## Department

# Mathematical Modelling and Numerical Analysis

The department of “Mathematical Modelling and Numerical Analysis” was created In March 2014, by merging the departments: “Mathematical Modelling”, “Computational Mathematics” and “Biomathematics”.

*Historical Notes on the Department of “Mathematical Modelling”*

The Department of Mathematical Modelling of the Institute for Mathematics and Informatics (IMI) of the Bulgarian Academy of Sciences (BAS) is the direct successor of the following units formed in the early 60’s:

- Department of Numerical Methods and Algorithms of the Institute for Mathematics with a Computing Centre of BAS;
- Chair of Computational Mathematics of the Faculty of Mathematics in the Sofia University (successor of the laboratory of Computational Mathematics at the Department for Advanced Analysis)

The Department was formed within the United Centre for Science and Education in Mathematics and Mechanics, following a Decision of the Bulgarian government “for endorsement of a new model in the education in mathematics and mechanics and integration of the activities of the Faculty of Mathematics in the Sofia University and the Institute for Mathematics with a Computing Centre of BAS”. The Department was called sector during the period of functioning of the united centers for science and education – till 1988. The following scientists entered on December 30, 1970 the new Department of Mathematical Modelling:

Acad. Blagovest Sendov, Acad. Borislav Bojanov, Corresponding member of BAS Vassil Popov, Prof. DSc Raycho Lazarov, Prof. DSc Stefka Dimova, Prof. DSc Svetoslav Markov, Prof. DSc Rumen Maleev, Prof. DSc Mihail Kaschiev, Prof. Dr Milko Petkov, Assoc. Prof. Dr Todor Boyanov, Assoc. Prof. Dr Vassil Vesselinov, Assoc. Prof. Dr Andrey Andreev, Assoc. Prof. Dr Nikolay Kyurkchiev, Assoc. Prof. Dr Evgeniya Kolarova-Sendova, Assist. Prof. Dr Mitko Tsvetanov, Assist. Prof. Dr Margarita Nikolcheva, Assist. Prof. Dr Emiliya Mateeva, Assist. Prof. Teodora Kirpikova-Jukanova, Assist. Prof. Mara Apostolova.

As of 1 January 2013 the Department of Mathematical Modelling consists of:

Prof. DSc Kamen Ivanov (head of the Department), Prof. DSc Pencho Petrushev, Prof. Dr Nikolay Kyurkchiev, Prof. Assoc. Prof. Dr Andrey Andreev, Assoc. Prof. Dr Vladimir Hristov, Assoc. Prof. Dr Ognyan Trifonov, Assoc. Prof. Dr Borislav Draganov, Assist. Prof. Dr Irina Georgieva, Daniela Stoyanova.

Two temporary groups existed in the Department of Mathematical Modelling till 1995, namely, a temporary problem group on mathematical modelling of the gravity impact of the Sun and the Moon on the Earth with staff Prof. DSc Ivan Ivanov, Assist. Prof. Petar Dabnishki, and Assist. Prof. Dimitar Dimitrov; Laboratory for Mathematical Chemistry and Chemical Informatics with staff Assoc. Prof. DSc Daniel Bonchev, Assist. Prof. Ivan Bangov.

Members of the Department of Mathematical Modelling were also:

Prof. DSc Ivan Dimov, Prof. DSc Ralitsa Kovacheva, DSc Lili Popova, Assoc. Prof. Dr Georgi Iliev, Assoc. Prof. Dr Spas Tashev, Assoc. Prof. Dr Nataliya Kolkovska, Assoc. Prof. Dr Denka Kutzarova, Assoc. Prof. Dr Tatyana Chernogorova, Assist. Prof. Dr Nikola Naydenov, Assoc. Prof. Dr Panayot Vassilevski, Assist. Prof. Dr Nikola Vladov, Assist. Prof. Dr Milena Moskova, Assist. Prof. Dr Hristo Jijev, Assist. Prof. Angelina Yotova, Assist. Prof. Nikolay Bankov, Assist. Prof. Petar Shopov, Veselin Kyurkchiev, Krasimira Popova, Maksim Chilev, Yanko Chernev.

Several new groups working in closely related mathematical fields originated from Department of Mathematical Modelling. Departments of Numerical methods and Biomathematics of IMI-BAS separated from Department of Mathematical Modelling. Essential parts of the founders of Institute for Parallel Processing of BAS and the Chair of Numerical Methods and Algorithms of the Faculty of Mathematics in the Sofia University were former members of the Department too.

Consecutive heads of Department of Mathematical Modelling are Acad. Blagovest Sendov, Prof. DSc Racho Denchev, Prof. DSc Pencho Petrushev, Assoc. Prof. Dr Vladimir Hristov, Prof. DSc Kamen Ivanov and Prof. Dr Nikolay Kyurkchiev.

The main field of research is the development of mathematical models in astronomy, biology, economics, medicine, fusion synthesis, chemistry. The Bulgarian school in approximation theory was founded and developed as a part of Department of Mathematical Modelling under the leadership of Acad. Bl. Sendov. Other fields of research are numerical analysis, numerical methods for solving differential and integral equations, functional analysis and analytic number theory.

The members of Depatment of Mathematical Modelling are also active as lecturers in a number of domestic and foreign universities. More than 120 PhD dissertations were prepared and defended under the supervision of staff of the Deparment. The Department was the main organizer of the international conferences Constructive Function Theory held in 1971, 1977, 1981, 1984, 1987, 1991, 2002, 2005, 20010, and 2013.

The international recognition of the mathematical results of the school in approximation theory resulted in the only prize for young scientists working in the field – the Vassil A. Popov prize. The prize is awarded by an international committee every third year. It was won by 5 different mathematicians from France, Belgium and the USA. The state Dimitrov Prize was awarded to academician Blagovest Sendov and corresponding member of BAS Vassil Popov, as the later is also a winner of the Nikola Obrechkoff Prize for remarkable achievements in the field of mathematics.

The old site of the department here.

*Historical Notes on the Department of “Computational Mathematics”*

The former Laboratory of Numerical Methods (presently Department of Computational Mathematics) was created in 1987 by some members of the Department of Mathematical Modelling. The aim was to further strengthen the direction of numerical methods for PDEs as the most important component in mathematical modelling as a research tool and means for industrial applications. Prof. Raytcho Lazarov was appointed for its Head and the first members were: Michail Kaschiev, Stefka Dimova, Ivan Dimov, Natalia Kolkovska, Oleg Iliev, Panayot Vassilevski, Tatyana Chernogorova and Angelina Yotova.

Further heads were Prof. Michail Kaschiev (1991-2004) and Assoc. Prof. Natalia Kolkovska (2004-2012). The scientific staff grew by Petar Shopov, Tanya Kostova-Vassilevska, Atanas Pehlivanov, Ivan Bazhlekov, Ludmil Zikatanov, Milena Dimova, Daniela Vasileva, Mariana Nikolova, Pavlin Entchev, Galin Dimitrov, Ivan Georgiev, Stanislava Stoilova.

Main fields of research are in the area of efficient numerical methods and algorithms for solving linear and nonlinear partial differential and integral equations and systems. Important results are obtained about the construction, stability and convergence analysis for finite element, finite difference and finite volume approximations; the construction and analysis of iterative methods, domain decomposition, a posteriori error control and adaptive grid refinement. The numerical methods and algorithms are applied in mathematical modelling and computer simulation of physical, engineering, environmental and other problems.

A number of applied projects were developed in collaboration with Institute of Metallurgy and Metal Sciences, Institute of Microelectronics, Sofia Technical University, Joint Institute for Nuclear Research (Dubna, Russia), Institute of Mathematical Modelling of Russian Academy of Sciences, Texas A&M University, Darmstadt University of Technology (Germany), Institute of Science and Technology of University of Manchester, the Engineering department of Queen Mary College (University of London), Fraunhofer Institute for Industrial Mathematics (Kaiserslautern, Germany).

The department was involved in the organization of six international conferences on Numerical Methods and Applications in Sofia and Borovets. Members of the department participate in the projects:

- Numerical and Analytical Tools for Localized Solutions of Generalized Wave Equations in Multidimension, Bulgarian Science Fund, 2011-2014.
- Mathematical modelling of nonlinear systems on multiprocessor clusters, Bulgarian State Agency for Atomic Regulation, 2011-2013.
- Efficient mu1tilevel methods and algorithms for problems with heterogeneous coefficients, Bulgarian Science Fund, 2012-2014.

The old site of the department here.

*Historical Notes on the Department of “Biomathematics”*

Section “Biomathematics” of IMI-BAS is successor of the former Research group on “Mathematical Modelling in Biology” within the Center of Biology at BAS (1977-1989) and the Institute of Biophysics at BAS (1990-1996). In 1996 the group was included in the IMI at BAS as a department on Biomathematics.

Research area: Biomathematics (mathematical modelling in biology, mathematical biology) with an emphasis on mathematical modelling in ecology, neurophysiology, microbiology, enzyme kinetics, botany, paleology, etc. Developed are numerical methods and tools for mathematical modelling under uncertainties. Related mathematical fields: error analysis, reliable computing, set-valued, convex and interval analysis, numerical methods with verification, controlability of dynamical systems, parameter identification under interval data, computer arithmetic, etc.