Stopping criteria, forward and backward errors for perturbed asynchronous linear fixed point methods in finite precision

International audienceThis paper deals with perturbed linear fixed point methods in the presence of round off errors. Successive approximations as well as the more general, asynchronous iterations are treated. Forward and backward error estimates are presented and are used in order to propose theoretical stoppig criteria for these methods. In the case of asynchronous iterations, macro iterations are used as a tool in order to obtain estimates

A new class of asynchronous iterative methods with order intervals

International audienceThis paper deals with a new class of parallel asynchronous iterative algorithms for the solution of nonlinear systems of equations. The main feature of the new class of methods preseted here is the possibility of flexible commmunication between processors. In particular partial updates can be exchanged. Approximation of the asssociated fixed point mapping is also considered. A detailed convergengence study is presented. A connection with the Schwarz alternating method is made for nonlinear boundary value problems. Computational results on a shared memory multiprocessotr IBM 3090 are presented

Asynchronous iterations with flexible communication: contracting operators

AbstractThe concept of flexible communication permits one to model efficient asynchronous iterations on parallel computers. This concept is particularly useful in two practical situations. Firstly, when communications are requested while a processor has completed the current update only partly, and secondly, in the context of inner/outer iterations, when processors are also allowed to make use of intermediate results obtained during the inner iteration in other processors.In the general case of nonlinear or linear fixed point problems, we give a global convergence results for asynchronous iterations with flexible communication whereby the iteration operators satisfy certain contraction hypotheses. In this manner we extend to a contraction context previous results obtained for monotone operators with respect to a partial ordering

Parallelization of subdomain methods with overlapping for linear and nonlinear convection-diffusion problems

International audienceLinear and nonlinear convection-diffusion problems are considered. The numerical solution of these problems via the Schwarz alternating method is studied. A new class of parallel asynchronous iterative methods with flexible communication is applied. The implementation of parallel asyn-chronous and synchronous algorithms on distributed memory multiprocessors is described. Experimental results obtained on an IBM SP2 by using PVM are presented and analyzed. The interest of asynchronous iterative methods with flexible communication is clearly shown

Mathematical study of perturbed asynchronous iterations designed for distributed termination

International audienceThis paper deals with the mathematical study of perturbed xed point asynchronous iterations designed for a distributed termination. The distributed termination of asynchronous iterations is considered by using a perturbed xed point mapping, which is an approximation of an exact xed point mapping. In the general framework of '-approximate contraction, it is shown that the perturbed asynchronous iteration converges in nite time and that the limit of the perturbed asynchronous iteration belongs to a ball of nite radius and center ~ u ? , solution of the exact problem. The value of the radius is given in the case of linear and quadratic convergence, respectively

Asynchronous iterative algorithms with flexible communication for nonlinear network flow problems

International audienceThe strictly convex network flow problem is considered. The dual of this problem is unconstrained continuously differentiable and well suited for solution via parallel or distributed iterative algorithms.A new class of asynchronou iterative methods is proposed ; the asynchronous iterations with flexibl communication

Design for Integrated Planar Spiral Inductor for MEMS

The main aim of this paper is to present the new design of an integrated planar spiral inductor with a new structure of an underpass to obtain a high inductance, high quality factor and minimum losses into winding and magnetic core. The performance of this structure dependent on the geometrical, electrical parameters and material properties. These parameters are calculated at 350 MHz and this is the high frequency used for MEMS applications. Furthermore, thermal analysis in inductor from finite difference method is described. The heat transfer model is based on heat conduction and heat convection. Moreover, the heat source is calculated by different losses. In addition, the simulation results from 3D finite element method using software also been presented in this paper. It is based on both the classical heat equation and certain condition limits. However, a new design of an underpass has been proposed where a via is fabricated with a circular layer. The input and output of the spiral are implanted in the same direction. In addition, the magnetic core is the solution to decrease the temperature. Finally, the results of the finite difference method are compared with simulation results from finite element method. The good agreement between the results is obtained. The proposed via and a core magnetic are responsible for enhancement the thermal behavior in integrated inductor. The result shows that the temperature of the air core inductor and magnetic core inductor could be 53 °C and 33 °C, respectively

High performance Peer-to-Peer distributed computing with application to obstacle problem

International audienceThis paper deals with high performance Peer-to-Peer computing applications. We concentrate on the solution of large scale numerical simulation problems via distributed iterative methods. We present the current version of an environment that allows direct communication between peers. This environment is based on a self-adaptive communication protocol. The protocol configures itself automatically and dynamically in function of application requirements like scheme of computation and elements of context like topology by choosing the most appropriate communication mode between peers. A first series of computational experiments is presented and analyzed for the obstacle problem