Dr. rer. nat. habil. Dmitrii Legatiuk

Picture of 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:

  1. S. Kraußhar, A. Legatiuk, D. Legatiuk, Discrete octonionic analysis: a unified approach to the split-octonionic and classical settings, under review.
  2. P. Cerejeiras, U. Kähler, D. Legatiuk, Application of the script geometry to the finite element exterior calculus, under review, 2024.
  3. S. Kraußhar, A. Legatiuk, D. Legatiuk, Hardy spaces of monogenic and discrete monogenic functions revisited on octonionic half-space, Montes Taurus Journal of Pure and Applied Mathematics, accepted for publication, 2024.
  4. S. Kraußhar, A. Legatiuk, D. Legatiuk, Application of the Weyl calculus perspective on discrete octonionic analysis in bounded domains, under review, 2024.
  5. D. Legatiuk, D. Luckey, Meta-metamodelling in Automation Construction by Help of Abstract Mathematics, under review, 2024.
  6. R.S. Kraußhar, A. Legatiuk, D. Legatiuk, The discrete octonionic Stokes’ formula revisited, Research Perspectives: Ghent Analysis and PDE Center, Springer, accepted for publication, 2024.
  7. D. Legatiuk, Mathematical modelling by help of category theory, Habilitation thesis, Bauhaus-Universität Weimar, 2024. DOI: 10.25643/dbt.62110
  8. R.S. Kraußhar, D. Legatiuk, Cauchy formulae and Hardy spaces in discrete octonionic analysis, Complex Analysis and Operator Theory, 18:23, 2024.
  9. R.S. Kraußhar, A. Legatiuk, D. Legatiuk, Towards discrete octonionic analysis, Springer Conference Proceedings, 2023.
  10. R.S. Kraußhar, D. Legatiuk, Weyl calculus perspective on the discrete Stokes' formula in octonions, Lecture Notes in Computer Sciences, 14498, 2023.
  11. 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
  12. S. Bernstein, D. Legatiuk, Brownian motion, martingales and Itô formula in Clifford analysis, Advances in Applied Clifford Algebras, 32, Article number: 27, 2022.
  13. K. Gürlebeck, D. Legatiuk, K. Webber, Operator calculus approach to comparison of elasticity models for modelling of masonry structures, Mathematics, 10(10), 1670, 2022.
  14. R.S. Kraußhar, D. Legatiuk, B. Schneider, T. Truong, A Dynamic Derivative for Fuzzy-Valued Functions, AIP Conference Proceedings, 2022.
  15. 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.
  16. 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.
  17. D. Legatiuk, Mathematical modelling by help of category theory: models and relations between them, Mathematics, 9(16), 1946, 2021.
  18. 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.
  19. 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.
  20. 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.
  21. M. Theiler, S. Ibanez, D. Legatiuk, K. Smarsly, Metaization concepts for monitoring-related information, Advanced Engineering Informatics, 46, 101158, 2020.
  22. 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.
  23. 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.
  24. 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.
  25. P. Cerejeiras, U. Kähler, D. Legatiuk, Finite element exterior calculus with script geometry, AIP Conference Proceedings, 2116, 2019.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. 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.
  31. 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.
  32. L. Abrahamczyk, Z. Jaouadi, U. Kähler, D. Legatiuk, Methoden zur Identifikation von Zugvorbeifahrten aus kontinuierlichen Messdaten, Bautechnik, 95(7), pp. 485-493, 2018.
  33. 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.
  34. Yu. Grigor'ev, K. Gürlebeck, D. Legatiuk, Quaternionic formulation of a Cauchy problem for the Lamé equation, AIP Conference Proceedings, 1978 (1), 280007, 2018.
  35. 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.
  36. 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.
  37. 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.
  38. 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.
  39. K. Gürlebeck, D. Legatiuk, Three-dimensional interpolation with monogenic polynomials, Complex Variables and Elliptic Equations, Vol. 62, pp. 1364-1373, 2017.
  40. 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.
  41. 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).
  42. 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.
  43. 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.
  44. K. Gürlebeck, D. Legatiuk, On some properties of pseudo-complex polynomials, Modern Trends in Hypercomplex Analysis, Birkhäuser, pp. 217-226, 2016.
  45. 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.
  46. 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.
  47. 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.
  48. 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.
  49. K. Gürlebeck, D. Legatiuk, On the continuous coupling of finite elements with holomorphic basis functions, Hypercomplex Analysis: New perspectives and applications, Birkhäuser, Basel, 2014.
  50. 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.
  51. 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.
  52. 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.
  53. S. Bock, K. Gürlebeck, D. Legatiuk, Convergence of the finite element method with holomorphic functions, AIP Conference proceedings, 1558, 513, 2013.
  54. 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.
  55. 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.
  56. S. Bock, K. Gürlebeck, D. Legatiuk, On a special finite element based on holomorphic functions, AIP Conference proceedings, 1479, 308, 2012.
  57. 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].