OpHoMat

Basic Information

The project Optimization and Homogenization for Models of Mathematical Physics (OpHoMat) focuses on the development of modern theoretical and numerical methods in the areas of homogenization, optimization, dynamical systems, and matrix equations, with applications to models describing various physical phenomena. Parameter-dependent dynamical systems are studied and order reduction methods are developed that preserve the structural properties of the models, with application to systems with dampers. In the area of matrix equations, the focus is on their application in stability analysis and spectral estimation of mechanical systems, as well as on the development of new methods and algorithms for solving them, with additional study of matrix equations with interval matrices. The project also addresses the development of a general homogenization theory in the operator sense (G- and H-convergence) for lower-dimensional models of linearized elasticity, such as elastic rods and plates. In the context of structural optimization, methods are developed for determining the optimal shape, viscous damping, and material distribution in a body, minimizing system energy or deformation by combining homogenization approaches and shape optimization. Additionally, generalized integral inequalities are used to improve numerical integration and error analysis.

Project duration: 1 October 2025 – 30 September 2029.

Work Packages

Work Package 1 (WP1): Modelling of Parameter-Dependent Dynamical Systems
This package is led by members working on the development of dynamical models and order reduction methods with preservation of structural properties.
Package leader: Assist. Prof. Matea Ugrica Vukojević, PhD

Work Package 2 (WP2): Matrix Equations and Their Applications
This package involves a team specializing in linear algebraic systems, stability and spectral analysis, and matrix equations, including those with interval matrices.
Package leader: Assoc. Prof. Ivana Kuzmanović Ivičić, PhD

Work Package 3 (WP3): Development of a General Homogenization Theory in the Operator Sense for Lower-Dimensional Models of Mathematical Physics
This package involves team members with expertise in homogenization, functional analysis, and partial differential equations. The focus is on the theoretical analysis of G- and H-convergence in models of elastic rods and plates.
Package leader: Assist. Prof. Jelena Jankov Pavlović, PhD

Work Package 4 (WP4): Structural Optimization for Elastic Structures
The team leading this package has experience in shape optimization, computational mechanics, and the application of homogenization methods in engineering design. Activities include determining the optimal material distribution, damping, and geometry of structures.
Package leader: Assist. Prof. Ivana Crnjac, PhD

Publications

Przybilla, J., Ugrica Vukojević, M., Truhar, N., Benner, P.: An adaptive scheme for the optimization of damping positions by decoupling controllability spaces in vibrational systems. Z Angew Math Mech. 106, e70353 (2026). https://doi.org/10.1002/zamm.70353

M. Miloloža Pandur, An indefinite LOBPCG type of algorithm for detecting a definite Hermitian matrix pair, Linear Algebra and its Applications 746 (2026), 111–139. https://www.sciencedirect.com/science/article/abs/pii/S0024379526002247

Conferences

M. Miloloža Pandur, A mixed-precision preconditioned “naive” Jacobi eigenvalue algorithm for general complex matrices, 13th Conference on Applied Mathematics and Scientific Computing, Dubrovnik, Croatia, September 21–25, 2026

I. Crnjac, Homogenization of δ-horizon fractional diffusion, 13th Conference on Applied Mathematics and Scientific Computing, Dubrovnik, Croatia, September 21–25, 2026

K. Burazin, 13th Conference on Applied Mathematics and Scientific Computing, Dubrovnik, Croatia, September 21–25, 2026

M. Damjanović, 13th Conference on Applied Mathematics and Scientific Computing, Dubrovnik, Croatia, September 21–25, 2026

I. Kuzmanović Ivičić, S. Miodragović, M. Nedović, B. Mihailović, Matrix equations with interval matrices, ALAMA 2026, July 17–19, 2026, Huelva, Spain

S. Miodragović, I. Kuzmanović Ivičić, N. Truhar, The sin Θ and tan Θ theorems for stable gyroscopic systems, ALAMA 2026, July 17–19, 2026, Huelva, Spain

J. Jankov Pavlović, H-convergence theory for anisotropic bending rods, The 15th AIMS Conference, July 6–10, 2026, Athens, Greece

M. Ribičić Penava, Generalizations of Weighted Hermite-Hadamard and Fejér Type Inequalities and Applications, MNA 2026, May 26–29, 2026, Budva, Montenegro

N. Truhar, SIAM Conference on Optimization, Edinburgh, Scotland, 2026.

Z. Tomljanović, Generating ideas for a numerical world, June 29 – July 3, 2026, France

Mobility

Visit of Zoran Tomljanović to Virginia Tech, Blacksburg, January 30 – February 7, 2026.

Visit of Prof. Y. Simsek and Assist. Prof. B. Simsek from Akdeniz University, Antalya, Turkey, May 31 – June 5, 2026.

Davide Palitta (Italy / MPI Magdeburg) – research visit, 2026.

Petar Kunštek (TU Graz, Austria) – research visit, 2026.

News

• The project Optimization and Homogenization for Models of Mathematical Physics (OpHoMat) has completed its first year of implementation (1 October 2025 – 30 September 2026). Research has been launched across all activities, and the first results have been published in prestigious international journals. Two scientific papers have been published in the Web of Science database: the first, co-authored by team members Maja Ugrica Vukojević and Ninoslav Truhar together with researchers from the Max Planck Institute and the University of Chemnitz, presents an adaptive scheme for the optimization of damping in vibrational systems and was published in ZAMM – Journal of Applied Mathematics and Mechanics (Q1); the second is a paper by Maša Miloloža Pandur in the field of numerical linear algebra, published in Linear Algebra and its Applications. International collaboration has also been strengthened. Zoran Tomljanović visited Virginia Tech in the United States as a visiting researcher, and the research group was also visited by foreign scientists: Davide Palitta (MPI Magdeburg, Germany), Yusuf Šimšek and Betül Šimšek (Akdeniz University, Turkey), and Petar Kunštek (TU Graz, Austria). Team members participated in scientific meetings and workshops in Spain, Montenegro, France, Germany, Greece, the United Kingdom, and Croatia, and Ninoslav Truhar presented at the SIAM Conference on Optimization in Edinburgh. In the second year of implementation, the completion of research equipment procurement, the organization of an international workshop in Osijek, and the continuation of intensive mobilities and collaborations with international partners are planned.
• 5th Workshop on Optimal Control of Dynamical Systems and Applications Osijek, Croatia | April/May 2027. Further information and registration: https://indico.mathos.hr/event/18/

This project is funded by the European Union – NextGenerationEU. The views and opinions expressed are solely those of the author(s) and do not necessarily reflect the official positions of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.