.e., interior variables of all subregions are first eliminated using a direct method.

We study a class of substructuring methods well-suited for iterative solution of large systems of linear equations arising from the p-version finite element p-version offers a natural decomposition with every element treated as a use the preconditioned conjugate gradient method with preconditioning constructed by a decomposition of the local function space on.

Purchase Iterative Methods for Large Linear Systems - 1st Edition. Print Book & E-Book. ISBNVarious iterative methods for solving the linear systems associated with finite element approximations to self-adjoint elliptic differential operators are compared based on their performance on serial and parallel machines.

The methods studied are all preconditioned conjugate gradient methods, differing only in the choice of preconditioner. The preconditioners considered arise from diagonal.

A Generalized FETI - DP Method for a Mortar Discretization of Elliptic Problems M. Dryja1,d2 1. Introduction. In this paper, an iterative substructuring method with La-grange multipliers is proposed for discrete problems arising from approximations of elliptic problem in two dimensions on non-matching meshes.

The problem is formu. We propose and study an iterative substructuring method for an h-p Nitsche-type discretization, following the original approach introduced in [Bramble, Pasciack, Schatz (Math Comp. )] for. Iterative substructuring methods are known to be efficient precondi-tioners for the large linear systems resulting from the discretization of second-order elliptic partial differential equations, e.g., those of modeling diffusion and linear elasticity.

However, it is also known that the convergence rate of domain decomposition methods can. This book presents an easy-to-read discussion of domain decomposition algorithms, their implementation and analysis.

The relationship between domain decomposition and multigrid methods is carefully explained at an elementary level, and discussions of the implementation of domain decomposition methods on massively parallel super computers are also included.4/5(1).

An iterative substructuring method for problem () is analyzed in [36], where the bound C(1 + log(H=h))2 is found for bounded polygonal domains in R2. The same bound is established in [35] for problems in H(div) under similar assumptions in R3. An iterative substructuring method for 2D problems is analyzed in [11] for irregular subdomains, where.

In the case of elliptic problems, we also provide an introduction to the convergence theory, which requires some knowledge of finite element spaces and elementary functional analysis.

O.B. (), ‘ Capacitance matrix methods for the helmholtz equation on general three-dimensional regions ’, Math. ‘Iterative substructuring methods. The BDDC method is currently one of the most popular methods of iterative substructuring.

It has been proposed independently in [10,11,12]; see [13,14] for the proof of equivalence. Even though BDDC has been originally formulated for elliptic problems, it has been successfully extended, for example, beyond elliptic cases [15,16] and to multiple. of the FETI method even in this case.

However, a theoretical justification for this kind of robustness is still lacking. In the following, we restrict ourselves to the model elliptic problem () −∇(α∇u) = f, in a bounded polygonal or polyhedral domain Ω ⊂ Rd, d = 2 or 3, subject to suitable boundary conditions on the boundary ∂Ω.

Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations.

Multigrid methods (e.g, [23], [46], [12]) are among the most efficient iterative algorithms for solving the linear systems associated with elliptic partial differential equations.

This book presents finite difference methods for solving partial differential equations (PDEs) and also general concepts like stability, boundary conditions etc.

Material is in order of increasing complexity (from elliptic PDEs to hyperbolic systems) with related theory included in appendices. we shall use an additive Schwarz method without overlap, that is, we shall use what is also referred to as an iterative substructuring method.

Recently, polylogarithmic conver- gence rates have been reported for elliptic problems in the context of three-dimensional spectral element discretiza- tions using this class of solution methods [40, 41]. Iterative Substructuring Methods Jan Mandela; Dohrmann, and Tezaur [19] have formulated the methods in terms of general coarse degrees of freedom without treating the corner degrees of freedom in a special way, proved that the eigenvalues of the preconditioned arise in the standard substructuring setting for a model elliptic problem.

Extension of theory for iterative substructuring methods The technical tools necessary for the traditional analysis of the rate of convergence of iterative substructuring methods are collected in Section of the T. & W. book. Among the tools necessary for the analysis of BDDC and FETI-DP in three dimensions is a bound on the energy of Ih(ϑ Fku).

FETI and BDDaretwo widelyused substructuring methods for the solution of large sparse systems of linear algebraic equations arizing from discretization of elliptic boundary value problems.

The two most advanced variants of these methods are the FETI-DP and the BDDC methods. Adaptive Selection of Face Coarse Degrees of Freedom in the BDDC and the FETI-DP Iterative Substructuring Methods Jan Mandela,∗,1, Bedˇrich Soused´ıka,b,2 aDepartment of Mathematical Sciences, University of Colorado at Denver, P.O.

Box. Buy Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic Partial Differential Equations: Technical Report ; September, (Classic Reprint) on FREE SHIPPING on qualified orders.

Domain Decomposition Parallel Multilevel Methods for Elliptic Partial Differential Equations. Barry Smith, Petter Bjorstad, and William Gropp. The emergence of parallel computers and their potential for the numerical solution of Grand Challenge problems has led to a large amount of research in domain decomposition methods.

numerical methods for Civil Engineering majors during and was modi ed to include Mechanical Engineering in The materials have been periodically updated since then and underwent a major revision by the second author in The main goals of these lectures are to introduce concepts of numerical methods and introduce.

A method for the numerical solution of non-separable (self-adjoint) elliptic equations is described in which the basic approach is the iterative application of direct methods.

Such equations may be transformed into Helmholtz form and this Helmholtz problem is solved by the iterative application of FFT methods. General Framework for Dynamic Substructuring: History, Review and Classification of Techniques A review on dynamic substructuring methods for model updating and damage detection of large-scale structures.

An iterative reduced-order substructuring approach to the calculation of eigensolutions and eigensensitivities. Variational analysis of some conjugate gradient methods by Widlund, Olof B at - the best online ebook storage.

Download and read online for free Variational analysis of some conjugate gradient methods by Widlund, Olof B. The method of lines (MOL, NMOL, NUMOL) is a technique for solving partial differential equations (PDEs) in which all but one dimension is discretized.

MOL allows standard, general-purpose methods and software, developed for the numerical integration of ordinary differential equations (ODEs) and differential algebraic equations (DAEs), to be used.

A large number of integration routines have.On the Origins of Iterative Substructuring Method, M.J. Gander and X. Tu, Domain Decomposition Methods in Science and Engineering XXI, LNCSE, Springer-Verlag, pp.Block Jacobi for discontinuous Galerkin discretizations: no ordinary Schwarz methods, M.J.

Gander and S. Hajian, Domain Decomposition Methods in Science and.In computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems. A specific implementation of an iterative method, including the termination criteria, is an algorithm of the iterative method.

An iterative method is called convergent if the corresponding sequence converges for given initial.

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