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Homogenization Methods for Problems with Multiphysics, Temporal and Spatial Coupling
There are many natural and man-made materials with heterogeneous micro- or nanostructure (fine-scale structure) which represent a great interest for industry. Therefore there is a great demand for computational methods capable to model mechanical behavior of such materials. Direct numerical simulation resolving all fine-scale details using very fine mesh often becomes very expensive. One of alternative effective group of methods is the homogenization methods allowing to model behavior of materials with heterogeneous fine-scale structure.
The essence of homogenization is to replace heterogeneous material with some equivalent effectively homogeneous material. The homogenization methods are proven to be effective in certain classes of problems while there is need to improve their performance, which includes extension of the range of applicability, simplification, usage with conventional FE software and reducing computational cost. In this dissertation methods extending the range of applicability of homogenization are developed.
Firstly, homogenization was extended of the case of full nonlinear electromechanical coupling with large deformations, which allows simulating effectively behavior of electroactive materials such as composites made of electroactive polymers. Secondly, homogenization was extended on wave problems where dispersion is significant and should be accounted for. Finally, the homogenization was extended on the case where the size of microstructure. The distinctive feature of the methods introduced in this dissertation is that they don't require higher order derivatives and can be implemented with conventional FE codes. The performance of methods is tested on various examples using Abaqus
Computational Methods in Science and Engineering : Proceedings of the Workshop SimLabs@KIT, November 29 - 30, 2010, Karlsruhe, Germany
In this proceedings volume we provide a compilation of article contributions equally covering applications from different research fields and ranging from capacity up to capability computing. Besides classical computing aspects such as parallelization, the focus of these proceedings is on multi-scale approaches and methods for tackling algorithm and data complexity. Also practical aspects regarding the usage of the HPC infrastructure and available tools and software at the SCC are presented
International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts
The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of
Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the
International Conference on Mathematical Analysis and Applications in Science and Engineering –
ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days).
Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering,
industry, and technology, to discuss the development of new mathematical models, theories, and
applications that contribute to the advancement of scientific knowledge and practice. Authors proposed
research in topics including partial and ordinary differential equations, integer and fractional order
equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization,
control, probability, computational mathematics, amongst others.
The conference was designed to maximize the involvement of all participants and will present the state-of-
the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio