Abstract: In order to identify the best technique to solve a class of fully three-dimensional geometrically multiscale model problems in thermoelasticity, the combination of several finite element approaches and solution techniques, is investigated. The criteria for optimality were robustness, accuracy and execution time. It will be shown that the primal-mixed finite element approach, where displacement and stress variables are simultaneously solved from large scale indefinite poorly scaled system of equations using sparse solver with aid of the matrix scaling routine during the factorization process, enables the reliable solution even if hexahedral finite elements in a mesh differ in size up to six orders of magnitude. A number of pathological benchmark model problems, with material interfaces or coating, with geometrical scale resolutions up to 8 orders of magnitude and aspect ratio of finite elements up to 7 orders of magnitude, are examined to test the robustness and execution times, on a standard PC computing platform. The comparison with simplified theories, as beam and plate, is evaluated in detail also. The new definition of multiscale reliability is given.

Brief Biography of the Speaker:
Dubravka Mijuca is a professor in the Department of Structural Engineering at the Faculty of Civil construction Management, University UNION, Belgrade. She received her MSc and PhD in Computational Mechanics at Department of Mechanics at Faculty of Mathematics University of Belgrade, Serbia, where she spent here academic career, before coming in present academic institution in 2007 to serve as a dean. Her research interests include the novel and reliable fully three-dimensional multiscale multifield mixed finite element procedures in thermomechanics for the isotropic, anisotropic and composite bodies with material interfaces, which can be bridged with simulations on micro and nano geometrical levels, without spurious oscillations of the results. The main goal in her research is reliable mechanical and thermal stress calculation on material interfaces, such as, interface between plies in composite, and over the interface of the coating, as well nonphysical interfaces, such as interface between boundary of the macro and nano simulation levels. In addition, her research interest, beside structural efficiency is also in simulation of the energy efficiency of buildings, influence of thermal characteristic of building envelope throughout the geometrical scales on integral energy efficiency of buildings, and interoperability of these two simulations. She is a vice president of Serbian Society of Computational Mechanics, member of general council of Serbian Society of Mechanics, member of NAFEMS and IUTAM. Professor Mijuca's publications have appeared in the journals Computational Mechanics, Computer Assisted Mechanics and Engineering Sciences, Facta Mechanics and Thermal Science. She has published a monograph entitled On Primal-Mixed formulation in Elasticity and Thermoelasticity.