Publications


    Lecture notes

  1. D. Lukas, Mathematical Modelling in Electromagnetism (in czech), VSB-Technical University of Ostrava, Czech Republic, 61 pp., September 2011. pdf-file

    2. Habilitation thesis

  2. D. Lukas, Hierarchical Finite and Boundary Elements for Maxwell's Equations and Shape Optimization (in czech), VSB-Technical University of Ostrava, Czech Republic, 47 pp., April 2010. pdf-file

    3. Doctoral thesis

  3. D. Lukas, Optimal Shape Design in Magnetostatics, VSB-Technical University of Ostrava, Czech Republic, 163 pp., September 2003. pdf-file

    4. Papers in refereed journals

  4. P. Vodstrcil, D. Lukas, Z. Dostal, M. Sadowska, D. Horak, O. Vlach, J. Bouchala, and J. Kruzik, On favorable bounds on the spectrum of discretized Steklov-Poincare operator and applications to domain decomposition methods, Computers and Mathematics with Applications, vol. 167, pp. 12-20, 2024. Preprint
  5. O. Axelsson, D. Lukas, and M. Neytcheva, An exact and approximate Schur complement method for time-harmonic optimal control problems, submitted. Preprint
  6. L. Foltyn, D. Lukas, and M. Zank, Robust PRESB preconditioning of a 3-dimensional space-time finite element method for parabolic problems, Computational Methods in Applied Mathematics, vol. 24, nr. 2, pp. 439-451, 2024. Preprint
  7. D. Lukas and T. Kot, Hierarchical real-time optimal planning of collision-free trajectories of collaborative robots, Journal of Intelligent & Robotic Systems, vol. 107, nr. 4, 57, 2023. open access
  8. D. Lukas and J. Schoeberl, Dispersion analysis of displacement-based and TDNNS mixed finite elements for thin-walled elastodynamics, Mathematics and Computers in Simulation, vol. 189, pp. 325-338, 2021. Preprint
  9. E. Strakova, D. Lukas, Z. Bobovsky, T. Kot, M. Mihola, and P. Novak, Matching point clouds with STL models by using the Principle Component Analysis and a decomposition into geometric primitives, Applied Sciences, vol. 11, nr. 5, 2268, 2021. open access
  10. L. Foltyn, D. Lukas, and I. Peterek, Domain decomposition methods coupled with parareal for the transient heat equation in 1 and 2 spatial dimensions, Applications of Mathematics, vol. 65, nr. 2, pp. 173-190, 2020. Preprint
  11. D. Lukas, G. Of, J. Zapletal, and J. Bouchala, A boundary element method for homogenization of periodic structures, Mathematical Methods in the Applied Sciences, vol. 43, nr. 3, pp. 1035-1052, 2020. Preprint
  12. O. Axelsson and D. Lukas, Preconditioning methods for eddy-current optimally controlled time-harmonic electromagnetic problems, Journal of Numerical Mathematics, vol. 27, nr. 1, pp. 1-21, 2019. Preprint
  13. D. Lukas, P. Kacor, L. Ivanek, V. Mach, and C. Scheffler, Coupling of finite and boundary elements for transient eddy current problems, Advances in Electrical and Electronic Engineering, vol. 15, nr. 2, pp. 280-285, 2017. Preprint
  14. E. Strakova, D. Lukas, and P. Vodstrcil, Finding zeros of analytic functions and local eigenvalue analysis using contour integral method in examples, Advances in Electrical and Electronic Engineering, vol. 15, nr. 2, pp. 286-295, 2017. Preprint
  15. A. Veit, M. Merta, J. Zapletal, and D. Lukas, Efficient solution of time-domain boundary integral equations arising in sound-hard scattering, International Journal for Numerical Methods in Engineering, vol. 107, nr. 5, pp. 430-449, 2016.
  16. D. Lukas, J. Bouchala, P. Vodstrcil, and L. Maly, 2-Dimensional Primal Domain Decomposition Theory in Detail, Application of Mathematics, vol. 60, nr. 3, pp. 265-283, 2015. Preprint
  17. D. Lukas, P. Kovar, T. Kovarova, and M. Merta A Parallel Fast Boundary Element Method Using Cyclic Graph Decompositions, Numerical Algorithms, vol. 70, nr. 4, pp. 807-824, 2015. Preprint
  18. D. Lukas, K. Postava, and O. Zivotsky, A Shape Optimization Method for Nonlinear Axisymmetric Magnetostatics Using a Coupling of Finite and Boundary Elements, Mathematics and Computers in Simulation, vol. 82, nr. 10, pp. 1721-1731, 2012. Preprint
  19. K. Postava, J. Hamrle, J. Hamrlova, O. Zivotsky, J. Pistora, and D. Lukas, Depth and material sensitivity in magneto-optic nanostructures, International Journal of Nanotechnology, vol. 9, nr. 8-9, pp. 784-808, 2012.
  20. D. Lukas, K. Postava, and O. Zivotsky, Optimization of Electromagnet for High-Field Polar Magneto-Optical Microscopy, Journal of Magnetism and Magnetic Materials, vol. 322, nr. 9-12, pp. 1471-1474, 2010. Preprint
  21. D. Lukas and Z. Dostal, Optimal Multigrid Preconditioned Semi-Monotonic Augmented Lagrangians Applied to the Stokes Problem, Numerical Linear Algebra with Applications, vol. 14, nr. 9, pp. 741-750, 2007. Preprint
  22. D. Lukas and P. Chalmoviansky, A Sequential Coupling of Optimal Toplogy and Multilevel Shape Design Applied to 2-Dimensional Nonlinear Magnetostatics, Computing and Visualization in Science, vol. 10, nr. 3, pp. 135-144, 2007. Preprint
  23. D. Lukas, On Solution to an Optimal Shape Design Problem in 3-Dimensional Linear Magnetostatics, Applications of Mathematics, vol. 49, nr. 5, pp. 441-464, 2004. Preprint

    24. Papers in refereed proceedings

  24. O. Axelsson, D. Lukas, and M. Neytcheva, An exact Schur complement method for time-harmonic optimal control problems, in: I. Lirkov and S. Margenov (eds.), Large-Scale Scientific Computing, Lecture Notes in Computer Science 13127, Springer-Verlag, 2022, pp. 91-100. Preprint
  25. O. Axelsson and D. Lukas, Preconditioner for time-harmonic optimal control eddy-current problems, in: I. Lirkov and S. Margenov (eds.), Large-Scale Scientific Computing, Lecture Notes in Computer Science 10665, Springer-Verlag, 2017, pp. 47-54. Preprint
  26. D. Lukas, Robust mixed finite element simulations of interactions of ultrasonic waves with cracks, in: Proceedings of 8th European Workshop on Structural Health Monitoring, 2016, pp. 1154-1161.
  27. D. Lukas, M. Sadowska, T. Kozubek, A. Markopoulos, and T. Brzobohaty A Comparison of TFETI and TBETI for Numerical Solution of Engineering Problems of Contact Mechanics, in: R. Bank, M. Holst, O. Widlund, and J. Xu (eds.), Domain Decomposition Methods in Science and Engineering XX, Lecture Notes in Computer Science and Engineering 91, Springer-Verlag, Berlin, Heidelberg, 2013, pp. 345-352. Preprint
  28. D. Lukas and Z. Dostal, Semi-Monotonic Augmented Lagrangians for Optimal Control and Parameter Identification, in: K. Kunisch, G. Of, and O. Steinbach (eds.), Proceedings of ENUMATH 2007, Numerical Mathematics and Advanced Applications, Springer-Verlag, Berlin, Heidelberg, 2008, pp. 621-628. Preprint
  29. D. Lukas and J.K. Kraus, A Fixed-Grid Finite Element Algebraic Multigrid Approach for Interface Shape Optimization Governed by 2-Dimensional Magnetostatics, in: I. Lirkov, S. Margenov, and J. Wasniewski (eds.), Proceedings of LSSC 2007, Lecture Notes in Computer Science, vol. 4818, Springer-Verlag, Berlin, Heidelberg, 2008, pp. 96-104. Preprint
  30. D. Lukas, Multigrid-Based Optimal Shape and Topology Design in Magnetostatics, in: T. Boyanov, S. Dimova, K. Georgiev, and G. Nikolov (eds.), Proceedings of NM&A 2006, Lecture Notes in Computer Science, vol. 4310, Springer-Verlag, Berlin, Heidelberg, 2007, pp. 82-91. Preprint
  31. D. Lukas, An Integration of Optimal Topology and Shape Design for Magnetostatics, in: A.M. Anile, G. Ali, and G. Mascali (eds.), Proceedings of SCEE 2004, Mathematics in Industry, vol. 9, Springer-Verlag, 2006, pp. 227-232. Preprint
  32. D. Lukas, A Multigrid Method for Coupled Optimal Topology and Shape design in Nonlinear Magnetostatic, in: A.B. de Castro, D. Gomes, P. Quintela, and P. Salgado (eds.), Proceedings of ENUMATH 2005, Numerical Mathematics and Advanced Applications, Springer-Verlag, Berlin, Heidelberg, 2006, pp. 1015-1022. Preprint
  33. D. Lukas, U. Langer, E. Lindner, R. Stainko, J. Pistora, Computational Shape and Topology Optimization with Applications to 3-Dimensional Magnetostatics, in: R. Hiptmair, R.W. Hoppe, and U. Langer (eds.), Proceedings of the Oberwolfach Workshop on Computational Electromagnetism 2004, Oberwolfach Reports, vol. 1, nr. 1, 2004, pp. 601-603. Preprint
  34. D. Lukas, D. Ciprian, J. Pistora, K. Postava, and M. Foldyna, Multilevel Solvers for 3-Dimensional Optimal Shape Design with an Application to Magneto-Optics, in: J. Pistora, K. Postava, M. Hrabovsky, and B.S. Rawat (eds.), Proceedings of the 9th International Symposium on Microwave and Optical Technology (ISMOT) 2003, Proceedings of the International Society for Optical Engineering (SPIE), vol. 5445, 2004, pp. 5445-5451. Preprint
  35. D. Lukas, Shape Optimization of Homogeneous Electromagnets, in: U. Van Rienen, M. Günther, and D. Hecht (eds.), Proceedings of SCEE 2000, Lecture Notes in Computational Science and Engineering, vol. 18, Springer-Verlag, Berlin, 2001, pp. 145-152. Preprint

    36. Others

  36. D. Lukas, Progress Report on Topology and Shape Optimization in Magnetostatics , SFB Report, 2004. Preprint
  37. D. Lukas, On the Road - between Sobolev Spaces and a Manufacture of Electromagnets, Transactions of the VSB - Technical University of Ostrava, Computer Science and Mathematics Series, vol. 2, 2003, pp. 81-90. Preprint
  38. D. Lukas, W. Mühlhuber, and M. Kuhn, An Object-Oriented Library for Shape Optimization Problems Governed by Systems of Linear Elliptic Partial Differential Equations, Transactions of the VSB - Technical University of Ostrava, Computer Science and Mathematics Series, vol. 1, 2001, pp. 115 - 128. Preprint
  39. D. Lukas, J. Vlcek, Z. Hytka, and Z. Dostal, Optimization of Dislocation of Magnets in a Magnetic Separator, Transactions of the VSB - Technical University of Ostrava, Electrical Engineering Series, nr. 1/1999, pp. 1-12. Preprint