@inproceedings{GuerlebeckBockFalcao2003, author = {G{\"u}rlebeck, Klaus and Bock, Sebastian and Falcao, M. Irene}, title = {Applications of Bergman kernel functions}, doi = {10.25643/bauhaus-universitaet.299}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2994}, year = {2003}, abstract = {In this paper we revisit the so-called Bergman kernel method (BKM) for solving conformal mapping problems. This method is based on the reproducing property of the Bergman kernel function. The main drawback of this well known technique is that it involves an orthonormalization process and thus is numerically unstable. This difficulty can be, in some cases, overcome by using the Maple system, which makes no use of numeric quadrature. We illustrate this implementation by presenting a numerical example. The construction of reproducing kernel functions is not restricted to real dimension 2. Results concerning the construction of Bergman kernel functions in closed form for special domains in the framework of hypercomplex function theory suggest that BKM can also be extended to mapping problems in higher dimensions, particularly 3-dimensional cases. We describe such a generalized BKM-approach and present numerical examples obtained by the use of specially developed software packages for quaternions.}, subject = {Konforme Abbildung}, language = {en} } @inproceedings{BockGuerlebeck, author = {Bock, Sebastian and G{\"u}rlebeck, Klaus}, title = {A Coupled Ritz-Galerkin Approach Using Holomorphic and Anti-holomorphic Functions}, editor = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten}, organization = {Bauhaus-Universit{\"a}t Weimar}, doi = {10.25643/bauhaus-universitaet.2928}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29281}, pages = {14}, abstract = {The contribution focuses on the development of a basic computational scheme that provides a suitable calculation environment for the coupling of analytical near-field solutions with numerical standard procedures in the far-field of the singularity. The proposed calculation scheme uses classical methods of complex function theory, which can be generalized to 3-dimensional problems by using the framework of hypercomplex analysis. The adapted approach is mainly based on the factorization of the Laplace operator EMBED Equation.3 by the Cauchy-Riemann operator EMBED Equation.3 , where exact solutions of the respective differential equation are constructed by using an orthonormal basis of holomorphic and anti-holomorphic functions.}, subject = {Architektur }, language = {en} } @article{AlYasiriMutasharGuerlebecketal., author = {Al-Yasiri, Zainab Riyadh Shaker and Mutashar, Hayder Majid and G{\"u}rlebeck, Klaus and Lahmer, Tom}, title = {Damage Sensitive Signals for the Assessment of the Conditions of Wind Turbine Rotor Blades Using Electromagnetic Waves}, series = {Infrastructures}, volume = {2022}, journal = {Infrastructures}, number = {Volume 7, Issue 8 (August 2022), article 104}, editor = {Shafiullah, GM}, publisher = {MDPI}, address = {Basel}, doi = {10.3390/infrastructures7080104}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220831-47093}, pages = {18}, abstract = {One of the most important renewable energy technologies used nowadays are wind power turbines. In this paper, we are interested in identifying the operating status of wind turbines, especially rotor blades, by means of multiphysical models. It is a state-of-the-art technology to test mechanical structures with ultrasonic-based methods. However, due to the density and the required high resolution, the testing is performed with high-frequency waves, which cannot penetrate the structure in depth. Therefore, there is a need to adopt techniques in the fields of multiphysical model-based inversion schemes or data-driven structural health monitoring. Before investing effort in the development of such approaches, further insights and approaches are necessary to make the techniques applicable to structures such as wind power plants (blades). Among the expected developments, further accelerations of the so-called "forward codes" for a more efficient implementation of the wave equation could be envisaged. Here, we employ electromagnetic waves for the early detection of cracks. Because in many practical situations, it is not possible to apply techniques from tomography (characterized by multiple sources and sensor pairs), we focus here on the question of whether the existence of cracks can be determined by using only one source for the sent waves.}, subject = {Windkraftwerk}, language = {en} } @inproceedings{AlYasiriGuerlebeck, author = {Al-Yasiri, Zainab and G{\"u}rlebeck, Klaus}, title = {ON BOUNDARY VALUE PROBLEMS FOR P-LAPLACE AND P-DIRAC EQUATIONS}, series = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, booktitle = {Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar}, editor = {G{\"u}rlebeck, Klaus and Lahmer, Tom}, organization = {Bauhaus-Universit{\"a}t Weimar}, issn = {1611-4086}, doi = {10.25643/bauhaus-universitaet.2792}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170314-27928}, pages = {8}, abstract = {The p-Laplace equation is a nonlinear generalization of the Laplace equation. This generalization is often used as a model problem for special types of nonlinearities. The p-Laplace equation can be seen as a bridge between very general nonlinear equations and the linear Laplace equation. The aim of this paper is to solve the p-Laplace equation for 2 < p < 3 and to find strong solutions. The idea is to apply a hypercomplex integral operator and spatial function theoretic methods to transform the p-Laplace equation into the p-Dirac equation. This equation will be solved iteratively by using a fixed point theorem.}, subject = {Angewandte Informatik}, language = {en} }