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In this thesis we study the efficient implementation of the finite element method for the numerical solution of partial differential equations (PDE) on modern parallel computer archi- tectures, such as Cray and IBM supercomputers. The domain-decomposition ...
The characteristic of effective properties of physical processes in heterogeneous media is a basic modeling and computational problem for many applications. As standard numerical discretization of such multiscale problems (e.g. with classical finite elemen ...
Real-time optimization (RTO) methods use measurements to offset the effect of uncertainty and drive the plant to optimality. Explicit RTO schemes, which are characterized by solving a static optimization problem repeatedly, typically require multiple itera ...
We propose a modified parallel-in-time - parareal-multi-level time integration method that, in contrast to previously proposed methods, employs a coarse solver based on a reduced model, built from the information obtained from the fine solver at each itera ...
We propose a modified parallel-in-time - Parareal - multi-level time integration method which, in contrast to previous methods, uses a coarse solver based on the information from the fine solver at each iteration through the construction of a reduced model ...
It is important to consider the microstructure of a material when studying the macroscopic mechanical properties. Although special equipments have been used for micromechanics study through experimental tests, it is limited by instruments and reproducibili ...
The pseudospectral abscissa and the stability radius are well-established tools for quantifying the stability of a matrix under unstructured perturbations. Based on first-order eigenvalue expansions, Guglielmi and Overton [SIAM J. Matrix Anal. Appl., 32 (2 ...
Among the efficient numerical methods based on atomistic models, the quasi-continuum (QC) method has attracted growing interest in recent years. The QC method was first developed for crystalline materials with Bravais lattice and was later extended to mult ...
We consider unconstrained minimax problem where the objective function is the maximum of a finite number of smooth convex functions. We present an iterative method to compute the optimal solution for the unconstrained convex finite minimax problem. The alg ...
In this thesis we address the numerical approximation of the incompressible Navier-Stokes equations evolving in a moving domain with the spectral element method and high order time integrators. First, we present the spectral element method and the basic to ...
