Publication

A dynamic preconditioner for Newton-Krylov algorithms. Application to fluid-structure interaction

Simone Deparis
2004
Reports

Abstract

We consider linear and nonlinear convergence acceleration techniques in the framework of Newton or inexact Newton methods. The proposed procedure is based on a new dynamic preconditioner to be used in combination with the GMRES method for reducing the cost of solving a sequence of linear systems. A nonlinear convergence acceleration technique based on a previous work by Washio et al. is also added. The benefits of this combination of acceleration techniques is shown on fluid-structure interaction problems in haemodynamics for two- and three-dimensional applications.

Official source

https://infoscience.epfl.ch/entities/publication/fc04a068-8463-4791-91dc-712bcad27dc8

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Simone Deparis
2004
Reports

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/fc04a068-8463-4791-91dc-712bcad27dc8

About this result

Related concepts (31)

Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.

Fluid mechanics

Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.

Preconditioner

In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods. Preconditioning is typically related to reducing a condition number of the problem. The preconditioned problem is then usually solved by an iterative method. In linear algebra and numerical analysis, a preconditioner of a matrix is a matrix such that has a smaller condition number than .

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A dynamic preconditioner for Newton-Krylov algorithms. Application to fluid-structure interaction

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