Matea Ugrica
Josip Juraj Strossmayer University of Osijek
Research Interests
Numerical linear algebra
Control theory
Numerical mathematics
Damping optimization in mechanical systems
Eigenvalue problems
Degrees
PhD in Mathematics, Department of Mathematics, University of Zagreb, Croatia,2020.
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
 N. Jakovčević Stor, T. Mitchell, Z. Tomljanović, M. Ugrica, Fast optimization of viscosities for frequencyweighted damping of secondorder systems, Journal of Applied Mathematics and Mechanics 103/5 (2023), 121We consider frequencyweighted damping optimization for vibrating systems described by a secondorder differential equation. The goal is to determine viscosity values such that eigenvalues are kept away from certain undesirable areas on the imaginary axis. To this end, we present two complementary techniques. First, we propose new frameworks using nonsmooth constrained optimization problems, whose solutions both damp undesirable frequency bands and maintain the stability of the system. These frameworks also allow us to weight which frequency bands are the most important to damp. Second, we also propose a fast new eigensolver for the structured quadratic eigenvalue problems that appear in such vibrating systems. In order to be efficient, our new eigensolver exploits special properties of diagonalplusrankone complex symmetric matrices, which we leverage by showing how each quadratic eigenvalue problem can be transformed into a short sequence of such linear eigenvalue problems. The result is an eigensolver that is substantially faster than standard techniques. By combining this new solver with our new optimization frameworks, we obtain our overall algorithm for fast computation of optimal viscosities. The efficiency and performance of our new approach are verified and illustrated on several numerical examples.
 I. Kuzmanović Ivičić, S. Miodragović, M. Ugrica, The tan Θ theorem for definite matrix pairs, Linear and multilinear algebra 70 (2022), 117In this paper, we consider the perturbation of a Hermitian matrix pair $(H,M)$, where $H$ and $M$ are nonsingular and positive definite Hermitian matrices, respectively. A novel upper bound on a tangent of the angles between the eigenspaces of perturbed and unperturbed pairs is derived under a perturbation to the offdiagonal blocks of $H$. The rotation of the eigenspaces under a perturbation is measured in the matrixdependent scalar product. We show that a $tanTheta$ bound for the standard eigenvalue problem is a special case of our new bound and that the obtained bound can be much sharper than the existing $sinTheta$ bounds.
 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.
 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.
 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
 Vibration Reduction in Mechanical Systems — scientific project (IP2019046774, VIMS). This project has been fully supported by Croatian Science Foundation for the period 01.01.2020.–31.12.2023. (postdoc)
 Isolation of the unwanted part of the spectrum in the quadratic eigenvalue problem. Project was funded by J. J. Strossmayer University of Osijek, for period November, 2018. May, 2020.
 Robustness optimization of damped mechanical systems, — scientific project; supported by the DAAD for period 2017–2018; 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.
 Accelerated solution of optimal damping problems, — scientific project; supported by the DAAD for period 2021–2022; cooperation with Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
Professional Activities
Committee Memberships and organization
 Member of Organizing committee of the 8th Croatian Mathematical Congress, 2.5.7.2024. at School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek
 Coorganizer of the Workshop on Optimal Control of Dynamical Systems and applications, 5.6.11. 2020. at Department of Mathematics, J. J. Strossmayer University of Osijek http://vims.mathos.unios.hr/home/workshop2020
 Coorganizer of the International Workshop on Optimal Control of Dynamical Systems and applications, 20.22.6.2018. 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”
 ApplMath2020, 14.18.9.2020., Brijuni, Croatia, gave talk on “Frequencyweighted damping via nonsmooth optimization and fast computation of QEPs with lowrank updates”
 GAMM ANLA Workshop, 24.25.09.2020. (online)
 Workshop on Control of Dynamical Systems, 14.16.6.2021., Dubrovnik, Croatia, gave talk on “Frequencyweighted damping via nonsmooth optimization and fast computation of QEPs with lowrank updates”
 GAMM ANLA Workshop, 16.17.9.2021. Potsdam, Njemačka, gave talk on “Fast optimization of viscosities for frequencyweighted damping of secondorder systems”
 3rd Workshop on Optimal Control of Dynamical Systems and applications, 2831 March 2022 at Department of Mathematics, J. J. Strossmayer University of Osijek, Osijek, Croatia, gave talk on “Fast optimization of viscosities for frequencyweighted damping of secondorder systems”
 ALAMA 2022, 13 June 2022 at University of Alcalá, Alcalá de Henares (Madrid), Spain, gave talk on “Fast optimization of viscosities for frequencyweighted damping of secondorder systems”
 SIAM Conference on Computational Science and Engineering (CSE23), 26.2. – 3.3. 2023., Amsterdam Netherlands
 School on Artificial Intelligence for Materials Science in the Exascale Era, BiGmax, 21. – 26.5.2023. Costa Brava, Spain
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 Planck Institut, Magdeburg, Germany April, 2127, 2018.
 visiting researcher at Max Planck Institut, Magdeburg, Germany September, 1215, 2021.
 postdoc at Max Planck Institut, Magdeburg, Germany September, 1 2022 – August, 31 2023.
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.
Zimski semestar 2019./2020.
Ljetni semestar 2019./2020.
 Metode numeričke matematike
 Matematičke logika u računalnoj znanosti
 Osnove teorije upravljanja s primjenama
Zimski semestar 2020./2021.
Ljetni semestar 2020./2021.
Zimski semestar 2021./2022.
 Primijenjena linearna algebra i znanstveno računarstvo
 Funkcijsko programiranje
 Matematika III (GFOS)
Ljetni semestar 2021./2022.
 Nelinearna optimizacija
 Redukcija modela i aproksimacijski pristupi
 Teorijske osnove računalne znanosti
Završni i diplomski radovi
 Dunja Majdenić, Spektar i pseudospektar matrice, završni rad (2021), u komentorstvu s doc.dr.sc. Ivana Kuzmanović Ivičić
 Marija Turić, Simetrične matrice, završni rad (2021), u komentorstvu s doc.dr.sc. Suzana Miodragović
 Andrea Arbutina, Simetričan svojstveni problem, završni rad (2022), u komentorstvu s doc.dr.sc. Suzana Miodragović
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