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Tuesday, July 21, 2020 | History

3 edition of Domain decomposition preconditioners for the spectral collocation method found in the catalog.

Domain decomposition preconditioners for the spectral collocation method

Alfio Quarteroni

Domain decomposition preconditioners for the spectral collocation method

by Alfio Quarteroni

  • 340 Want to read
  • 11 Currently reading

Published by National Aeronautics and Space Administration, Langley Research Center, Institute for Computer Applications in Science and Engineering in Hampton, Va .
Written in English

    Subjects:
  • Differential equations, Elliptic.,
  • Collocation methods.

  • Edition Notes

    StatementAlfio Quarteroni, Giovanni Sacchi-Landriani ; operated by the Universities Space Research Association.
    SeriesICASE report -- no. 88-11., NASA contractor report -- 181620., NASA contractor report -- NASA CR-181620.
    ContributionsSacchi-Landriani, Giovanni., Universities Space Research Association., Institute for Computer Applications in Science and Engineering.
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL15392045M

      Domain Decomposition Methods - Algorithms and Theory (Springer Series in Computational Mathematics Book 34) - Kindle edition by Toselli, Andrea, Widlund, Olof. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Domain Decomposition Methods - Algorithms and Theory (Springer Reviews: 1. The p-version finite element method for linear, second order elliptic equations in an arbitrary, sufficiently smooth domain is studied in the framework of the Domain Decomposition (DD) method. Two types of square reference elements are used with the products of the integrated Legendre polynomials for coordinate functions.

    A domain decomposition spectral collocation method is developed for steady‐state, viscoelastic flow simulations through model porous media. The method is first tested on the one‐dimensional linear equation set resulting from the first‐order domain perturbation analysis of the flow of an upper convected Maxwell (UCM) fluid in an undulating channel. The splitting of the domain in the. the code dealing with the spectral method and domain decomposition. For a new PDE, the user has to supply only the code that computes the residual and its linearization. Mappings are employed to control how collocation points and thus resolution are distributed within each .

      All these collocation methods are in fact implicit Runge–Kutta methods. The coefficients c k in the Butcher tableau of a Runge–Kutta method are the collocation points. However, not all implicit Runge–Kutta methods are collocation methods. [1] Example: The trapezoidal rule. Pick, as an example, the two collocation points c 1 = 0 and c 2. DOMAIN DECOMPOSITION PRECONDITIONERS FOR THE SPECTRAL COLLOCATION METHOD ABSTRACT We propose and analyze several block iteration preconditioners for the solution of elliptic prob- lema by spectral collocation methods in a region partitioned into several rectangles.


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Domain decomposition preconditioners for the spectral collocation method by Alfio Quarteroni Download PDF EPUB FB2

We propose and analyze several block iteration preconditioners for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles. It is shown that convergence is achieved with a rate that does not.

Domain decomposition preconditioners for the spectral collocation method. (OCoLC) Microfiche: Quarteroni, Alfio. Domain decomposition preconditioners for the spectral collocation method.

(OCoLC) Material Type: Document, Government publication, National government publication, Internet resource: Document Type: Internet Resource. Domain decomposition preconditioners for the spectral collocation method.

(OCoLC) Online version: Quarteroni, Alfio. Domain decomposition preconditioners for the spectral collocation method. (OCoLC) Material Type: Government publication, National government publication: Document Type: Book: All Authors / Contributors.

We propose and analyze several block iteration preconditioners for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles.

It is shown that convergence is achieved with a rate that does not depend on the polynomial degree of the spectral solution. The iterative methods here presented can be effectively implemented on multiprocessor Cited by: Domain decomposition preconditioners for the spectral collocation method Article (PDF Available) in Journal of Scientific Computing 3(1) March with 31 Reads How we measure 'reads'.

Domain decomposition methods are typically used as preconditioners for Krylov space iterative methods, such as the conjugate gradient method or GMRES. In overlapping domain decomposition methods, the subdomains overlap by more than the interface.

Overlapping domain decomposition methods include the Schwarz alternating method and the additive. This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations.

It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral.

This book focuses on domain decomposition methods as preconditioners. Its purpose is to provide background rather than to provide a complete analysis of the algorithms. The book is divided into five chapters, the first three of which refer to the class of domain decomposition algorithms that use overlapping domains (Schwarz methods).

A global-in-time domain decomposition method for the coupled nonlinear Stokes and Darcy flows | Thi-Thao-Phuong Hoang Hyesuk Lee. We study a decoupling iterative algorithm based on domain decomposition for the time-dependent nonlinear Stokes-Darcy model, in which different time steps can be used in the flow region and in the porous medium.

[QSL1] A. Quarteroni, G. Sacchi-Landriani,Domain decomposition preconditioners for the spectral collocation method, J. Scientific Comput, Vol. 3, 1 (). The distinguishing feature of this book is a comprehensive and rigorous treatment of convergence bounds based on the theory of infinite elements.

The bibliography is quite complete for the fields covered. The book belongs on the desk of all specialists involved in domain decomposition and substructuring ."Reviews: 1. Efficient domain decomposition preconditioners (of both Schwarz and Schur type) that are amenable to parallel implementation are surveyed.

The discussion of spectral algorithms for fluid dynamics in single domains focuses on proven algorithms for the boundary-layer equations, linear and nonlinear stability analyses, incompressible Navier-Stokes.

A domain decomposition algorithm for nonlinear interface problem (SASSI) (pdf,ps) Fast Solvers. A preconditioner for the Schur complement domain decomposition method (CROS) (pdf,ps) Fast Solvers and Schwarz Preconditioners for Spectral N´ed´elec Elements for a Model Problem in H(curl) (HIENTZSCH) (pdf,ps) Mortar Method.

Spectral methods, particularly in their multidomain version, have become firmly established as a mainstream tool for scientific and engineering computation. While retaining the tight integration between the theoretical and practical aspects of spectral methods that was the hallmark of their book, Canuto et al.

now incorporate the many improvements in the algorithms and the 5/5(1). Spectral methods have been using a domain decomposition approach for handling irregular domains. The main focus has been on appropriate matching conditions for the solutions across the subdomain boundaries.

Quarteroni and G. Sacchi Landriani, Domain decomposition preconditioners for the spectral collocation method, Tech. Rept.ICASE. Domain Decomposition Methods in Science and Engineering XVII, Huazhong Tang and Gerald Warnecke. () On Convergence of a Domain Decomposition Method for a Scalar Conservation Law.

Domain decomposition methods (DDM) constitute a broad category of solution methods capable of solving large-scale problems in computational mechanics. Over the last years, considerable improvements in DDM have been made, leading to faster calculation times and reduced memory requirements for the solution of increasingly larger problems [ 6 ].

Pavarino, L.F. ( b), ‘Some Schwarz algorithms for the spectral element method’, in Sixth Conf. on Domain Decomposition Methods for Partial Differential Equations (Quarteroni, A., ed.), American Mathematical Society (Providence, RI), to appear. Technical ReportDepartment of Computer Science, Courant Institute.

In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the.

Proceedings of the 6th International Conference on Domain Decomposition Methods in Como, Italy (June ) Domain decomposition preconditioners for convection diffusion problems (PDF). An iterative finite-element collocation method for parabolic problems using domain decomposition. Domain Decomposition Methods in Science and Engineering XXII, () Two-level mortar domain decomposition preconditioners for heterogeneous elliptic problems.

Computer Methods in Applied Mechanics and EngineeringDomain decomposition preconditioners for the spectral collocation method. By Giovanni Sacchilandriani and Alfio Quarteroni. Abstract. Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles.

It is shown that.Based on this decomposition, domain decomposition methods of three basic type—additive, multiplicative and hybrid Schwarz methods—have been studied in the literature (cf. [4, 5, 6]).