Multilevel Preconditioning of Discontinuous-Galerkin Spectral Element Methods, Part I: Geometrically Conforming Meshes

This paper is concerned with the design, analysis and implementation of preconditioning concepts for spectral Discontinuous Galerkin discretizations of elliptic boundary value problems. While presently known techniques realize a growth of the condition numbers that is logarithmic in the polynomial degrees when all degrees are equal and quadratic otherwise, our main objective is to realize full robustness with respect to arbitrarily large locally varying polynomial degrees degrees, i.e., under mild grading constraints condition numbers stay uniformly bounded with respect to the mesh size and variable degrees. The conceptual foundation of the envisaged preconditioners is the auxiliary space method. The main conceptual ingredients that will be shown in this framework to yield "optimal" preconditioners in the above sense are Legendre-Gauss-Lobatto grids in connection with certain associated anisotropic nested dyadic grids as well as specially adapted wavelet preconditioners for the resulting low order auxiliary problems. Moreover, the preconditioners have a modular form that facilitates somewhat simplified partial realizations. One of the components can, for instance, be conveniently combined with domain decomposition, at the expense though of a logarithmic growth of condition numbers. Our analysis is complemented by quantitative experimental studies of the main components.Comment: 41 pages, 11 figures; Major revision: rearrangement of the contents for better readability, part on wavelet preconditioner adde

Animal Models to Translate Phage Therapy to Human Medicine

Phagotherapy, the use of bacteriophages to fight bacterial infections as an alternative to antibiotic treatments, has become of increasing interest in the last years. This is mainly due to the diffusion of multi-drug resistant (MDR) bacterial infections that constitute a serious issue for public health. Phage therapy is gaining favor due to its success in agriculture and veterinary treatments and its extensive utilization for human therapeutic protocols in the Eastern world. In the last decades, some clinical trials and compassionate treatments have also been performed in the Western world, indicating that phage therapy is getting closer to its introduction in standard therapy protocols. However, several questions concerning the use of phages in human therapeutic treatments are still present and need to be addressed. In this review, we illustrate the state of art of phage therapy and examine the role of animal models to translate these treatments to humans

Cooperative Learning Approach to Delivering Professional Modules to Bachelor and Master Students: TPU Experience

Modern tendencies in engineering education set certain requirements on the competences to be obtained. To enable a future engineer to work at a highly competitive level and become an internationally recognized specialist, they must possess advanced English speaking and writing skills. At present most universities introduce educational programs that attract bright domestic and international students to ensure that they are in demand at the global market. The Strategic Program on Competitiveness Enhancement of National Research Tomsk Polytechnic University proposes that modules of professional training should be developed and delivered in English as a language of instruction so that the quality of teaching could be raised. To develop their own approaches to teaching, improve their language proficiency and develop courses and their elements in English, TPU teachers are to meet these challenging requirements and design course documentation and teaching aids, and engage modern teaching approaches in order to ensure high quality work with student groups which are often mixed in their abilities in both professional subjects and language proficiency levels. This paper addresses the course "Professional Training in English" which was developed upon completion of the joint program of TPU and the University of Southampton "Delivering through the Medium of English" and has successfully been delivered to bachelor students with the major "Oil and Gas Engineering" using the cooperative learning approach. The cooperative learning approach has proved to be one of the most successful in terms of teaching professional English to groups of students with mixed abilities