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New trends in coupled simulations featuring domain decomposition and metacomputing

Philippe d'Anfray, Laurence Halpern, Juliette Ryan (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we test the feasibility of coupling two heterogeneous mathematical modeling integrated within two different codes residing on distant sites. A prototype is developed using Schwarz type domain decomposition as the mathematical tool for coupling. The computing technology for coupling uses a CORBA environment to implement a distributed client-server programming model. Domain decomposition methods are well suited to reducing complex physical phenomena into a sequence of parallel subproblems...

New trends in coupled simulations featuring domain decomposition and metacomputing

Philippe d'Anfray, Laurence Halpern, Juliette Ryan (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we test the feasibility of coupling two heterogeneous mathematical modeling integrated within two different codes residing on distant sites. A prototype is developed using Schwarz type domain decomposition as the mathematical tool for coupling. The computing technology for coupling uses a CORBA environment to implement a distributed client-server programming model. Domain decomposition methods are well suited to reducing complex physical phenomena into a sequence of parallel subproblems...

New unifying convergence criteria for Newton-like methods

Ioannis K. Argyros (2002)

Applicationes Mathematicae

We present a local and a semilocal analysis for Newton-like methods in a Banach space. Our hypotheses on the operators involved are very general. It turns out that by choosing special cases for the "majorizing" functions we obtain all previous results in the literature, but not vice versa. Since our results give a deeper insight into the structure of the functions involved, we can obtain semilocal convergence under weaker conditions and in the case of local convergence a larger convergence radius....

Newton and conjugate gradient for harmonic maps from the disc into the sphere

Morgan Pierre (2004)

ESAIM: Control, Optimisation and Calculus of Variations

We compute numerically the minimizers of the Dirichlet energy E ( u ) = 1 2 ∫ B 2 | ∇ u | 2 d x among maps u : B 2 → S 2 from the unit disc into the unit sphere that satisfy a boundary condition and a degree condition. We use a Sobolev gradient algorithm for the minimization and we prove that its continuous version preserves the degree. For the discretization of the problem we use continuous P 1 finite elements. We propose an original mesh-refining strategy needed to preserve the degree with the discrete version of the algorithm (which is a preconditioned...

Newton and conjugate gradient for harmonic maps from the disc into the sphere

Morgan Pierre (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We compute numerically the minimizers of the Dirichlet energy E ( u ) = 1 2 ∫ B 2 | ∇ u | 2 d x among maps u : B 2 → S 2 from the unit disc into the unit sphere that satisfy a boundary condition and a degree condition. We use a Sobolev gradient algorithm for the minimization and we prove that its continuous version preserves the degree. For the discretization of the problem we use continuous P1 finite elements. We propose an original mesh-refining strategy needed to preserve the degree with the discrete version of the algorithm (which...

Newton methods for solving two classes of nonsmooth equations

Yan Gao (2001)

Applications of Mathematics

The paper is devoted to two systems of nonsmooth equations. One is the system of equations of max-type functions and the other is the system of equations of smooth compositions of max-type functions. The Newton and approximate Newton methods for these two systems are proposed. The Q-superlinear convergence of the Newton methods and the Q-linear convergence of the approximate Newton methods are established. The present methods can be more easily implemented than the previous ones, since they do not...

Newton's iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition

Jonas Koko (2004)

International Journal of Applied Mathematics and Computer Science

Newton's iteration is studied for the numerical solution of an elliptic PDE with nonlinear boundary conditions. At each iteration of Newton's method, a conjugate gradient based decomposition method is applied to the matrix of the linearized system. The decomposition is such that all the remaining linear systems have the same constant matrix. Numerical results confirm the savings with respect to the computational cost, compared with the classical Newton method with factorization at each step.

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