P. Absil, R. Mahony, and R. Sepulchre, Optimization algorithms on matrix manifolds, 2009.

D. Amsallem, Interpolation on manifolds of CFD-based fluid and finite element-based structural reduced-order models for on-line aeroelastic predictions, 2010.

D. Amsallem and C. Farhat, Interpolation method for adapting reduced-order models and application to aeroelasticity, AIAA journal, vol.46, issue.7, p.1803, 2008.

D. Amsallem and C. Farhat, Stabilization of projection-based reduced-order models, International Journal for Numerical Methods in Engineering, vol.91, issue.4, pp.358-377, 2012.

A. C. Antoulas, Approximation of large-scale dynamical systems, vol.6, 2005.

M. Ao-leite, B. Delinchant, J. Guichon, and J. Vasconcelos, Simplexbased adaptive parametric model order reduction for applications in optimization, International Journal of Numerical Modelling, 2016.

W. E. Arnoldi, The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quarterly of applied mathematics, vol.9, issue.1, pp.17-29, 1951.
URL : https://hal.archives-ouvertes.fr/hal-01712943

R. B. Ayed, J. Gong, S. Brisset, F. Gillon, and P. Brochet, Three-level output space mapping strategy for electromagnetic design optimization, IEEE Transactions on Magnetics, vol.48, issue.2, pp.671-674, 2012.

M. H. Bakr, J. W. Bandler, K. Madsen, and J. Søndergaard, Review of the space mapping approach to engineering optimization and modeling, Optimization and Engineering, vol.1, issue.3, pp.241-276, 2000.

C. A. Balanis, Advanced engineering electromagnetics, BIBLIOGRAPHY, vol.167, 1999.

K. Ball, Eigenvalues of euclidean distance matrices, Journal of Approximation Theory, vol.68, issue.1, pp.74-82, 1992.

J. Bandler, R. Biernacki, S. Chen, P. Grobelny, H. et al., Exploitation of coarse grid for electromagnetic optimization, Microwave Symposium Digest, pp.381-384, 1994.

J. W. Bandler, R. M. Biernacki, S. H. Chen, P. A. Grobelny, and R. H. Hemmers, Space mapping technique for electromagnetic optimization, IEEE Transactions on Microwave Theory and Techniques, vol.42, issue.12, pp.2536-2544, 1994.

R. H. Bartels and G. Stewart, Solution of the matrix equation ax+ xb= c, vol.4, 1972.

, Communications of the ACM, vol.15, issue.9, pp.820-826

V. Baudoui, Optimisation robuste multiobjectifs par modèles de substitution, 2012.

P. Benner, S. Gugercin, and K. Willcox, A survey of projection-based model reduction methods for parametric dynamical systems, SIAM review, vol.57, issue.4, pp.483-531, 2015.

G. Berkooz, P. Holmes, and J. L. Lumley, The proper orthogonal decomposition in the analysis of turbulent flows, Annual review of fluid mechanics, vol.25, issue.1, pp.539-575, 1993.

B. N. Bond and L. Daniel, Guaranteed stable projection-based model reduction for indefinite and unstable linear systems, Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design, pp.728-735, 2008.

B. N. Bond and L. Daniel, Guaranteed stable projection-based model reduction for indefinite and unstable linear systems, Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design, pp.728-735, 2008.

A. Bondeson, T. Rylander, and P. Ingelström, Computational electromagnetics, vol.51, 2005.

A. Bouhamidi, M. Heyouni, J. , and K. , Block arnoldi-based methods for large scale discrete-time algebraic riccati equations, Journal of Computational and Applied Mathematics, vol.236, issue.6, pp.1531-1542, 2011.

S. Boyd and L. Vandenberghe, Convex optimization, 2004.

M. D. Buhmann, Radial basis functions: theory and implementations, BIBLIOGRAPHY, vol.12, 2003.

M. J. Burfeindt, T. J. Colgan, R. O. Mays, J. D. Shea, N. Behdad et al., Mri-derived 3-d-printed breast phantom for microwave breast imaging validation. IEEE antennas and wireless propagation letters, vol.11, pp.1610-1613, 2012.

A. Chatterjee, An introduction to the proper orthogonal decomposition, Current science, vol.78, issue.7, pp.808-817, 2000.

C. Chen, Linear system theory and design, 1995.

E. Chiprout and M. S. Nakhla, Asymptotic waveform evaluation, Asymptotic Waveform Evaluation, pp.15-39, 1994.

I. Clark and W. Harper, Practical geostatistics: Ecosse north american llc, 2000.

J. Coggon, Electromagnetic and electrical modeling by the finite element method. Geophysics, vol.36, pp.132-155, 1971.

T. J. Colgan, S. C. Hagness, and B. D. Van-veen, A 3-d level set method for microwave breast imaging, IEEE Transactions on Biomedical Engineering, vol.62, issue.10, pp.2526-2534, 2015.

A. R. Conn, K. Scheinberg, V. , and L. N. , Introduction to derivative-free optimization, 2009.

J. Coulomb and J. Sabonnadière, CAO en électrotechnique, 1985.

R. Courant, Variational methods for the solution of problems of equilibrium and vibrations, Bull. Amer. Math. Soc, vol.49, issue.1, pp.1-23, 1943.

J. Cullum, A. Ruehli, and T. Zhang, A method for reduced-order modeling and simulation of large interconnect circuits and its application to peec models with retardation, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol.47, issue.4, pp.261-273, 2000.

I. G. Currie, Fundamental mechanics of fluids, 2012.

B. Delinchant, D. Lahaye, F. Wurtz, and J. Coulomb, Manifold mapping optimization with or without true gradients, Mathematics and Computers in Simulation, vol.90, pp.256-265, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00600301

N. Demerdash and T. Nehl, An evaluation of the methods of finite elements and finite differences in the solution of nonlinear electromagnetic fields in electrical machines, IEEE Transactions on Power Apparatus and Systems, issue.1, pp.74-87, 1979.

J. Ding and A. Zhou, Eigenvalues of rank-one updated matrices with some applications, Applied Mathematics Letters, vol.20, issue.12, pp.1223-1226, 2007.

A. Z. Elsherbeni and V. Demir, The finite-difference time-domain method for electromagnetics with MATLAB simulations, The Institution of Engineering and Technology, 2016.

D. F. Enns, Model reduction with balanced realizations: An error bound and a frequency weighted generalization, The 23rd IEEE Conference on, pp.127-132, 1984.
DOI : 10.1109/cdc.1984.272286

F. W. Fairman, Linear control theory: the state space approach, 1998.

T. Fennell, P. Deen, A. Wildes, K. Schmalzl, D. Prabhakaran et al., Magnetic coulomb phase in the spin ice ho2ti2o7, Science, vol.326, issue.5951, pp.415-417, 2009.
DOI : 10.1126/science.1177582

R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, vol.1, 2013.

R. P. Feynman, R. B. Leighton, and M. L. Sands, The Feynman Lectures on Physics: electromagnetism and matter, vol.2, 1964.

R. Fletcher, Practical methods of optimization, 2013.
DOI : 10.1002/9781118723203

D. G. Franco and M. T. Steiner, New strategies for initialization and training of radial basis function neural networks, IEEE Latin America Transactions, vol.15, issue.6, pp.1182-1188, 2017.

F. Freschi, G. Gruosso, R. , and M. , Unstructured peec formulation by dual discretization, IEEE microwave and wireless components letters, vol.16, issue.10, pp.531-533, 2006.
DOI : 10.1109/lmwc.2006.882407

R. W. Freund, Krylov-subspace methods for reduced-order modeling in circuit simulation, Journal of Computational and Applied Mathematics, vol.123, issue.1, pp.395-421, 2000.
DOI : 10.1016/s0377-0427(00)00396-4

URL : https://hal.archives-ouvertes.fr/hal-01615923

R. W. Freund, The sprim algorithm for structure-preserving order reduction of general rcl circuits, Model reduction for circuit simulation, pp.25-52, 2011.

R. W. Freund, The sprim algorithm for structure-preserving order reduction of general rcl circuits, Model reduction for circuit simulation, p.170, 2011.

B. Friedland, Control system design: an introduction to state-space methods, Courier Corporation, 2012.

P. Garcia and J. Webb, Optimization of planar devices by the finite element method, IEEE transactions on microwave theory and techniques, vol.38, pp.48-53, 1990.

S. A. Gershgorin, Uber die abgrenzung der eigenwerte einer matrix, Bulletin de l'Academie des Sciences de l'URSS, issue.6, pp.749-754, 1931.

D. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. Artificial Intelligence, 1989.

G. H. Golub and C. F. Van-loan, Matrix computations, vol.3, 2012.

B. Gustavsen, Improving the pole relocating properties of vector fitting, IEEE Transactions on Power Delivery, vol.21, issue.3, pp.1587-1592, 2006.
DOI : 10.1109/pes.2006.1708940

B. Gustavsen and A. Semlyen, Rational approximation of frequency domain responses by vector fitting, IEEE Transactions on power delivery, vol.14, issue.3, pp.1052-1061, 1999.
DOI : 10.1109/61.772353

B. Gustavsen and A. Semlyen, Enforcing passivity for admittance matrices approximated by rational functions, IEEE Transactions on Power Systems, vol.16, issue.1, pp.97-104, 2001.
DOI : 10.1109/59.910786

URL : https://tspace.library.utoronto.ca/bitstream/1807/9973/1/Semlyen_9842_2918.pdf

W. H. Hayt and J. A. Buck, Engineering electromagnetics, vol.6, 1981.

T. Henneron and S. Clenet, Model order reduction of non-linear magnetostatic problems based on pod and dei methods, IEEE Transactions on Magnetics, vol.50, issue.2, pp.33-36, 2014.

J. P. Hespanha, Linear systems theory, 2009.

E. H. Isaaks, Applied geostatistics. Number 551.72 I86, 1989.

M. Jamil and X. Yang, A literature survey of benchmark functions for global optimisation problems, International Journal of Mathematical Modelling and Numerical Optimisation, vol.4, issue.2, pp.150-194, 2013.

J. Jin, The finite element method in electromagnetics, 2014.

J. Jin, The finite element method in electromagnetics, 2015.

I. Jolliffe, Principal component analysis, Wiley Online Library. BIBLIOGRAPHY, vol.171, 2002.

D. R. Jones, M. Schonlau, W. , and W. J. , Efficient global optimization of expensive black-box functions, Journal of Global optimization, vol.13, issue.4, pp.455-492, 1998.

J. Knowles, Parego: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems, IEEE Transactions on Evolutionary Computation, vol.10, issue.1, pp.50-66, 2006.

Y. Kuwabara, K. Wada, J. M. Guichon, J. L. Schanen, R. et al., Implementation and performance of a current sensor for a laminated bus bar, IEEE Energy Conversion Congress and Exposition (ECCE), pp.1-7, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01372808

C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, 1950.
URL : https://hal.archives-ouvertes.fr/hal-01712947

A. Laub, Efficient multivariable frequency response computations, 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes, number 19, pp.39-41, 1980.

A. Laub, M. Heath, C. Paige, W. , and R. , Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms, IEEE Transactions on Automatic Control, vol.32, issue.2, pp.115-122, 1987.

J. M. Lee, Smooth manifolds, Introduction to Smooth Manifolds, pp.1-29, 2003.

M. Li, C. Li, C. Ong, and W. Tang, A novel multilevel matrix compression method for analysis of electromagnetic scattering from pec targets, IEEE Transactions on Antennas and Propagation, vol.60, issue.3, pp.1390-1399, 2012.

S. N. Lophaven, H. B. Nielsen, and J. Søndergaard, Dace-a matlab kriging toolbox, version 2.0, 2002.

D. G. Luenberger, Introduction to dynamic systems; theory, models, and applications, 1979.

J. C. Maxwell, A treatise on electricity and magnetism, vol.1, 1881.

D. C. Montgomery, Design and analysis of experiments, 2017.

B. Moore, Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE transactions on automatic control, vol.26, issue.1, pp.17-32, 1981.

T. S. Nguyen, Réduction de modèles issus de la méthode PEEC pour la modélisation électromagnétique des interconnexions électriques, 2012.

J. Nitsch, F. Gronwald, and G. Wollenberg, Radiating nonuniform transmissionline systems and the partial element equivalent circuit method, 2009.

A. Odabasioglu, M. Celik, and L. T. Pileggi, Prima: passive reduced-order interconnect macromodeling algorithm, Proceedings of the, pp.58-65, 1997.

G. W. Oehlert, A first course in design and analysis of experiments, 2010.

A. Oppenheim, A. Willsky, and S. Nawab, Signals and Systems. Prentice-Hall signal processing series, 1997.

C. A. Paixão and F. C. Coelho, Matrix compression methods, 2015.

H. Panzer, J. Hubele, R. Eid, and B. Lohmann, Generating a parametric finite element model of a 3d cantilever timoshenko beam using matlab, Tech. reports on aut. control, Inst. Aut. Control, 2009.

H. Panzer, J. Mohring, R. Eid, and B. Lohmann, Parametric model order reduction by matrix interpolation. at-Automatisierungstechnik Methoden und Anwendungen der Steuerungs-, Regelungs-und Informationstechnik, vol.58, pp.475-484, 2010.

B. Peherstorfer and K. Willcox, Data-driven operator inference for nonintrusive projection-based model reduction, Computer Methods in Applied Mechanics and Engineering, vol.306, pp.196-215, 2016.

A. C. Polycarpou, Introduction to the finite element method in electromagnetics, Synthesis Lectures on Computational Electromagnetics, vol.1, issue.1, pp.1-126, 2005.

G. Prando and A. Chiuso, Model reduction for linear bayesian system identification, 54th IEEE Conference on Decision and Control (CDC), pp.2121-2126, 2015.

W. H. Press, Numerical recipes 3rd edition: The art of scientific computing, 2007.

Z. Qiang, Z. Ya-bo, and M. Shu, Effective global searching method based on radial basis function, 2011 International Conference on Electric Information and Control Engineering, vol.173, 2011.

S. S. Rao, Engineering optimization: theory and practice, 2009.

N. Recipes, The art of scientific computing, 2007.

J. Roudet, E. Clavel, J. Guichon, and J. Schanen, Inca3d a cad tool for stray elements computation in electrical engineering, ECPE Seminar:«Virtual Prototyping in Power Electronics, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00293271

D. Rudolph and G. Stitt, An interpolation-based approach to multi-parameter performance modeling for heterogeneous systems, 2015 IEEE 26th International Conference on Application-specific Systems, Architectures and Processors (ASAP), pp.174-180, 2015.

A. Ruehli, G. Antonini, J. , and L. , Circuit Oriented Electromagnetic Modeling Using the Peec Techniques, 2017.

A. E. Ruehli, Equivalent circuit models for three-dimensional multiconductor systems, IEEE Transactions on Microwave theory and techniques, vol.22, issue.3, pp.216-221, 1974.

A. Ruhe, The rational krylov algorithm for nonsymmetric eigenvalue problems. iii: Complex shifts for real matrices, BIT Numerical Mathematics, vol.34, issue.1, pp.165-176, 1994.

Y. Saad, Iterative methods for sparse linear systems, SIAM, 2003.
DOI : 10.1137/1.9780898718003

J. Sacks, W. J. Welch, T. J. Mitchell, W. , and H. P. , Design and analysis of computer experiments, Statistical science, pp.409-423, 1989.

M. Sarma, Magnetostatic field computation by finite element formulation, IEEE Transactions on Magnetics, vol.12, issue.6, pp.1050-1052, 1976.
DOI : 10.1109/tmag.1976.1059162

URL : https://repository.library.northeastern.edu/files/neu:330532/fulltext.pdf

J. B. Schneider, Understanding the finite-difference time-domain method. School of electrical engineering and computer science Washington State University, 2010.

H. Seifi and M. S. Sepasian, Electric power system planning: issues, algorithms and solutions, 2011.
DOI : 10.1007/978-3-642-17989-1

A. Semlyen and B. Gustavsen, Vector fitting by pole relocation for the state equation approximation of nonrational transfer matrices. Circuits, Systems and Signal Processing, vol.19, pp.549-566, 2000.

J. Siau, Unstructured PEEC formulations considering resistive, inductive and capacitive effects for power electronics, 2016.
URL : https://hal.archives-ouvertes.fr/tel-01633697

P. Silvester, Finite element solution of homogeneous waveguide problems, Alta Frequenza, vol.38, issue.Speciale, pp.313-317, 1969.

D. Simic, T. Bäuml, and F. Pirker, Modeling and simulation of different hybrid electric vehicles in modelica using dymola, Proceedings of International Conference on Advances in Hybrid Powertrains, Conference on Advances in Hybrid Powertrains, 2008.

M. Spivak, Calculus on manifolds: a modern approach to classical theorems of advanced calculus, 1965.
DOI : 10.1201/9780429501906

G. Strang, Computational science and engineering, vol.1, 2007.

G. Strang, Introduction to linear algebra, 2011.

G. Strang and K. Aarikka, Introduction to applied mathematics, vol.16, 1986.

T. Stykel, Analysis and numerical solution of generalized lyapunov equations, 2002.

A. Taflove and S. C. Hagness, Computational electrodynamics: the finite-difference time-domain method, 2005.

L. N. Trefethen, I. Bau, and D. , Numerical linear algebra, vol.50, 1997.

J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite element method electromagnetics: antennas, microwave circuits, and scattering applications, vol.6, 1998.

J. D. Walecka, Introduction to general relativity, 2007.
DOI : 10.1142/10644

URL : http://www.worldscientific.com/doi/pdf/10.1142/9789813227705_fmatter

X. Wang, W. Zhou, and R. Dou, Analysis of harmonic current in permanent magnet synchronous motor and its effect on motor torque, Journal of Electromagnetic Analysis and Applications, vol.4, issue.01, p.15, 2012.
DOI : 10.4236/jemaa.2012.41003

URL : http://www.scirp.org/journal/PaperDownload.aspx?paperID=17148

K. Warwick and R. Craddock, An introduction to radial basis functions for system identification. a comparison with other neural network methods, Proceedings of 35th IEEE Conference on Decision and Control, vol.1, pp.464-469, 1996.
DOI : 10.1109/cdc.1996.574355

H. Wendland, Scattered data approximation, vol.17, 2004.

K. Willcox and J. Peraire, Balanced model reduction via the proper orthogonal decomposition, AIAA journal, vol.40, issue.11, pp.2323-2330, 2002.

B. Xia, Z. Ren, and C. Koh, Utilizing kriging surrogate models for multiobjective robust optimization of electromagnetic devices, IEEE Transactions on Magnetics, vol.50, issue.2, pp.693-696, 2014.