### Ivana Crnjac

Head of Applied Mathematics and Optimization Research Group

School of Applied Mathematics and Informatics

Josip Juraj Strossmayer University of Osijek

Josip Juraj Strossmayer University of Osijek

### Research Interests

- Partial Differential Equations
- Functional Analysis
- Optimal Design

### Degrees

- PhD in Mathematics, Department of Mathematics, University of Zagreb, Croatia, 2019. (PhD thesis)
- MSc in Mathematics, Department of Mathematics, University of Osijek,Croatia, 2013. (Master thesis)
- BSc in Mathematics, Department of Mathematics, University of Osijek, Croatia, 2011.

### Publications

Journal Publications

- K. Burazin, I. Crnjac, M. Vrdoljak, Explicit Hashin-Shtrikman bounds in 3D linearized elasticity, Filomat
**1**(2024)In this paper, we are dealing with Hashin-Shtrikman bounds in the context of linearized elasticity. We give an explicit computation of the upper bound on the primal energy in three space dimensions and the corresponding microstructure that saturates this bound. Due to equivalency between the upper Hashin-Shtrikman bound on the primal energy and the lower Hashin-Shtrikman bound on the complementary energy, the explicit calculation of the latter arises. These calculations have straightforward applications in evaluation of experimental results and numerical schemes regarding composite elastic materials, as well as structural optimization problems. - I. Crnjac, J. Jankov Pavlović, P. Kunštek, Optimal design of elastic plates, ESAIM: Mathematical Modelling and Numerical Analysis
**58**/3 (2024), 1137-1151 - K. Burazin, I. Crnjac, Application of explicit energy bounds in optimization of 3D elastic structures, Optimization and Engineering
**2023**(2023)We present a novel numerical method for calculating optimal design in topology optimization problems for 3D linear elastic structures. The algorithm is based on necessary conditions of optimality for problem which was obtained by relaxing the original one via the homogenization method in the sense of operators (G- or H-convergence), and can be implemented for self-adjoint problems. The method relies on recently obtained explicit expressions for the lower Hashin–Shtrikman bound on complementary energy and information on the microstructure that saturates the bound. We tested the algorithm on two benchmark examples, namely the cantilever and the bridge problem. The algorithm provides the solution in a ﬁrst few iterations and the true composites appear in the optimal design. We also implement a penalization procedure to obtain classical design with slight increase of the cost functional. - K. Burazin, I. Crnjac, M. Vrdoljak, Optimality criteria method in 2D linearized elasticity problems, Applied Numerical Mathematics
**160**(2021), 192-204 - K. Burazin, I. Crnjac, Convergence of the optimality criteria method for multiple state optimal design problems, Computers & Mathematics with Applications
**79**/5 (2020), 1382-1392 - K. Burazin, I. Crnjac, M. Vrdoljak, Variant of optimality criteria method for multiple state optimal design problems, Communications in Mathematical Sciences
**16**/6 (2018), 1597-1614 - N. Antonić, K. Burazin, I. Crnjac, M. Erceg, Complex Friedrichs systems and applications, Journal of Mathematical Physics
**58**/10 (2017), 1-22

Others

- I. Crnjac, R. Ledenčan, Eulerova diferencijalna jednadžba, Math.e : hrvatski matematički elektronski časopis
**44**/1 (2023) - I. Soldo, I. Vuksanović, Pitagorine trojke, Matematičko fizički list
**255**(2014), 179-184 - K. Burazin, Z. Tomljanović, I. Vuksanović, Prigušivanje mehaničkih vibracija, Math.e : hrvatski matematički elektronski časopis
**24**(2014)

### Projects

**Homogenization and optimization in mechanics of solids**The project is funded by Croatian Science Foundation (December 2023 – December 2027). Project leader: Krešimir Burazin.**Homogenization, dimension reduction and structural optimization in continuum mechanics**

The project is funded by Croatian Science Foundation from October 2018 until April 2023. Project leader: prof. Igor Velčić from University of Zagreb.

**Calculus of variations, optimisation and applications**

This is bilateral project with Serbia (cofinanced by Serbian Ministry of Science) that run from

2016 until 2017. Project leaders: ass.prof. Krešimir Burazin from University of Osijek (croatian side)

and prof. Nataša Krejić from University of Novi Sad (serbian side).

**Damping optimization in mechanics systems excited with external force**

Project run in 2015/16, supported by University of Osijek. Project leader: Zoran Tomljanović

**Evolution Fredrichs systems**

Project run in 2013/14., supported by University of Osijek. Project leader: Krešimir Burazin.

### Professional Activities

**Schools and Conferences**– With talk:

- Tenth Conference on Applied Mathematics and Scientific Computing, Dubrovnik, Croatia, September, 23-27, 2024
- 8th Croatian Mathematical Congress, Osijek, Croatia, July, 2-5, 2024
- Tenth Conference on Applied Mathematics and Scientific Computing, Brijuni, Croatia, September, 14-18, 2020
- VIII Partial Differential Equations, Optimal Design and Numerics, Benasque, Spain, August 18-24,2019
- International Conference on Elliptic and Parabolic Problems, Gaeta, Italy, May 20-24, 2019
- Ninth Conference on Applied Mathematics and Scientific Computing, Šibenik, Croatia, September 17-20, 2018
- International Workshop on Optimal Control of Dynamical Systems and Applications, Osijek, Croatia, June 20-22, 2018
- International Workshop on PDEs: analysis and modelling, Zagreb, Croatia, June 17-20, 2018
- Applications of Generalized Functions in Harmonic Analysis, Mechanics, Stochastics and PDE, Novi Sad, Serbia, October 25 – 27, 2017
- VII Partial Differential Equations, Optimal Design and Numerics, Benasque, Spain, August 20-29, 2017
- Young Women in Harmonic Analysis and PDE, Bonn, Germany, December, 2-4 2016
- International Conference on Generalized Functions, Dubrovnik, Croatia, September 4-9, 2016
- 6th Croatian Mathematical Congress, Zagreb, Croatia, June 14-17, 2016
- International Workshop on PDEs: analysis and modelling; Celebrating 80th anniversary of professor Nedžad Limić, Zagreb, Croatia, June 19-22,2016

– *Other:*

- GMT, Shape Optimisation and Free Boundaries, Trieste, Italy, October 25-28, 2016
- DAAD Intensive course on New Aspects of the Time Frequency Analysis involving Frechet Frames, Novi Sad, Serbia, September, 2016
- Workshop on Model Reduction Methods and Optimization, Opatija, Croatia, September 2016
- Student visit to the University of Zagreb in the frame of DAAD project “Center of Excellence of Applications of Mathematics”, May 2 – June 1, 2016
- Partial Differential Equations, Optimal Design and Numerics, Benasque, Spain, August-September 2015
- Winter School on Calculus of Variations in Physics and Materials Science, Würzburg, Germany, February 2014
- Nonsmooth Analysis with Applications, Cluj-Napoca, Romania, September 2014
- Workshop New Trends in Calculus of Variations, Linz, Austria, October 2104
- Student visit to the University of Dubrovnik in the frame of DAAD project “Center of Excellence of Applications of Mathematics”, June, 2014
- PDEs, Continuum Mechanics and Numerical Analysis, A Conference in Honor of the 80th Anniversary of professor Ibrahim Aganović, Dubrovnik, May 2014
- Microlocal Analysis, Wave Fronts and Propagation of Singularities, Novi Sad,Serbia, September 2013
- DAAD International School on Linear Optimal Control of Dynamic Systems, Osijek, September 2013

**Service Activities**

- 2024. organizacija natjecanja Mathos Cup
- 2023. radionica “Space Math” u okviru Večeri matematike u III. Gimnaziji u Osijeku
- Simpozij studenata doktorskih studija PMF-a u Zagrebu, 9. veljače 2018. – postersko priopćenje
- 2017. predavanje “Svemir i matematika” u okviru tjedna svemira u III. Gimnaziji u Osijeku
- Festival znanosti:
- 2011. radionica – Primjena Sunčeve svjetlosti pri određenim izračunavanjima
- 2012. radionica – 10 u svijetu računala
- 2013. radionica – Koji broj je sljedeći?
- 2014. radionica – Brojevi u valovima
- 2016. radionica – Origami

- Zimska škola matematike:
- 2011. predavanje – Pitagorine trojke

- Pripreme studenata za natjecanje 2014./2015. (IMC)
- Pripreme studenata za natjecanje 2015./2016. (IMC)
- Pripreme studenata za natjecanje 2016./2017. (IMC)
- Pripreme studenata za natjecanje 2017./2018. (IMC)

### Teaching

**Winter semester 2024/2025**

- Obične diferencijalne jednadžbe
- Mjera i integral

**Summer semester 2024/2025**

- Kompleksna analiza (Complex analysis)
- Linearna algebra II (Linear algebra II)

**Past**

- Funkcije više varijabli (Multivariable calculus)
- Metrički prostori (Metric spaces)
- Normirani prostori (Normed spaces)
- Diferencijalne jednadžbe (Differential equations, Odjel za fiziku)
- Matematika I (Građevinski fakultet u Osijeku)
- Matematika II (Građevinski fakultet u Osijeku)
- Matematika (Poljoprivredni fakultet u Osijeku, izvanredni studij)
- Matematika (Poljoprivredni fakultet u Osijeku, stručni studij)
- Matematika I (PTF)
- Matematika III (GRAFOS)

**Konzultacije (Office Hours):** Konzultacije su moguće nakon nastave i po dogovoru.

### Personal

- Birthdate: September 29, 1989
- Birthplace: Osijek
- Family: married, one child