Matea Puvača
PhD student Department of Mathematics Josip Juraj Strossmayer University of Osijek Trg Ljudevita Gaja 6 Osijek, HR31000, Croatia¸

Research Interests
 Numerical linear algebra
 Control Theory
 Numerical mathematics
 Damping optimization in mechanical systems
 Eigenvalues problems
Degrees
 MSc in Mathematics, Mathematics and Computer Science,Department of Mathematics, University of Osijek, Croatia, 2015.
 BSc in Mathematics, Department of Mathematics, University of Osijek, Croatia, 2013.
Publications
Journal Publications
 N. Truhar, Z. Tomljanović, M. Puvača, Approximation of damped quadratic eigenvalue problem by dimension reduction, Applied mathematics and computation 347 (2019), 4053This paper presents an approach to the efficient calculation of all or just one important part of the eigenvalues of the parameter dependent quadratic eigenvalue problem $(lambda^2(mathbf{;v};) M + lambda(mathbf{;v};) D(mathbf{;v};) + K) x(mathbf{;v};) = 0$, where $M, K$ are positive definite Hermitian $ntimes n$ matrices and $D(mathbf{;v};)$ is an $ntimes n$ Hermitian semidefinite matrix which depends on a damping parameter vector $mathbf{;v};= begin{;bmatrix}; v_1 & ldots & v_k end{;bmatrix};in mathbb{;R};_+^k$. With the new approach one can efficiently (and accurately enough) calculate all (or just part of the) eigenvalues even for the case when the parameters $v_i$, which in this paper represent damping viscosities, are of the modest magnitude. Moreover, we derive two types of approximations with corresponding error bounds. The quality of error bounds as well as the performance of the achieved eigenvalue tracking are illustrated in several numerical experiments.
 Y. Kanno, M. Puvača, Z. Tomljanović, N. Truhar, Optimization Of Damping Positions In A Mechanical System, Rad HAZU, Matematičke znanosti. 23 (2019), 141157This paper deals with damping optimization of the mechanical system based on the minimization of the socalled "average displacement amplitude". Further, we propose three different approaches to solving this minimization problems, and present their performance on two examples.
 N. Truhar, Z. Tomljanović, M. Puvača, An Efficient Approximation For Optimal Damping In Mechanical Systems, International journal of numerical analysis and modeling 14/2 (2017), 201217This paper is concerned with an efficient algorithm for damping optimization in mechanical systems with a prescribed structure. Our approach is based on the minimization of the total energy of the system which is equivalent to the minimization of the trace of the corresponding Lyapunov equation. Thus, the prescribed structure in our case means that a mechanical system is close to a modally damped system. Although our approach is very efficient (as expected) for mechanical systems close to modally damped system, our experiments show that for some cases when systems are not modally damped, the proposed approach provides efficient approximation of optimal damping.
Others
 Z. Tomljanović, M. Ugrica, QR decomposition using Givens rotations and applications, Osječki matematički list 14/2 (2015), 117141In this paper, we describe Givens rotations and their applications. We present basic properties of Givens rotation matrices and their application to calculation of QR decomposition of the given matrix which can be used for solving linear systems or the least squares problem. Givens rotations play an important role if the matrix considered has a special structure; thus, we additionally describe usage of Givens rotations for structured matrices such as tridiagonal or Hessenberg matrices. Givens rotations and their application are illustrated by examples.
Technical Reports
 N. Truhar, Z. Tomljanović, M. Puvača, An efficient approximation for the optimal damping in mechanical systems (2016)This paper is concerned with the efficient algorithm for damping optimization in mechanical systems with prescribed structure. Our approach is based on the minimization of the total energy of the system which is equivalent with the minimization of the trace of the corresponding Lyapunov equation. Thus, the prescribed structure in our case means that a mechanical system is close to the modally damped system. Even though our approach is very efficient (as it was expected) for the mechanical systems close to modally damped system, our experiments show that for some cases when systems are not modally damped the proposed approach provides efficient approximation of the optimal damping.
Projects
 Robustness optimization of damped mechanical systems,  scientific project; supported by the DAAD for period 20172018; cooperation with TU Berlin, Germany
 Optimization of parameter dependent mechanical systems (IP2014099540; OptPDMechSys). This project has been fully supported by Croatian Science Foundation for the period 01.07.2015.30.06.2019.
Professional Activities
Committee Memberships and organization
 International Workshop on Optimal Control of Dynamical Systems and applications, 2022 June 2018 at Department of Mathematics, J. J. Strossmayer University of Osijek, web page
Schools and Conferences
 The third International School on Model Reduction for Dynamical Control Systems, Dubrovnik, Croatia, October, 5  10, 2015.
 DAAD  Krylov Subspaces and Applications, Golem, Kavaja, Albania, September, 1117 2016.
 Workshop on Model Reduction Methods and Optimization, 2021 September 2016, in Opatija, Croatia.
 Reduced Basis Summer School 2016, (Kloster Hedersleben, Germany, October 37 ,2016), gave a talk
on "An efficient approximation for the optimal damping in mechanical systems".  Model reduction course HYDRA, March 69, 2017, Eindhoven, The Netherlands.
 Gene Golub Summer School, May 29June 9, 2017, Berlin, Germany.
 17th GAMM Workshop ANLA, September 78, 2017, Cologne, Germany.
 Simpozij studenata doktorskih studija PMFa u Zagrebu, 9. veljače 2018. usmeno priopćenje “Optimizacija prigušenja vibracijskih sustava”.
 GAMM Annual Meeting, March 1923, Munich, Germany, gave talk on "Perturbation Bounds for Parameter Dependent Quadratic Eigenvalue Problem"
 GAMMFachausschusses „Dynamik und Regelungstheorie“, 1920 April, Berlin, Germany, gave talk on "Perturbation Bounds for Parameter Dependent Quadratic Eigenvalue Problem"
 International Workshop on Optimal Control of Dynamical Systems and applications, 2022 June 2018, Osijek, Croatia, gave talk on "Approximations of Eigenpairs for Parameter Dependent Quadratic Eigenvalue Problem and Applications"
 ApplMath18, 17.20.9.2018., Solaris, Šibenik, Croatia, gave talk on "Approximations of Eigenpairs for Parameter Dependent Quadratic Eigenvalue Problem and Applications"
 GAMM ANLA Workshop, 10.12.10.2018. Lund, Švedska
 ICIAM 2019, July, 1519, Valencia, Spain, gave talk on "Approximation of damped quadratic eigenvalue problem by dimension reduction"
Study Visits Abroad and Professional Improvement
 visiting researcher at TU Berlin, Germany September, 1829, 2017.
 visiting researcher at TU Berlin, Germany April, 1620, 2018.
 visiting researcher at Max  Plank Institut, Magdeburg, Germany April, 2127, 2018.
Teaching
Zimski semestar 2015./2016.
Ljetni semestar 2015./2016.
Zimski semestar 2016./2017.
Ljetni semestar 2016./2017.
Zimski semestar 2017./2018.
Zimski semestar 2018./2019.
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