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In this work, we are interested in elaborating models and numerical methods in order to study some phenomena which arise in the solidification of binary alloys. We propose two distinct models based on the mass and energy conservation laws as well as on cla ...
We propose an extension of secant methods for nonlinear equations using a population of previous iterates. Contrarily to classical secant methods, where exact interpolation is used, we prefer a least squares approach to calibrate the linear model. We propo ...
In this paper we present a family of iterative methods to solve numerically second order elliptic problems with multi-scale data using multiple levels of grids. These methods are based upon the introduction of a Lagrange multiplier to enforce the continuit ...
The aim of this thesis is the study of the simulation of electrically large structures and the application of the results to automotive Electromagnetic Compatibility (EMC). The theoretical and experimental work carried out has led to the development of com ...
Two of the most basic problems encountered in numerical optimization are least-squares problems and systems of nonlinear equations. The use of more and more complex simulation tools on high performance computers requires solving problems involving an incre ...
In this thesis we will show that unsteady, incompressible fluid-flow problems, as described by the three-dimensional Navier-Stokes equations, can efficiently be simulated by a parallel computer code based on a spectral element discretization. This efficien ...
A new class of methods for solving systems of nonlinear equations is introduced. The main idea is to build a linear model using a population of previous iterates. Contrarily to classical secant methods, where exact interpolation is used, we prefer a least ...
We propose an extension of secant methods for nonlinear equations using a population of previous iterates. Contrarily to classical secant methods, where exact interpolation is used, we prefer a least squares approach to calibrate the linear model. We propo ...
Parametrized systems of Differential Algebraic Equations (DAEs) stand at the base of several mathematical models in Microelectronics, Computational Fluid Dynamics and other Engineering fields. Since the dimension of these systems can be huge, high computat ...
We propose a domain decomposition method for advection-diffusion- reaction equations based on Nitsche's transmission conditions. The advection-dominated case is stabilized using a continuous interior penalty approach based on the jumps in the gradient over ...
