Fast algorithms of electromagnetics, high-performance computing, quantum computing, modeling of interconnects, and inverse problems.


Electromagnetics, computing.

Research description

Theme 1:: Tensor train decomposition based fast algorithm for EM analysis:: Tensor train (TT) decomposition of a (NxN) matrix allows to compress it and reduce its general storage requirement from O(N2) down to O(NlogN) and possibly to O(logN) depending on the matrix properties. We applied TT decomposition to matrices resulting from discretization of volume integral equation of electromagnetics and demonstrated O(logN) CPU time and memory usage for solution of specialized scattering problems and O(NlogN) usage in general cases. Such demonstration opens an avenue for development of a new class of fast algorithms based on TT decomposition for 3D general scattering problems on objects of arbitrary shape.

Theme 2:: Quantum algorithm for solution of matrix equations:: Quantum computing is promising to revolutionize the field of computational physics through exponentially more efficient solution of the matrix equations resulting from discretization of the pertinent differential and integral equations. We augmented Harrow-Hassidim-Lloyd quantum matrix equation solver with Hamiltonian simulations based on walk operators. This allowed us to develop fully quantum algorithm for solution of matrix equation, which was deployed and tested both on the IBM Q 7-qubit quantum computer and Qiskit quantum simulator.

Theme 3:: Fast direct electromagnetic analysis framework for electronic packages:: Signal integrity analysis of electronic packages requires electromagnetic simulations of all its essential components such as the interconnects embedded, multilayered substrate, surface roughness, excitation ports, and others. Analysis of such structures is particularly challenging because of the very large sizes of the computational models and their multiscale features. This complexity of the models and their large size make good solutions unavailable. The iterative fast methods which can handle such sizes do not converge while the direct (non-iterative) methods cannot handle the problems of such sizes. This creates a deadlock which prevents signal integrity engineers at the companies from analyzing large fragments of the electronic packages. To resolve this deadlock we are developing of a novel fast direct computational framework based on the theory of Hierarchical matrices (H-Matrices), which allowed to both tackle the large size of the computational models and remained robust under conditions multiscale nature of the interconnect layouts. This work was recognized with Intel Outstanding Researcher Award in 2017.


Vladimir Okhmatovski was born in Moscow, Russia, in 1974. He received the M.S. degree (with distinction) in radiophysics and Ph.D. degree in antennas and microwave circuits from the Moscow Power Engineering Institute, Moscow, Russia, in 1996 and 1997, respectively.

In 1997, he joined the Radio Engineering Department, Moscow Power Engineering Institute, as an Assistant Professor. He was a Post-Doctoral Research Associate with the National Technical University of Athens from 1998 to 1999 and with the University of Illinois at Urbana-Champaign from 1999 to 2003. From 2003 to 2004, he was with the Department of Custom Integrated Circuits, Cadence Design Systems, as a Senior Member of Technical Staff, and from 2004 to 2008 as an independent consultant. In 2004, he joined the Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, Canada, where is currently a Full Professor.

Since 2017, Prof. Okhmatovski has served on the Technical Program Review Committee (TPRC) of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium (IMS), and since 2020 on IEEE MTT-S Technical Committee on Field Theory and Computational Electromagnetics. He was a TPC Co-Chair of 2021 Applied and Computational Electromagnetics Society Symposium, and General Chair of 2023 IEEE MTT-S International Conference on Numerical Electromagnetic Modeling and Optimization (NEMO).

Prof. Okhmatovski has been an active volunteer for the IEEE Antennas and Propagation Society (IEEE AP-S) as well as IEEE MTT-S serving as a Chapter Chair of the IEEE Winnipeg Waves Chapter from 2006 to 2011 and as Chair and Co-Chair of the Membership and Benefits Committee of the IEEE AP-S since 2018.

He was a recipient of the 2017 Intel Corporate Research Council Outstanding Researcher Award, 1995 scholarship of the Government of Russian Federation and the 1996 scholarship of the President of the Russian Federation. He was the recipient of the 1996 Best Young Scientist Report of the VI International Conference on Mathematical Methods in Electromagnetic Theory. He was also a co-recipient of the Best Paper Award at the 3rd Electronic Packaging Technology Conference in 2001 and Outstanding ACES Journal Paper Award in 2007.

Prof. Okhmatovski is a Registered Professional Engineer in the Province of Manitoba, Canada.

Graduate Student Opportunities

Graduating M.Sc. students interested in being at the frontlines of climate change research done through rigorous remote sensing and computational science are wanted. We are seeking a candidate for a fully-funded PhD position in Computational and Applied Electromagnetics in the Department of Electrical & Computer Engineering (ECE) with collaborations in the Centre for Earth Observation Science (CEOS). The multidisciplinary research program will focus on the development and application of numerical and analytical models for remote sensing of Arctic sea ice. The successful candidate will have a strong background in mathematics, numerical methods, programming, and electromagnetic theory, as evidenced by their academic transcripts. They will have demonstrated programming skills in a coding language, such as C, C++, Python, or equivalent. Past experience in high performance parallel computing environments would be an asset. The student will be expected to exhibit a high level of research independence while simultaneously working in a team environment. Additionally, they will be expected to generate research results, which will be suitable for publication in the peer-reviewed literature and in summary research reports.
The University of Manitoba is at the forefront of Climate Change research with internationally recognized programs and faculty members working in all aspects of Arctic Science. As part of this project, the Sea-ice Environmental Research Facility (SERF) and the new Churchill Marine Observatory (CMO) will be used provide experimental data that will be used to test, validate, and demonstrate the operational capability of the EM models.
As part of the interview process, candidates will be asked to demonstrate their capabilities by providing a solution to an applicable problem in electromagnetics, which will require generation of code and interpretation of results.
The University of Manitoba is strongly committed to equity and diversity within its community and especially welcomes applications from women, racialized persons, Indigenous peoples, persons with disabilities, persons of all sexual and gender identities, and others who may contribute to the further diversification of ideas. This posting will remain open until an appropriate candidate has been found and accepted for graduate studies by the University of Manitoba. Application materials, including letters of reference, will be handled in accordance with the protection of privacy provision of The Freedom of Information and Protection of Privacy (Manitoba). Please note that curriculum vitae may be provided to participating members of the search process.
Candidates should send an email expression of interest with a CV to Dr. Isleifson and Dr. Okhmatovski ( and The position will remain open until a suitable candidate has been accepted.

Selected Publications

1. V. Okhmatovski and S. Zheng, Theory and Computation of Electromagnetic Fields in Layered Media, IEEE Press/Wiley, (to appear in 2023).
2. J. Aronsson, F. Ling, S. Zheng, A. Menshov, and V. Okhmatovski, “New trends in analysis of electromagnetic field in multilayered media,” in New Trends in CEM, Ergul, O., (ed.), IET, 2019.

1. M. E. Keleshteri, V. Okhmatovski, I. Jeffrey, T. Isernia, and J. LoVetri, “Demonstration of quantitative microwave imaging using an ideal Veselago lens,” IEEE Open J. Antennas Propag., vol. 3, pp. 1324-1340, 2022.
2. C. Phillips and V. Okhmatovski, “A quantum computer amenable matrix equation solver with applications to computational electromagnetics,” IEEE Trans. Quantum Eng. Tech., (under review).
3. O. Goni and V. Okhmatovski, “Exact solution of new magnetic current based surface-volume-surface EFIE and analysis of its spectral properties,” IEEE J. Multiscale Multiphys. Comp. Tech., vol. 7, pp. 102-116, 2022.
4. X. Li, I. Jeffrey, V. Okhmatovski, “Closed-form evaluation of mixed-potential shielded layered media Green’s functions with spectral differential equation approximation method,” IEEE Trans. Microw. Theory Tech., vol. 70, no. 5, pp. 2553-2565, May 2022.
5. M. E. Keleshteri, V. Okhmatovski, J. LoVetri, “Analytic sinusoidal steady-state electromagnetic field expressions for the ideal Veselago lens,” IEEE Open J. Antennas Propag., vol. 2, no. 10, pp. 1057-1070, Oct. 2021.
6. M. Wang, C. Qian, E. Di Lorenzo, L. Gomez, V. Okhmatovski, A. Yucel, “SuperVoxHenry: Tucker-enhanced and FFT-accelerated inductance extraction for voxelized superconducting structures,” IEEE Trans. Applied Superconductivity, vol. 31, no. 7, pp. 1101911, Oct. 2021.
7. X. Li, I. Jeffrey, M. Al-Qedra, and V. Okhmatovski, “Error-controlled static layered medium Green’s function computation via hp-adaptive spectral differential equation approximation method,” IEEE Trans. Comp. Packag Manuf. Tech., vol. 11, no. 9, pp. 1329-1342, Sept. 2021.
8. O. Goni and V. Okhmatovski, “Analytic solution of Surface-Volume-Surface Electric Field Integral Equation on dielectric sphere and analysis of its spectral properties,” IEEE Trans. Antennas Propag., vol. 69, no. 12, pp. 8479-8493, Dec. 2021.
9. A. Menshov and V. Okhmatovski, “Superlens enhanced 2-D microwave tomography with contrast source inversion method,” IEEE Open J. Antennas Propag., vol. 2, pp. 453-463, 2021.
10. J. Massey, A. Hajiaboli, and V. Okhmatovski, “On the reciprocity relation in general multiport circuits and errata to vector-short-open-calibration de-embedding,” IEEE Trans. Microwave Theory Tech., vol. 69, no. 2, pp. 1250-1254, Feb. 2021.
11. R. Gholami and V. Okhmatovski, “Surface-Volume-Surface EFIE for fast direct solution of scattering problems on general 3D composite metal-dielectric objects,” IEEE Trans. Antennas Propag., vol. 68, no. 7, pp. 5742-5747, July 2020.
12. R. Gholami, S. Zheng, and V. Okhmatovski, “Surface-Volume-Surface EFIE for electromagnetic analysis of 3D composite dielectric objects in multilayered media,” IEEE J. Multiscale Multiphys. Comp. Tech., vol. 4, pp. 364-372, Dec. 2019.
13. Z. Cheng, L. Gomez, S. Zheng, A. Yucel, Z. Zhang, and V. Okhmatovski, “Sparsity aware pre-corrected tensor train algorithm for fast solution of 2-D scattering problems and current flow modelling on unstructured meshes,” IEEE Trans. Microwave Theory Tech., vol. 67, no. 12, pp. 4833-4847, Dec. 2019.
14. R. Gholami, A. Menshov, and V. Okhmatovski, “H-matrix accelerated solution of Surface-Volume-Surface EFIE for fast electromagnetic analysis of 3-D composite dielectric objects,” IEEE J. Multiscale Multiphys. Comp. Tech., vol. 4, pp. 152-162, May 2019.
15. Z. Cheng, S. Zheng, and V. Okhmatovski, “Tensor train accelerated solution of VIE for 2D scattering problems and magneto-static characterization of MTLs,” IEEE Trans. Microwave Theory and Tech., vol. 67, no. 6, pp. 2181-2196, 2019.