Matea Ugrica

1. N. Truhar, Z. Tomljanović, M. Puvača, Approximation of damped quadratic eigenvalue problem by dimension reduction, Applied mathematics and computation 347 (2019), 40-53
   Abstract

   This 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.
2. Y. Kanno, M. Puvača, Z. Tomljanović, N. Truhar, Optimization Of Damping Positions In A Mechanical System, Rad HAZU, Matematičke znanosti. 23 (2019), 141-157
   Abstract

   This paper deals with damping optimization of the mechanical system based on the minimization of the so-called "average displacement amplitude". Further, we propose three different approaches to solving this minimization problems, and present their performance on two examples.
3. 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), 201-217
   Abstract

   This 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.

1. Z. Tomljanović, M. Ugrica, QR decomposition using Givens rotations and applications, Osječki matematički list 14/2 (2015), 117-141
   Abstract

   In 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.

1. N. Truhar, Z. Tomljanović, M. Puvača, An efficient approximation for the optimal damping in mechanical systems (2016)
   Abstract

   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 (IP-2019-04-6774, 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 (IP-2014-09-9540; 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

• Co-organizer of the Workshop on Optimal Control of Dynamical Systems and applications, 5-6 November 2020 at Department of Mathematics, J. J. Strossmayer University of Osijek http://vims.mathos.unios.hr/home/workshop2020  
• Co-organizer of the International Workshop on Optimal Control of Dynamical Systems and applications, 20-22 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, 11-17 2016.
• Workshop on Model Reduction Methods and Optimization, 20-21 September 2016, in Opatija, Croatia.
• Reduced Basis Summer School 2016, (Kloster Hedersleben, Germany, October 3-7 ,2016), gave a talk
  on "An efficient approximation for the optimal damping in mechanical systems".
• Model reduction course HYDRA, March 6-9, 2017, Eindhoven, The Netherlands.
• Gene Golub Summer School, May 29-June 9, 2017, Berlin, Germany.
• 17th GAMM Workshop ANLA, September 7-8, 2017, Cologne, Germany.
• Simpozij studenata doktorskih studija PMF-a u Zagrebu, 9. veljače 2018.- usmeno priopćenje “Optimizacija prigušenja vibracijskih sustava”.
• GAMM Annual Meeting, March 19-23, Munich, Germany, gave talk on "Perturbation Bounds for Parameter Dependent Quadratic Eigenvalue Problem"
• GAMM-Fachausschusses „Dynamik und Regelungstheorie“, 19-20 April, Berlin, Germany, gave talk on "Perturbation Bounds for Parameter Dependent Quadratic Eigenvalue Problem"
  
• International Workshop on Optimal Control of Dynamical Systems and applications, 20-22 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, 15-19, Valencia, Spain, gave talk on "Approximation of damped quadratic eigenvalue problem by dimension reduction"
• ApplMath2020, 14.-18.9.2020., Brijuni, Croatia, gave talk on "Frequency-weighted damping via nonsmooth optimization and fast computation of QEPs with low-rank updates"

Study Visits Abroad and Professional Improvement

• visiting researcher at TU Berlin, Germany September, 18-29, 2017.
• visiting researcher at TU Berlin, Germany April, 16-20, 2018.
• visiting researcher at Max - Plank Institut, Magdeburg, Germany April, 21-27, 2018.

Teaching

Zimski semestar 2015./2016.

• Elementarna matematika 1
• Numerička linearna algebra

Ljetni semestar 2015./2016.

• Elementarna matematika 2
• Primjena diferencijalnog i integralnog računa 1

Zimski semestar 2016./2017.

• Numerička linearna algebra

Ljetni semestar 2016./2017.

• Elementarna matematika 2

Zimski semestar 2017./2018.

• Numerička linearna algebra
• Linearna algebra 2

Zimski semestar 2018./2019.

• Numerička linearna algebra
• Matematički praktikum

Zimski semestar 2019./2020.

• Matematički praktikum

Ljetni semestar 2019./2020.

• Metode numeričke matematike
• Matematičke logika u računalnoj znanosti
• Osnove teorije upravljanja s primjenama

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