@inproceedings{HaefnerKoenke,
  author    = {H{\"a}fner, Stefan and K{\"o}nke, Carsten},
  title     = {MULTIGRID PRECONDITIONED CONJUGATE GRADIENT METHOD IN THE MECHANICAL ANALYSIS OF HETEROGENEOUS SOLIDS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2962},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29626},
  pages     = {29},
  abstract  = {A fast solver method called the multigrid preconditioned conjugate gradient method is proposed for the mechanical analysis of heterogeneous materials on the mesoscale. Even small samples of a heterogeneous material such as concrete show a complex geometry of different phases. These materials can be modelled by projection onto a uniform, orthogonal grid of elements. As one major problem the possible resolution of the concrete specimen is generally restricted due to (a) computation times and even more critical (b) memory demand. Iterative solvers can be based on a local element-based formulation while orthogonal grids consist of geometrical identical elements. The element-based formulation is short and transparent, and therefore efficient in implementation. A variation of the material properties in elements or integration points is possible. The multigrid method is a fast iterative solver method, where ideally the computational effort only increases linear with problem size. This is an optimal property which is almost reached in the implementation presented here. In fact no other method is known which scales better than linear. Therefore the multigrid method gains in importance the larger the problem becomes. But for heterogeneous models with very large ratios of Young's moduli the multigrid method considerably slows down by a constant factor. Such large ratios occur in certain heterogeneous solids, as well as in the damage analysis of solids. As solution to this problem the multigrid preconditioned conjugate gradient method is proposed. A benchmark highlights the multigrid preconditioned conjugate gradient method as the method of choice for very large ratio's of Young's modulus. A proposed modified multigrid cycle shows good results, in the application as stand-alone solver or as preconditioner.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@inproceedings{AhmadZabelKoenke,
  author    = {Ahmad, Sofyan and Zabel, Volkmar and K{\"o}nke, Carsten},
  title     = {WAVELET-BASED INDICATORS FOR RESPONSE SURFACE MODELS IN DAMAGE IDENTIFICATION OF STRUCTURES},
  series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
  booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  issn      = {1611-4086},
  doi       = {10.25643/bauhaus-universitaet.2758},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170306-27588},
  pages     = {14},
  abstract  = {In this paper, wavelet energy damage indicator is used in response surface methodology to identify the damage in simulated filler beam railway bridge. The approximate model is addressed to include the operational and surrounding condition in the assessment. The procedure is split into two stages, the training and detecting phase. During training phase, a so-called response surface is built from training data using polynomial regression and radial basis function approximation approaches. The response surface is used to detect the damage in structure during detection phase. The results show that the response surface model is able to detect moderate damage in one of bridge supports while the temperatures and train velocities are varied.},
  subject      = {Angewandte Mathematik},
  language  = {en}
}