A multi-iterate method to solve systems of nonlinear equations
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In this thesis, we focus on standard classes of problems in numerical optimization: unconstrained nonlinear optimization as well as systems of nonlinear equations. More precisely, we consider two types of unconstrained nonlinear optimization problems. On t ...
The purpose of this thesis is to investigate methods for the solution of multiscale problems both from the mathematical and numerical point of view, with a particular concern on applications to flows through heterogeneous porous media. After an overview of ...
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 ...
We present a method for the structural identification of genetic regulatory networks (GRNs), based on the use of a class of Piecewise-Linear (PL) models. These models consist of a set of decoupled linear models describing the different modes of operation o ...
Mary Ann Liebert, Inc. 2 Madison Avenue Larchmont, NY 10538 USA2008
In the past few years, the problem of distributed consensus has received a lot of attention, particularly in the framework of ad hoc sensor networks. Most methods proposed in the literature attack this problem by distributed linear iterative algorithms, wi ...
Finding the range of motion for the human joints is a popular method for diagnosing joint diseases. By current technology, it is more trustable and easier to find the range of motion by employing computer based models of the human tissues. In this paper we ...
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 ...
Many complex transportation models can be formulated as fixed-point problems. Typical examples are the equilibrium-like models, motivated by the need to capture the interaction between the transport supply (that is, the infrastructure) and transport demand ...
Theoretical and numerical aspects of multi-scale problems are investigated. On one hand, mathematical analysis is done on a new method for numerically solving problems with multi-scale behavior using multiple levels of not necessarily nested grids. A parti ...
We present iterative subdomain methods based on a domain decomposition approach to solve the coupled Stokes/Darcy problem using finite elements. The dependence of the convergence rate on the grid parameter h and on the physical data is discussed; some diff ...