# Alexander Andreevich Samarskii

### Quick Info

Amvrosiivka, Donetsk, Ukraine

Moscow, Russia

**Alexander Andreevich Samarskii**was a Ukranian-born mathematician who worked in mathematical physics, applied mathematics, numerical analysis and mathematical modelling.

### Biography

**Alexander Andreevich Samarskii**was the youngest child of Andrei Efimovich Samarskii. Sadly he never knew his mother who died when he was one year old. His older sister, Anastasia Andreevna Samarskaya, played a large role in bringing up Alexander Andreevich. Andrei Efimovich was a peasant who worked hard farming at Novo-Ivanovskoye in the Amvrosiivka region and had many other skills which he used to help provide a living for his family. However, times were difficult in Ukraine for the peasants. Beginning in 1928 special measures were introduced against peasants as the country moved to industrialisation. Taxes were increased and, by the 1930s, peasants were dispossessed of all property. Farms were collectivised which led to mass resistance in the form of revolts which in turn led to even harsher conditions being imposed. The Samarskii family were forced to leave their farm and went first to Donetsk and then to Taganrog, the birthplace of the famous author Anton Chekhov. Alexander Andreevich's father lived apart from the family and Alexander Andreevich was looked after by his sister Anastasia Andreevna Samarskaya.

At the age of 14, Samarskii entered the Anton Chekhov school in Taganrog. This was the school which Anton Chekhov had attended and it was by this time named after him. Perhaps not surprisingly, the school had a strong reputation for literature and Samarskii was attracted to this as well as to mathematics and physics. He wrote poetry and decided that he should follow a literary career and enrol in the Institute of Philosophy, Literature and History. However, his teachers of mathematics and physics made it plain to him that his talents lay in these areas and insisted that he follow a course in mathematics and physics at university. He took their advice and, after graduating from the Anton Chekhov School in 1936, entered the Faculty of Physics and Mathematics at the Moscow State University.

When Samarskii began his university studies he was 17 years old and went to live in Moscow were he had no friends or family. He devoted all his efforts to studying but he had a problem since he did not have financial support to allow him to meet the basic needs of living, namely food and clothing. He was forced, therefore, to take a year out from his studies during which he made money from tutoring. Living as frugally as possible he was able to build up sufficient funds to be able to continue his studies after the year.

Andrei Nikolaevich Tikhonov was appointed as a professor at Moscow State University in 1936 following his defence of his habilitation thesis

*Functional equations of Volterra type and their applications to mathematical physics.*In 1939, the year World War II began, Samarskii began studying in Tikhonov's seminar. The Molotov-Ribbentrop non-aggression pact between Germany and the Soviet Union meant that initially the war had little effect on life in Moscow and Samarskii continued his studies there. However, things changed dramatically on 22 June 1941 when Germany broke the non-aggression pact and invaded the Soviet Union. As a student, Samarskii could have avoided military service but on 6 July he submitted an application to join the military feeling that the most important thing was defending his homeland. Despite having no military experience and having eyesight problems which should have prevented him taking part in active service, he was assigned to the 8th Krasnopresnenskaya Peoples' Militia Rifle Division commanded by the Moscow Military District.

After working on the construction of defensive lines, the Division became part of the 32nd Army and, in August, took up positions on the Rzhev-Vyazma defensive lines. After the German offensive, named Operation Typhoon, aimed at taking Moscow, began in October Samarskii was part of the Division that moved east of Yelnya to engage the German advance. Fighting on the 4th and 5th of October was fierce and half the men in the Division were killed. Samarskii, however, survived and went to join those defending Naro-Fominsk. This town, about 70 km southwest of Moscow, fell to the Germans on 21 October. With the Rifle Division destroyed, Samarskii joined the 108th Infantry Division.

A second assault by the Germans on Moscow began on 13 November. The Germans advanced to within 25 km of the centre of Moscow but the Russian defences held out. On 5 December the Russians began a counter-attack to the north and, on the following day towards the south. Samarskii was with those in the south and he was given the task of acting as a scout behind the German lines. On 12 December he stood on a mine which exploded and somehow his colleagues managed to carry him back behind their own lines. The Russian advance was successful and by January 1942 Moscow was no longer in danger. Samarskii saw none of this, however, for he was in hospital for nine months, enduring many operations which removed 30 bomb fragments from his body. He had been transferred round several different hospitals during this time, in Moscow, Gorky, Krasnoyarsk, and Minusinsk. Eight fragments remained which the medical people were unable to remove. He remained in hospital until September 1942 when he was discharged. He was still on crutches when he finally left the hospital in Khakassia.

Samarskii's family had remained in Taganrog but he could not return there since it was occupied by the Germans. Although by this time Moscow was not being threatened by the Germans, the University of Moscow had been evacuated to Tashkent in Uzbekistan. He was sent to teach mathematics in a school in the Krasnoyarsk region where he had ended up after being a patient in several hospitals. He taught for over a year and during this time he corresponded with one of his friends who was studying at the Military Academy in Moscow. This friend went to the University, now back in Moscow, and arranged for Samarskii to return there to complete his studies. By December 1943 he was back in Moscow working again with Andrei Nikolaevich Tikhonov. Samarskii said [5]:-

I attended many seminars and wanted to learn much science. I was active and curious, and because of that many professors had asked me to study with them. But fortunately I chose Tikhonov. He was young, adventurous and extremely talented.Samarskii undertook research on mathematics and theoretical physics and Tikhonov suggested that he might try to do some experimental physics. Samarskii said [6]:-

The teacher's word is the law! I hobbled on my crutches into the laboratory and immediately hated this field of physics. I returned to theoretical work.In 1945, having completed research for his candidate's degree (equivalent to a Ph.D.), he was examined and offered the degree. However, Tikhonov advised him not to graduate since if he did so, being a foreigner, he would have been required to leave Moscow. However, if he decided not to graduate, he would be able to remain in Moscow working towards his doctorate (equivalent to a D.Sc. or habilitation in standard). Samarskii took Tikhonov's advice and during the next three years he published around 20 papers. He was awarded his candidate's degree in 1948 for his dissertation which [2]:-

... was small, about 20 pages of introduction and 20 of content, and was about the study of the perturbation of the discrete spectrum of the Laplace operator with the change of the boundary. This problem arose in connection with some models of the atom.His thesis examiner had been Ivan Georgievich Petrovsky.

On 10 July 1948, laboratory number 8 of the Geophysical Institute of the USSR Academy of Sciences was created with Tikhonov as the head and Samarskii as a leading researcher. This laboratory was involved in carrying out numerical calculations and a staff of around 30 young women were employed as computers. In addition to this position, Samarskii was employed as a lecturer in the Mathematics Department at the Moscow State University where he taught mathematical physics. Much of Samarskii's research at this time involved numerical techniques to solve problems associated with the Soviet atomic weapons programme [1]:-

In those years Samarskii, together with A N Tikhonov, wrote a series of papers on electrodynamics and the excitation of electromagnetic waves in waveguides. In 1949, a direct numerical analysis of the nuclear explosion was performed for the first time under the supervision of Tikhonov and Samarskii; later, their scientific group computed the explosion dynamics of the thermonuclear bomb. That was the time of rapid development of computers and computational mathematics. It was at this time that Samarskii began to work actively in the field of finite-difference schemes and created a scientific school in this direction. Samarskii became one of the leading world authorities in the theory of finite-difference schemes.Igor Tamm, Andrei Sakharov and Yakov Zeldovich were the main physicists working on the bomb and they would come to Samarskii and his fellow mathematicians and computers to seek mathematical solutions to their physical problems. One of the major advances made by Samarskii in the atomic weapons programme was to discover a method to allow parallel calculations by the 30 girl computers. The problem to be solved consisted of several hundred partial differential equations. At the time this was thought to be impossible but Samarskii developed an approach based on finite difference schemes. He then divided up the problem in such a way that each of the girl computers had about 10 equations to solve and they had to pass their data to each other as they progressed the calculations. These were not hand calculations but rather done using adding machines and electromechanical calculators. By doing parallel calculations, the problem was solved about 15 times quicker than it would have been had this method not been used and the solution was completed in two months. Of course the research Samarskii did on the atomic bomb project was classified and he worked on this until about 1980, writing around 500 classified papers. However, when there were celebrations on the 50th anniversary of the first atomic bomb test, Samarskii was not invited. In the interview [5] he said that he was offended not to have been invited. He was sad that people seemed to have forgotten the role played by his laboratory in the project. He said:-

... still we cannot forget the role of the people who made the first calculations of the atomic bomb.He explained that, as a mathematician, the specific problems he was told to solve were less important that finding general methods of solution [5]:-

Mathematicians explore fundamental problems ... At first, it was different - we were required to answer a specific question, but because it is not possible to get anything new from specific problems, therefore I, of course, was interested in global issues. It's just fun!In 1951 Tikhonov and Samarskii published

*Equations of mathematical physics*(Russian). An English translation of this book appeared in 1963. We note that this book went through many editions and was translated into 13 different languages. You can read extracts from a review of both the Russian and the English editions at THIS LINK.

In 1953 Mstislav Vsevolodovich Keldysh was appointed as the first director of the newly created Institute of Applied Mathematics of USSR Academy of Sciences. Tikhonov was appointed as deputy director and Samarskii became the head of the largest department. He continued teaching at Moscow State University so at this time he had a number of different positions. He was awarded a Stalin prize in 1954. In 1957 he defended his doctoral thesis (equivalent to the D.Sc. or habilitation in standard) at the Institute of Applied Mathematics. The thesis was around 800 pages long and dealt with finite-difference methods for solving nonlinear problems in mathematical physics. In the following year he became a professor. A summary of his contributions to mathematics, particularly to computational methods in applied mathematics, is given in [1]:-

Alexander Andreevich Samarskii, an outstanding Russian mathematician, is considered a supreme authority in computational mathematics and mathematical modelling. His scientific interests included mathematical physics, numerical simulation of complex nonlinear systems and phenomena, and finite-difference methods. Samarskii was the author of the principal results in the theory of differential equations with smooth and discontinuous coefficients and the theory of nonlinear equations; he posed and studied a number of nonclassical problems in mathematical physics. The scientific activity of Aleksander Samarskii typically involved the stating of problems related to numerical experiments performed on modern computers, the development of the theory of mathematical and numerical simulation of complex physical processes, and the devising of efficient finite-difference methods.He has a remarkable list of textbooks and monographs and he said in the interview [5]:-

I'm a kind of a champion in the number of books in the field of computational mathematics.For short extracts from reviews of some of these books see THIS LINK.

Samarskii was honoured for his contributions with the award of the Lenin Prize in 1962. His outstanding contributions were recognised with his election to corresponding member of the USSR Academy of Sciences in 1966 and, ten years later, to full membership. Further recognition came with the award of the title Hero of Socialist Labour in 1979.

In 1982 Samarskii was appointed as head of the department of Computational Methods in the Faculty of Computational Mathematics and Cybernetics. Four years later he founded the National Institute of Mathematical Modelling as part of the USSR Academy of Sciences and he was appointed as its first director. He held this position until 1998. He undertook various editorial duties, was appointed Editor-in-Chief of the journal

*Mathematical Modelling*(Russian) and served on the editorial boards of the

*Journal of Computational Mathematics and Mathematical Physics*(Russian), and

*Surveys on Mathematics for Industry*, and

*Mathematical and Computer Modelling*.

Let us quote from [1] again regarding his scientific contributions:-

Of Samarskii's papers on mathematical physics and differential equations, we distinguish the brilliant work on nonclassical problems for partial differential equations and a large cycle of papers on the theory of nonlinear equations of mathematical physics that model peaking regimes. He also developed new analytical and numerical methods for studying the nonlinear stage of the processes proceeding in the peaking regime (approximate self-similar solutions, linearization of solutions and matching them with the asymptotics, and operator comparison methods), the averaging method, and a method for the investigation of group-invariant solutions of quasi-linear parabolic and nonlinear elliptic problems. These theoretical investigations made it possible to predict new phenomena such as inertia of heat and combustion and the localization of diffusion processes. Samarskii was the first to study the diffusion chaos phenomena.Samarskii was married to a medical doctor from Uzbek whose father was an expert in mechanics and a member of the USSR Academy of Sciences.

We have already mentioned some honours which were given to Samarskii. Let us mention a few more. He received three Orders of Lenin (1954, 1956 and 1979), the Order of the Patriotic War 1st degree (1985), to honour his contributions in World War II, and Laureate of the State Prize in Science and Technology (1999). He received an honorary doctorates from the Technical University of Chemnitz (Germany), Tbilisi University (Georgia), and Taganrog University (South Russia). As well as the USSR Academy of Sciences, he was elected to the academies of Byelorussia and of Ukraine. In June 2014 an International Scientific Conference dedicated to his memory was held at Moscow State University.

Samarskii died following a long and difficult illness. He was buried in Troekurov cemetery in Moscow.

### References (show)

- Alexander Samarskii,
*Computational Methods in Applied Mathematics***9**(1) (2009), 3-4. - Biography of Academician A A Samarskii. http://samarskii.ru/en/biografiya
- D A Conrad, Review: Equations of mathematical physics, by A N Tikhonov and A A Samarskii,
*American Scientist***52**(4) (1964), 456A. - I P Grant, Review: A Collection of Problems on Mathematical Physics, by B M Budak, A A Samarskii and A N Tikhonov,
*The Mathematical Gazette***51**(376) (1967), 184-185. - V Gubarev, Interview with Academician A A Samarskii. A Cup of Tea at the Academy of Sciences,
*Literary Gazette*(October 2001). - M K Kerimov, On the 85th Birthday of Academician Alexander Andreevich Samarskii (Russian),
*Zh. Vychisl. Mat. Mat. Fiz.*,**44**(10) (2004), 1723-1725 . - M K Kerimov, On the 85th Birthday of Academician Alexander Andreevich Samarskii,
*Computational Mathematics and Mathematical Physics***44**(10) (2004), 1637-1639. - H Levine, Review: Blow-up in Quasilinear Parabolic Equations, by A A Samarskii, V A Galaktionov, S P Kurdyumov and A P Mikhailov,
*SIAM Review***38**(4) (1996), 692-694. - Z Leyk, Review: Numerical Methods for Grid Equations, by A A Samarskii and E S Nikolaev,
*Mathematics of Computation***55**(192) (1990), 867-868. - J Lorenz, Review: Difference Schemes with Operator Factors, by A A Samarskii, P P Matus and P N Vabishchevich,
*SIAM Review***46**(4) (2004), 752-753. - F Steinhardt, Review: A Collection of Problems on Mathematical Physics, by B M Budak, A A Samarskii and A N Tikhonov,
*Amer. Math. Monthly***75**(1) (1968), 99.

### Additional Resources (show)

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Written by J J O'Connor and E F Robertson

Last Update July 2015

Last Update July 2015