Σεμινάριο Αριθμητικής Ανάλυσης και Επιστημονικών Υπολογισμών

Numerical Analysis and Scientific Computation Seminar

Τμήμα Μαθηματικών και Εφαρμοσμένων Μαθηματικών - Department of Mathematics and Applied Mathematics


16 May 2016 Manolis Paspalakis (U. of Patras, Department of Materials Science)
                      Modeling the interaction of light and matter in nanostructures
                      12:15, A303 (Seminar Room - Mathematics Building)
Abstract:  In recent years there is increasing interest in the study of the interaction of quantum emitters with metallic nanostructures. The main reason for this is that the large fields and the strong light confinement associated with the plasmonic resonances of the metallic nanostructures enable strong interaction between light and the quantum emitters. In this seminar, we present new theoretical results on the controlled dynamics and the optical properties of quantum emitters near metallic nanostructures, with emphasis to systems with applications in nanophotonics and quantum computing. For the modeling of the light-matter interaction, we combine the density matrix approach for the quantum systems with classical electromagnetic calculations for the metallic nanostructures.

13 Oct 2015  Enrico Scalas (University of Sussex, UK)
                      Exactly-solvable non-Markovian dynamic network
                      13:15, A303 (Seminar Room - Mathematics Building)
Abstract: Non-Markovian processes are widespread in natural and human-made systems, yet explicit modelling and analysis of such systems is underdeveloped. In this talk we consider a dynamic network with random link activation and deletion (RLAD) with non-exponential inter-event times. We study a semi-Markov random process when the inter-event times are heavy tailed Mittag-Leffler distributed, thus considerably slowing down the corresponding Markovian dynamics and study the system far from equilibrium. We derive an analytically and computationally tractable system of forward equations utilizing the Caputo derivative for the probability of having a given number of active links in the network.

Paper: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.042801


10 Dec 2014  Peter J. Veerman (Portland State Univ. (Math.& Stat.), & QCN, Physics, UOC )

                      Synchronization of high dimensional coupled dynamical systems
                      12:15, A302 (Seminar Room - Mathematics Building)
Abstract: We give some simple examples of identical linear dynamical systems coupled along a so-called communication graph. We are interested in the the dynamical behavior of these systems if the number of dynamical systems (or ``agents") is large. In particular the questions we consider in these examples are: What is the set of parameter values so that the behavior is stable, that is: initial eventually die out. In the case the system is stable, we also want to know exactly what the response to a 'kick' is.

These questions can be completely or partially answered (depending on what system we consider) by making certain conjectures about these systems. We describe those conjectures, and the results they lead to.

In the applications we consider, it is desirable if the response to the 'kick' dies out as fast as possible. Hence the notion of synchronization.

20 Nov 2014  K. Chrysafinos (National Technical University of Athens)
                      Error estimates for discontinuous time-stepping schemes for the velocity tracking problem
                      11:15, A302 (Seminar Room - Mathematics Building)
Abstract: (.pdf)

15 May 2014  A. Hadjidimos (U. of  Crete)
                      On the choice of parameters in MAOR type splitting methods for the linear complementarity problem
                      13:05, A302 (Seminar Room - Mathematics Building)
Abstract: (.pdf)

30 Apr 2014  E. Georgoulis (U. of  Leicester)

                      On multiscale discontinuous Galerkin methods for elliptic problems.
                      13:05, A302 (Seminar Room - Mathematics Building)
Abstract:   I will present an adaptive multiscale discontinuous Galerkin (dG) method for elliptic problems, based on the variational multiscale methods paradigm, driven by energy norm a posteriori bounds. Localized fine scale constituent problems are solved on patches of the domain and are used to obtain a modified coarse scale equation. The a posteriori error estimate is used within an adaptive algorithm to tune the critical parameters, i.e., the refinement level and the size of the different patches on which the fine scale constituent problems are solved. The fine scale computations are completely parallelizable, since no communication between different processors is required for solving the constituent fine scale problems. The convergence of the method, the performance of the adaptive strategy and the computational effort involved are investigated through a series of numerical experiments. Moreover, some a priori bounds for the proposed method will be presented.

If time permits, I will also briefly discuss two directions of related ongoing work. First, I will discuss the possibility of using polytopical meshes in the context of multiscale dG methods. Second, I will comment on the incorporation of the multiscale dG method above into a stochastic collocation framework for the case of elliptic problems with random diffusion and forcing coefficients. The stochastic collocation is based on a recent high dimensional approximation framework based on combinations of anisotropic kernels (radial basis functions).


10 Apr 2014  P. Chatzipantelidis (U. of  Crete)

                      Error estimates bounded only by data of the finite volume element method for a parabolic problem.
                      13:05, A302 (Seminar Room - Mathematics Building)
Abstract: We discretize in space a model parabolic problem by the finite volume method on polygonal domains in $R^2$. This method can be formulated as a Petrov-Galerkin method and analysed using techniques developed for the finite element method. We derive error bounds of the error in $L_2$ norm that depend only on the data and compare the results with the corresponding ones for the finite element method. In the case of the homogeneous parabolic problem with initial data only in $L_2$, special assumptions on the mesh are required for optimal convergence rate.