Dr. rer. nat. habil. Dmitrii Legatiuk
Lehrgebäude 2 / Raum 109a
dmitrii.legatiuk(at)uni-erfurt.de
Current research interests:
- Complex analysis and its applications
- Clifford analysis
- Numerical analysis
- Applied category theory
- Functional programming and type theory
- Mathematical modelling and its abstraction
- Analysis of partial differential equations
- Stochastic analysis
- Discrete function and potential theories
- Discrete Clifford analysis
- Octonions
A complete information about research activities of the Chair of Mathematics can be found on the web-page.
International peer reviewed publications:
- S. Kraußhar, A. Legatiuk, D. Legatiuk, Application of the Weyl calculus perspective on discrete octonionic analysis in bounded domains, under review, 2024.
- R.S. Kraußhar, A. Legatiuk, D. Legatiuk, The discrete octonionic Stokes’ formula revisited, Research Perspectives: Ghent Analysis and PDE Center, Springer, under review, 2024.
- D. Legatiuk, Mathematical modelling by help of category theory, Habilitation thesis, Bauhaus-Universität Weimar, 2024. DOI: 10.25643/dbt.62110
- R.S. Kraußhar, D. Legatiuk, Cauchy formulae and Hardy spaces in discrete octonionic analysis, Complex Analysis and Operator Theory, 18:23, 2024.
- R.S. Kraußhar, A. Legatiuk, D. Legatiuk, Towards discrete octonionic analysis, Springer Conference Proceedings, accepted for publications, 2023.
- R.S. Kraußhar, D. Legatiuk, Weyl calculus perspective on the discrete Stokes' formula in octonions, Lecture Notes in Computer Sciences, 14498, 2023.
- D. Legatiuk, D. Luckey, Formalising autonomous construction sites by help of abstract mathematics, Eng, 4(1), 799-815, 2023. Online available on: https://www.mdpi.com/2673-4117/4/1/48
- S. Bernstein, D. Legatiuk, Brownian motion, martingales and Itô formula in Clifford analysis, Advances in Applied Clifford Algebras, 32, Article number: 27, 2022.
- K. Gürlebeck, D. Legatiuk, K. Webber, Operator calculus approach to comparison of elasticity models for modelling of masonry structures, Mathematics, 10(10), 1670, 2022.
- R.S. Kraußhar, D. Legatiuk, B. Schneider, T. Truong, A Dynamic Derivative for Fuzzy-Valued Functions, AIP Conference Proceedings, 2022.
- P. Cerejeiras, U. Kähler, A. Legatiuk, D. Legatiuk, Discrete Hardy spaces for bounded domains in $\mathbb{R}^{n}$, Complex Analysis and Operator Theory, 15(4), 2021.
- H. Fritz, J. Peralta, D. Legatiuk, M. Steiner, K. Dragos, K. Smarsly, Fault diagnosis in structural health monitoring systems using signal processing and machine learning techniques, Structural health monitoring based on data science techniques, Springer, 2021.
- D. Legatiuk, Mathematical modelling by help of category theory: models and relations between them, Mathematics, 9(16), 1946, 2021.
- D. Legatiuk, D. Weisz-Patrault, Coupling of complex function theory and finite element method for crack propagation through energetic formulation: conformal mapping approach and reduction to a Riemann-Hilbert problem, Computational Methods and Function Theory, 2021. DOI: 10.1007/s40315-021-00403-7.
- D. Luckey, H. Fritz, D. Legatiuk, J. Peralta, C. Walther, K. Smarsly, Explainable artificial intelligence to advance structural health monitoring, Structural health monitoring based on data science techniques, Springer, 2021.
- D. Legatiuk, K. Lossev, K. Smarsly, A. Volkov, Abstract life-cycle modeling of cyber-physical systems in civil engineering, Proceedings of European Conference on Product and Process Modelling (ECPPM), Moscow, Russia, 2020.
- M. Theiler, S. Ibanez, D. Legatiuk, K. Smarsly, Metaization concepts for monitoring-related information, Advanced Engineering Informatics, 46, 101158, 2020.
- D. Luckey, H. Fritz, D. Legatiuk, K. Dragos, K. Smarsly, Artificial intelligence techniques for smart city applications, Lecture Notes in Civil Engineering, 98, pp. 3-15, 2020.
- S. Bock, D. Legatiuk, Constructive orthonormalisation of monogenic polynomials on a finite cylinder, Topics in Clifford Analysis, Springer series "Trends in Mathematics", pp. 235-250, 2019.
- P. Cerejeiras, U. Kähler, A. Legatiuk, D. Legatiuk, Boundary values of discrete monogenic functions over bounded domains in $\mathbb{R}^{3}$, Operator Theory: Advances and Applications, Vol. 275, pp. 149-165, 2019.
- P. Cerejeiras, U. Kähler, D. Legatiuk, Finite element exterior calculus with script geometry, AIP Conference Proceedings, 2116, 2019.
- Yu. Grigor'ev, K. Gürlebeck, D. Legatiuk, On quaternionic functions for the solution of an ill-posed Cauchy problem for a viscous fluid, AIP Conference Proceedings, 2116:1, 2019.
- K. Gürlebeck, D. Legatiuk, Quaternionic operator calculus for boundary value problems of micropolar elasticity, Topics in Clifford Analysis, Springer series "Trends in Mathematics", pp. 221-234, 2019.
- K. Gürlebeck, D. Legatiuk, H. Nilsson, K. Smarsly, Conceptual modelling: towards detecting modelling errors in engineering applications, Mathematical Methods in the Applied Sciences, 43(3), pp. 1243-1252, 2019.
- I. Kavrakov, D. Legatiuk, K. Gürlebeck, G. Morgenthal, A categorical perspective towards aerodynamic models for aeroelastic analyses of bridges, Royal Society Open Science, 6: 181848, 2019.
- K. Smarsly, T. Fitz, D. Legatiuk, Metamodeling wireless communication in cyber-physical systems, The 26th International Workshop on Intelligent Computing in Engineering (EG-ICE)At: Leuven, Belgium, 2019.
- M. Steiner, D. Legatiuk, K. Smarsly, A support vector regression-based approach towards decentralized fault diagnosis in wireless structural health monitoring systems, Proceedings of the 12th International Workshop on Structural Health Monitoring (IWSHM), 2019.
- L. Abrahamczyk, Z. Jaouadi, U. Kähler, D. Legatiuk, Methoden zur Identifikation von Zugvorbeifahrten aus kontinuierlichen Messdaten, Bautechnik, 95(7), pp. 485-493, 2018.
- P. Cerejeiras, U. Kähler, D. Legatiuk, Interpolation of monogenic functions by using reproducing kernel Hilbert spaces, Mathematical Methods in the Applied Sciences, 41(17), pp. 8100-8114, 2018.
- Yu. Grigor'ev, K. Gürlebeck, D. Legatiuk, Quaternionic formulation of a Cauchy problem for the Lamé equation, AIP Conference Proceedings, 1978 (1), 280007, 2018.
- D. Legatiuk, K. Smarsly, An abstract approach towards modeling intelligent structural systems, Proceedings of the European Workshop on Structural Health Monitoring Series (EWSHM). Manchester, UK, 2018.
- Yu. Grigor'ev, K. Gürlebeck, D. Legatiuk, Interpolation problem for the solutions of linear elasticity equations based on monogenic functions, AIP Conference proceedings, 1907, 030054, 2017.
- K. Gürlebeck, D. Hofmann, D. Legatiuk, Categorical approach to modelling and to coupling of models, Mathematical Methods in the Applied Sciences, 40(3), 523-534, 2017.
- K. Gürlebeck, U. Kähler, D. Legatiuk, Error estimates for the coupling of analytical and numerical solutions, Complex Analysis and Operator Theory, 11(5), 1221-1240, 2017.
- K. Gürlebeck, D. Legatiuk, Three-dimensional interpolation with monogenic polynomials, Complex Variables and Elliptic Equations, Vol. 62, pp. 1364-1373, 2017.
- D. Legatiuk, K. Dragos, K. Smarsly, Modeling and evaluation of cyber-physical systems in civil engineering, Proceedings in Applied Mathematics and Mechanics, 17 (1), pp. 807-808, 2017.
- D. Legatiuk, H. Nilsson, Abstract modelling: towards a typed declarative language for the conceptual modelling phase, Proceedings of 8th International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools, Munich, Germany, December 2017 (EOOLT 2017).
- D. Legatiuk, M. Theiler, K. Dragos, K. Smarsly, A categorical approach towards metamodeling cyber-physical systems, Proceedings of the 11th International Workshop on Structural Health Monitoring (IWSHM). Stanford, CA, USA, 2017.
- L. Göbel, F. Mucha, Z. Jaouadi, I. Kavrakov, D. Legatiuk, L. Abrahamczyk, M. Kraus, K. Smarsly, Monitoring the structural response of reinforced concrete poles along high-speed railway tracks, Proceedings of the International RILEM Conference Materials, Systems and Structures in Civil Engineering, 2016.
- K. Gürlebeck, D. Legatiuk, On some properties of pseudo-complex polynomials, Modern Trends in Hypercomplex Analysis, Birkhäuser, pp. 217-226, 2016.
- F. Scheiber, H.B. Motra, D. Legatiuk, F. Werner, Uncertainty-based evaluation and coupling of mathematical and physical models, Probabilistic Engineering Mechanics, 45, pp. 52-60, 2016.
- S. Bock, K. Gürlebeck, D. Legatiuk, H. M. Nguyen, $\psi$-Hyperholomorphic Functions and a Kolosov-Muskhelishvili Formula, Mathematical Methods in the Applied Sciences, 38(18), 5114-5123, 2015.
- K. Gürlebeck, U. Kähler, D. Legatiuk, Interpolation problem arising in a coupling of finite element method with holomorphic basis functions, AIP Conference proceedings, 1648, 2015.
- D. Legatiuk, Evaluation of the coupling between an analytical and a numerical solution for boundary value problems with singularities. PhD Thesis, Weimar. ISBN: 978-3-95773-193-7, 2015.
- K. Gürlebeck, D. Legatiuk, On the continuous coupling of finite elements with holomorphic basis functions, Hypercomplex Analysis: New perspectives and applications, Birkhäuser, Basel, 2014.
- K. Gürlebeck, H.M. Nguyen, D. Legatiuk, An additive decomposition of harmonic functions in $\mathbb{R}^{3}$, Lecture Notes in Computer Science, 8579, 189-204, 2014.
- D. Legatiuk, H.M. Nguyen, Improved convergence results for the finite element method with holomorphic functions, Advances in Applied Clifford Algebra, 24(4), pp. 1077-1092, 2014.
- F. Scheiber, H.B. Motra, D. Legatiuk, F. Werner, Model coupling in structural engineering application, Proceedings of the International Probabilistic Workshop (IPW 2014), Weimar, 2014.
- S. Bock, K. Gürlebeck, D. Legatiuk, Convergence of the finite element method with holomorphic functions, AIP Conference proceedings, 1558, 513, 2013.
- D. Legatiuk, K. Gürlebeck, G. Morgenthal, Modelling of concrete hinges through coupling of analytical and finite element solutions, Bautechnik Sonderdruck, ISSN 0932-8351, A 1556, 2013.
- S. Bock, K. Gürlebeck, D. Legatiuk, On the continuous coupling between analytical and finite element solutions, Le Hung Son & Wolfgang Tutschke eds. Interactions between real and complex analysis, 3-19. Science and Technics Publishing House, Hanoi, 2012.
- S. Bock, K. Gürlebeck, D. Legatiuk, On a special finite element based on holomorphic functions, AIP Conference proceedings, 1479, 308, 2012.
- S. Bock, K. Gürlebeck, D. Legatiuk, The problem of coupling between analytical solution and finite element method, in: 19th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering IKM 2012, 04.-06. Juli 2012, Weimar [eds. K. Gürlebeck, T. Lahmer, F. Werner].