Preconditioning Techniques in Linear Model Order Reduction

نویسندگان

  • W.H.A. Schilders
  • J. Rommes
چکیده

Krylov subspace methods have become very popular, not only for solving large scale linear systems, but also in the area of model order reduction. It is also well known that the performance of iterative solution techniques depends crucially on the choice of preconditioning matrix. Within the area of model order reduction, the concept of preconditioning has not yet been introduced. However, recent reduction problems arising in electronics applications clearly demonstrate the need for some kind of preconditioning step prior to the actual model order reduction. In this paper, we present initial ideas and some test results.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Solving large systems arising from fractional models by preconditioned methods

This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...

متن کامل

An Assessment of Some Preconditioning Techniques in Shell Problems

Preconditioned Krylov subspace methods have proved to be ecient in solving large, sparse linear systems in many areas of scienti®c computing. The success of these methods in many cases is due to the existence of good preconditioning techniques. In problems of structural mechanics, like the analysis of heat transfer and deformation of solid bodies, iterative solution of the linear equation syst...

متن کامل

Effect of discretization order on preconditioning and convergence of a high-order unstructured Newton-GMRES solver for the Euler equations

This article studies the effect of discretization order on preconditioning and convergence of a high-order Newton–Krylov unstructured flow solver. The generalized minimal residual (GMRES) algorithm is used for inexactly solving the linear system arising from implicit time discretization of the governing equations. A first-order Jacobian is used as the preconditioning matrix. The complete lower–...

متن کامل

Reduced order solution of structured linear systems arising in certain PDE-constrained optimization problems

The solution of PDE-constrained optimal control problems is a computationally challenging task, and it involves the solution of structured algebraic linear systems whose blocks stem from the discretized first-order optimality conditions. In this paper we analyze the numerical solution of this large-scale system: we first perform a natural order reduction, and then we solve the reduced system it...

متن کامل

Preconditioning Techniques for the Bidomain Equations

In this work we discuss parallel preconditioning techniques for the bidomain equations, a non-linear system of partial differential equations which is widely used for describing electrical activity in cardiac tissue. We focus on the solution of the linear system associated with the elliptic part of the bidomain model, since it dominates computation, with the preconditioned conjugate gradient me...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009