{"id":52228,"date":"2025-12-18T12:06:47","date_gmt":"2025-12-18T11:06:47","guid":{"rendered":"https:\/\/www.mathos.unios.hr\/?page_id=52228"},"modified":"2026-11-02T15:46:49","modified_gmt":"2026-11-02T14:46:49","slug":"ophomat","status":"publish","type":"page","link":"https:\/\/www.mathos.unios.hr\/en\/ophomat\/","title":{"rendered":"OpHoMat"},"content":{"rendered":"\n
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Basic Information<\/h2>\n\n\n\n

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.<\/p>\n\n\n\n

Project duration: 1 October 2025 \u2013 30 September 2029.<\/p>\n\n\n\n

Work Packages<\/p>\n\n\n\n

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 Vukojevi\u0107, PhD<\/p>\n\n\n\n

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 Kuzmanovi\u0107 Ivi\u010di\u0107, PhD<\/p>\n\n\n\n

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 Pavlovi\u0107, PhD<\/p>\n\n\n\n

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<\/p>\n\n\n\n

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Publications<\/h2>\n\n\n\n

Przybilla, J., Ugrica Vukojevi\u0107, 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<\/a><\/p>\n\n\n\n

M. Milolo\u017ea Pandur, An indefinite LOBPCG type of algorithm for detecting a definite Hermitian matrix pair, Linear Algebra and its Applications 746 (2026), 111\u2013139. https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S0024379526002247<\/a><\/p>\n\n\n\n

Conferences<\/h2>\n\n\n\n

M. Milolo\u017ea 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\u201325, 2026<\/p>\n\n\n\n

I. Crnjac, Homogenization of \u03b4-horizon fractional diffusion, 13th Conference on Applied Mathematics and Scientific Computing, Dubrovnik, Croatia, September 21\u201325, 2026<\/p>\n\n\n\n

K. Burazin, 13th Conference on Applied Mathematics and Scientific Computing, Dubrovnik, Croatia, September 21\u201325, 2026<\/p>\n\n\n\n

M. Damjanovi\u0107, 13th Conference on Applied Mathematics and Scientific Computing, Dubrovnik, Croatia, September 21\u201325, 2026<\/p>\n\n\n\n

I. Kuzmanovi\u0107 Ivi\u010di\u0107, S. Miodragovi\u0107, M. Nedovi\u0107, B. Mihailovi\u0107, Matrix equations with interval matrices, ALAMA 2026, July 17\u201319, 2026, Huelva, Spain<\/p>\n\n\n\n

S. Miodragovi\u0107, I. Kuzmanovi\u0107 Ivi\u010di\u0107, N. Truhar, The sin \u0398 and tan \u0398 theorems for stable gyroscopic systems, ALAMA 2026, July 17\u201319, 2026, Huelva, Spain<\/p>\n\n\n\n

J. Jankov Pavlovi\u0107, H-convergence theory for anisotropic bending rods, The 15th AIMS Conference, July 6\u201310, 2026, Athens, Greece<\/p>\n\n\n\n

M. Ribi\u010di\u0107 Penava, Generalizations of Weighted Hermite-Hadamard and Fej\u00e9r Type Inequalities and Applications, MNA 2026, May 26\u201329, 2026, Budva, Montenegro<\/p>\n\n\n\n

N. Truhar, SIAM Conference on Optimization, Edinburgh, Scotland, 2026.<\/p>\n\n\n\n

Z. Tomljanovi\u0107, Generating ideas for a numerical world, June 29 \u2013 July 3, 2026, France<\/p>\n\n\n\n

Mobility<\/h2>\n\n\n\n

Visit of Zoran Tomljanovi\u0107 to Virginia Tech, Blacksburg, January 30 \u2013 February 7, 2026.<\/p>\n\n\n\n

Visit of Prof. Y. Simsek and Assist. Prof. B. Simsek from Akdeniz University, Antalya, Turkey, May 31 \u2013 June 5, 2026.<\/p>\n\n\n\n

Davide Palitta (Italy \/ MPI Magdeburg) \u2013 research visit, 2026.<\/p>\n\n\n\n

Petar Kun\u0161tek (TU Graz, Austria) \u2013 research visit, 2026.<\/p>\n\n\n\n

News<\/h2>\n\n\n\n