Numerical modeling of initial boundary value problems of mathematician physics;
Object-oriented implementation of coupled finite-boundary element approximations;
Adaptive and parallel numerical schemes of finite-boundary element analysis;
Design and implementation of databases.

The scientific advisor of five PhD’s theses:

Makar V.M. “Mathematical modeling of mechanical oscillatory processes in power semiconductor devices based on the finite element method”, 01.05.02; 1999.
Golovach N.P. “Hybrid Boundary-finite-element approximation for modeling processes thermoelasticity”, 01.05.02; 2000.
Makar I.G. “The Construct of the combined methods of boundary and finite element simulation for the modelling of deformation processes in heterogeneous environments”, 01.05.02; 2009.
Prokopyshyn I.I. “Domain decom¬position schemes on the basis of the penalty method for contact prob¬lems of elastic bodies”, 01.05.02; 2010.
Yashchuk Y.O. “Computer modeling of elasticity problems based on the new h-adaptive scheme”, 01.05.02; 2014.

• Numerical Methods of Mathematical Physics (System Analysis)

More than 170 scientific and educational publications, among them:

• Dyyak I.I., Prokopyshyn I.I., Martynyak R.M., Prokopyshyn I.A. Domain Decomposition Methods for Problems of Unilateral Contact Between Elastic Bodies with NonlinearWinkler Covers // Lecture Notes in Computational Science and Engineering. – Springer Int. Publ. Switzerland. – 2014. – p. 739-748.
• Dyyak I.I., Prokopyshyn I.I. and Yashchuk Yu.O. A Combined Algorithm of Decomposition of a Domain and h–Adaptation for the Solution of Contact Problems of Elasticity Theory // Journal of Mathematical Sciences, Vol. 174, No. 4, February, 2014. – p. 101-117.
• Dyyak I.I., Prokopyshyn I.I., Martynyak R.M., Prokopyshyn I.A. Penalty Robin-Robin Domain Decomposition Schemes for Contact Problems of Non­linear Elasticity // Lecture Notes in Computational Science and Engineering. –Springer. – 2013. – 647-654.
• Dyyak I.I., Savula Ya., Styahar A. Numerical investigation of plain strain state for a body with thin cover using domain decomposition // Journal of Numerical & Applied Mathematics. 2012, №3(109). – pp. 23-33.
• Dyyak I.I., Yashchuk Yu. Investigation of stress error estimator in elasticity problems // Contemporary problems of mathematics, mechanics and computing sciences. – Kharkov: Publishing house PPBVirovec’A.P., 2011. – 33-43
• Dyyak I.I., Prokopyshyn I.I. Domain Decomposition Schemes for Frictionless Multibody Contact Problems of Elasticity // Numerical Mathematics and Adv­aced Applications. – G. Kreiss et al. (eds), 2009. – p. 295-303.
• Dyyak I.I., Savula Y.H., Shahin M. Investigation of the Heterogeneous Problems of the Elasticity with Coupled Boundary-Finite Element Schemes // Advances in Applied and Computational Mathematics. – Nova Science Publishers, 2006. – p. 47-62
• Savula Y.H., Dyyak I.I, Krevs V.V. Heterogeneous Mathematical Models in Numerical Analysis of Structures // An Int. Journ. COMPUTERS & MATHEMATICS with applications, 42(2001). – p. 1201-1216.
• Dyyak I.I., Makar V.M., Grigorenko O.Ya. The solution of 3D dynamic problems for anisotropic cylindrical bodies: semi-analytical finite element approach // On CD-ROM, Proceed.of 2nd European Conference on Compu­tational Mechanics, Cracow, Poland, June 26-29, 2001. – 10 p.
• Savula Ya., Mang H., Dyyak I., Pauk N. Coupled boundary and finite element analysis of a special class of 2D problems of the theory of elasticity // Comput. & Struct., Vol. 75, No.2, 2000. – p. 157-165.
• Savula Ya.H., Dyyak I. D-adaptive model for the elasticity problem // Computer Assisted Mechanics & Engineering Sciences,Vol.5, No.1, 1998. – p. 65-74.

1958 – Born in Koropets, Ternopil reg.

EDUCATION
2012 – Scientific fellowship at the Wien University of Technology( Prof. H.Mang).
2008 –  Scientific fellowship at Warsaw University (Prof. S. Matysiak)
2005 – Scientific fellowship at State University of Delaware (Dover)
1995 –  Soros Associate Professor
1991 – Associate Professor
1989 – Scientific fellowship at Technical University of Brno.(Prof. M. Zlamal);
1984 – Ph D dissertation “High-precision finite element method for problems of thermoelasticity”;
1979 – 1982 – PhD program of Applied Mathematics in Ivan Franko State University of Lviv
1974 – 1989 – studied at Faculty of Applied Mathematics and Mechanics in Ivan Franko State University of Lviv;
1964 – 1974 – studied at school Zalozhtsi, Ternopil reg.

WORK
2015 – present – Dean of Faculty of Applied Mathematics and Informatics;
2014-2015 – Head of Department of Applied Mathematics;
2008-2014 – Depute Executive Secretary of the Admissions Committee;
1991-present – Associate Professor of Applied Mathematics Department;
1982-1989 – Engineer – Senior Researcher of Research Laboratory of  Lviv University.

1st semester
2nd semester