Research

 

Research interests

• Numerical methods for PDEs (finite difference method, finite element method, meshless methods, isogeometric analysis)
• Computer aided geometric design (applications in isogeometric analysis)

Publications

Refereed journal publications

1. S. Sajavičius. Radial basis function collocation method for an elliptic problem with nonlocal multipoint boundary condition. Engineering Analysis with Boundary Elements, 67, 2016, pp. 164–172. DOI: 10.1016/j.enganabound.2016.03.010
2. S. Sajavičius. Radial basis function method for a multidimensional linear elliptic equation with nonlocal boundary conditions. Computers and Mathematics with Applications, 67(7), 2014, pp. 1407–1420. DOI: 10.1016/j.camwa.2014.01.014
3. S. Sajavičius. Optimization, conditioning and accuracy of radial basis function method for partial differential equations with nonlocal boundary conditions—A case of two-dimensional Poisson equation. Engineering Analysis with Boundary Elements, 37(4), 2013, pp. 788–804. DOI: 10.1016/j.enganabound.2013.01.009
4. S. Sajavičius. Stability of the weighted splitting finite-difference scheme for a two-dimensional parabolic equation with two nonlocal integral conditions. Computers and Mathematics with Applications, 64(11), 2012, pp. 3845-3899. DOI: 10.1016/j.camwa.2012.08.009
5. S. Sajavičius. On the eigenvalue problems for differential operators with coupled boundary conditions. Nonlinear Analysis: Modelling and Control, 15(4), 2010, pp. 493-500 [PDF]
6. S. Sajavičius. On the eigenvalue problems for finite-difference operators with coupled boundary conditions. Šiauliai Mathematical Seminar, 5(13), 2010, pp. 87-100 [PDF]
7. S. Sajavičius, M. Sapagovas. Numerical analysis of the eigenvalue problem for one-dimensional differential operator with nonlocal integral conditions. Nonlinear Analysis: Modelling and Control, 14(1), 2009, pp. 115-122 [PDF]

Publications in refereed conference proceedings

1. S. Sajavičius. The splitting finite-difference scheme for two-dimensional heat conduction equation with four nonlocal integral conditions. In: CD-ROM Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Vienna, Austria, September 10–14, 2012, CD-ROM, eds. J. Eberhardsteiner, H. J. Böhm, F. G. Rammerstorfer. Vienna, Austria, Paper ID 1081, 12 p. 2012.
2. S. Sajavičius. On the stability of fully-explicit finite-difference scheme for two-dimensional parabolic equation with nonlocal conditions. In: Computational Science and Its Applications – ICCSA 2011, International Conference, Santander, Spain, June 20-23, 2011, Proceedings, Part IV. Lecture Notes in Computer Science, 6785, eds. B. Murgante, O. Gervasi, A. Iglesias, D. Taniar, B. O. Apduhan, p. 1-10. Springer-Verlag Berlin Heidelberg, 2011. DOI: 10.1007/978-3-642-21898-9_1
3. S. Sajavičius. On the stability of locally one-dimensional method for two-dimensional parabolic equation with nonlocal integral conditions. In: Proceedings of the V European Conference on Computational Fluid Dynamics (ECCOMAS CFD 2010), eds. J. C. F. Pereira, A. Pereira, J. M. C. Sequeira. Lisbon, Portugal, Paper ID 01668, 11 p., 2010.
4. S. Sajavičius. On the stability of alternating direction method for two-dimensional parabolic equation with nonlocal integral conditions. In: Proceedings of International Conference Differential Equations and Their Applications (DETA 2009), eds. V. Kleiza, S. Rutkauskas, A. Štikonas, p. 42-48. Panevėžys, 2009.

Extended abstracts

1. S. Sajavičius. The splitting finite-difference schemes for two-dimensional parabolic equation with nonlocal weighted integral conditions. In: Proceedings of ECCOMAS Thematic Conference on Computational Analysis and Optimization (ECCOMAS CAO 2011), eds. S. Repin, T. Tiihonen, T. Tuovinen, p. 81–84. Jyväskylä, Finland, 2011.
2. S. Sajavičius. The splitting finite-difference schemes for two-dimensional parabolic equation with nonlocal conditions. In: Proceedings of NSCM23: the 23rd Nordic Seminar on Computational Mechanics / Technical report 2010:07, eds. A. Eriksson, G. Tibert, p. 345-348. Stockholm, Sweden, 2010.
3. S. Sajavičius. The stability of alternating direction method for two-dimensional parabolic equation with nonlocal integral conditions. In: DCE Technical Memorandum No. 11 / Proceedings of the Twenty Second Nordic Seminar on Computational Mechanics, eds. E. Lund, L. Damkilde, A. S. Andersen, E. Kristensen, p. 87-90. Aalborg, Denmark, 2009.

Participation in international conferences

• 9th International Conference on Mathematical Methods for Curves and Surfaces (MMCS9), 23–28 June, 2016, Tønsberg, Norway
• Equadiff’13 conference, 26–30 August, 2013, Prague, Czech Republic
• Congress on Numerical Methods in Engineering (CMN 2013), 25–28 June 2013, Bilbao, Spain
• 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), 10–14 September 2012, Vienna, Austria
• International Conference on Applied Mathematics and Approximation Theory (AMAT2012), 17–20 May 2012, Ankara, Turkey
• 7th International Congress on Industrial and Applied Mathematics (ICIAM2011), 18–22 July 2011, Vancouver, BC, Canada
• 16th International Conference Mathematical Modelling and Analysis, 25–28 May 2010, Sigulda, Latvia
• 23rd Nordic Seminar on Computational Mechanics, 21–22 October, 2010, Stockholm, Sweden
• V European Conference on Computational Fluid Dynamics (ECCOMAS CFD 2010), 14–17 June, 2010, Lisbon, Portugal
• 15th International Conference Mathematical Modelling and Analysis, 26–29 May, 2010, Druskininkai, Lithuania
• 22nd Nordic Seminar on Computational Mechanics, 22–23 October, 2009, Aalborg, Denmark
• International Conference Differential Equations and Their Applications dedicated to Professor M. Sapagovas 70th anniversary, 10–12 September, 2009, Panevėžys, Lithuania
• 14th International Conference Mathematical Modelling and Analysis, 27–30 May, 2009, Daugavpils, Latvia

Projects

• MOTOR – Multi-ObjecTive design Optimization of fluid eneRgy machines(funded by European Commission through Horizon 2020 programme, project reference: 678727), since 2015
• BalticGrid-II project (funded by the EU within the framework of the 7th Framework Programme, Contract No. 223807); certificate: [PDF]
• Development of Bioelectrocatalysis for Synthesis and Analysis (BIOSA), #N–08007, Lithuanian State and Science Foundation, 2008
• Computer Simulation of the Behavior of Heterogeneous Processes and Systems (MODELITA), #C–03048, Lithuanian State and Science Foundation, 2005, 2006