High-order Sobolev preconditioning
نویسنده
چکیده
This paper compares the use of firstand second-order Sobolev gradients to solve differential equations using the method of least-squares steepest descent. The use of high-order Sobolev gradients offers a very effective preconditioning strategy for the linear part of a nonlinear differential equation. 2005 Elsevier Ltd. All rights reserved.
منابع مشابه
Constructive Sobolev Gradient Preconditioning for Semilinear Elliptic Systems
We present a Sobolev gradient type preconditioning for iterative methods used in solving second order semilinear elliptic systems; the n-tuple of independent Laplacians acts as a preconditioning operator in Sobolev spaces. The theoretical iteration is done at the continuous level, providing a linearization approach that reduces the original problem to a system of linear Poisson equations. The m...
متن کاملSobolev gradients: a nonlinear equivalent operator theory in preconditioned numerical methods for elliptic PDEs
Solution methods for nonlinear boundary value problems form one of the most important topics in applied mathematics and, similarly to linear equations, preconditioned iterative methods are the most efficient tools to solve such problems. For linear equations, the theory of equivalent operators in Hilbert space has proved an efficient organized framework for the study of preconditioners [6, 9], ...
متن کاملNonlinear least squares and Sobolev gradients
Least squares methods are effective for solving systems of partial differential equations. In the case of nonlinear systems the equations are usually linearized by a Newton iteration or successive substitution method, and then treated as a linear least squares problem. We show that it is often advantageous to form a sum of squared residuals first, and then compute a zero of the gradient with a ...
متن کاملVariational Level Set Segmentation in Riemannian Sobolev Spaces
Gradient flows in the Sobolev space H1 have been shown to enjoy favorable regularity properties. We propose a generalization of prior approaches for Sobolev active contour segmentation by changing the notion of distance in the Sobolev space, which is achieved through treatment of the function and its derivative in Riemannian manifolds. The resulting generalized Riemannian Sobolev space provides...
متن کاملRenormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces
The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega, $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005