Boris Galerkin
Encyclopedia
Boris Grigoryevich Galerkin ' onMouseout='HidePop("56903")' href="/topics/Romanization">romanized
Romanization
In linguistics, romanization or latinization is the representation of a written word or spoken speech with the Roman script, or a system for doing so, where the original word or language uses a different writing system . Methods of romanization include transliteration, for representing written...

 as Galyorkin; – July 12, 1945), born in Polozk, Belarus
Belarus
Belarus , officially the Republic of Belarus, is a landlocked country in Eastern Europe, bordered clockwise by Russia to the northeast, Ukraine to the south, Poland to the west, and Lithuania and Latvia to the northwest. Its capital is Minsk; other major cities include Brest, Grodno , Gomel ,...

, Russian Empire
Russian Empire
The Russian Empire was a state that existed from 1721 until the Russian Revolution of 1917. It was the successor to the Tsardom of Russia and the predecessor of the Soviet Union...

 was a Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...

n/Soviet mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 and an engineer
Engineer
An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...

.

Early days

Galerkin was born on in Polotsk, Russian Empire
Russian Empire
The Russian Empire was a state that existed from 1721 until the Russian Revolution of 1917. It was the successor to the Tsardom of Russia and the predecessor of the Soviet Union...

, now part of Belarus
Belarus
Belarus , officially the Republic of Belarus, is a landlocked country in Eastern Europe, bordered clockwise by Russia to the northeast, Ukraine to the south, Poland to the west, and Lithuania and Latvia to the northwest. Its capital is Minsk; other major cities include Brest, Grodno , Gomel ,...

. His parents owned a house in the town, but the homecraft they made did not bring enough money, so at the age of 12, Boris started working as calligrapher in the court. He had finished school in Polotsk, but still needed the exams from an additional year which granted him the right to continue education at a higher level. He passed those in Minsk
Minsk
- Ecological situation :The ecological situation is monitored by Republican Center of Radioactive and Environmental Control .During 2003–2008 the overall weight of contaminants increased from 186,000 to 247,400 tons. The change of gas as industrial fuel to mazut for financial reasons has worsened...

 in 1893, as an external student. The same year he was enrolled at the St. Petersburg Technological Institute, at the mechanics department. Due to the lack of funds Boris Grigoryevich had to combine studying at the institute with working as a draftsman and giving private lessons.

Political activities and imprisonment

Like many other students/technologists, he was involved in political activities, and joined the social-democratic group. In 1899, the year of graduating from the institute, he became a member of the Russian Social-Democratic Party (future Communist Party
Communist party
A political party described as a Communist party includes those that advocate the application of the social principles of communism through a communist form of government...

). This provides a plausible explanation for his frequent job changes. The first three years after graduation Boris Grigoryevich was an engineer at the Russian Mechanical and Steam-locomotive Union factory in Kharkov, while simultaneously teaching workers at special courses. From the end of 1903 he was an engineer on the construction of the China Far East Railway
China Far East Railway
The Chinese Eastern Railway or was a railway in northeastern China . It connected Chita and the Russian Far East. English-speakers have sometimes referred to this line as the Manchurian Railway...

, half a year later he became the technical head at the 'North mechanical and boiler factory' . He participated in organizing the Union of Engineers in St. Petersburg and, in 1905 he was arrested for organizing a strike among the engineers. In 1906, Boris Grigoryevich became a member of the Social-Democratic Party's St. Petersburg Committee and did not work anywhere else.

On the police surrounded his house No.13 in Alexeyevskaya Street, not far from Udelnaya railway station and arrested almost everyone of the Committee members. On , the St. Petersburg Court Chamber passed a sentence, which was surprisingly light, taken into account that at the moment of arrest some of the Committee members fired at policemen. One of the 19 Committee members was imprisoned for two years, 8, including B.G.Galerkin (or "Zakhar", according to his underground nickname) - for 1.5 years, others were discharged.

In prison, known under the name "Kresty", Boris Grigoryevich has lost interest to revolutionary activities and devoted himself to science and engineering. Prison conditions of that time were giving such opportunities. And what is more, in his work-book it is written that Boris Grigoryevich worked as an engineer at designing and constructing the boiler power plant from 1907. This fact was not explained, and Boris Grigoryevich did not like to remind others about his revolutionary youth. Later, in Soviet questionnaires he would not give clear answers on the persistent questions about membership in different parties. Of course, he was familiar with the fate of old Party members, but the main reason for it was that he had been elected to the Committee from the Mensheviks (a Party group with non-radical views, which members later were accused of contra-revolutionary activities and repressed). Galerkin's life could become the price if this fact became known to the public.

Academic

Same year his first scientific work was published by the institutes "Transactions". The article was titled "A theory of longitudinal curving and an experience of longitudinal curving theory application to many-storied frames, frames with rigid junctions and frame systems". The length of the title was indicative of the length of the work itself, 130 pages. It was written in the "Kresty" prison. In the summer of 1909 Boris Grigoryevich had a trip abroad to see constructions and buildings which interested him. During the next four years, i.e., before World War I, he, as well as many other institute staff, visited Europe to stimulate their scientific interests. Galerkin visited Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...

, Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...

, Switzerland
Switzerland
Switzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....

, Belgium
Belgium
Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...

 and Sweden
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....

.

Galerkin taught students at the mechanical department structural mechanics, i.e., conducted exercises and designing. The lecturer was professor V.L.Kirpichov - a famous scientist in the field of mechanics and per se the head of the Petersburg mechanical scientific school. However, most members also worked in the Polytechnical Institute
Saint Petersburg Polytechnical University
Saint Petersburg State Polytechnical University is a major Russian technical university situated in Saint Petersburg. Previously it was known as the Peter the Great Polytechnical Institute and Kalinin Polytechnical Institute .-Imperial Russia:...

, for example: I.G. Bubnov, A.N. Krylov, I.V. Meshcherskiy and S.P. Timoshenko.

From autumn 1911, Galerkin also worked at the Women's Polytechnical Institute. In 1913 he worked with the design of the metallic frame for a boiler power plant in St. Petersburg - the first building with metallic frame under big loads in Russia. Later it was considered to be one of the unique European engineering objects. Galerkin regularly published his works in the institutes "Transactions", and since 1915 - also in Engineering News
Engineering News
Engineering News may refer to* Engineering News , a weekly publication in South Africa* Engineering News-Record, a weekly magazine published by The McGraw-Hill Companies...

. Before 1915 pivot systems were at the center of his scientific interest, later he started researching plates.

In 1915 Galerkin published an article, in which he put forward an idea of an approximate method for differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...

s, in particular boundary value problem
Boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional restraints, called the boundary conditions...

s. He had applied his method to a big number of pivot and plate
Plate theory
In continuum mechanics, plate theories are mathematical descriptions of the mechanics of flat plates that draws on the theory of beams. Plates are defined as plane structural elements with a small thickness compared to the planar dimensions . The typical thickness to width ratio of a plate...

 analysis problems. Some time before I.G.Bubnov developed a similar approach for the variational problem
Calculus of variations
Calculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...

 solution, which he interpreted as a variant of Ritz method
Ritz method
The Ritz method is a direct method to find an approximate solution for boundary value problems. The method is named after Walter Ritz.In quantum mechanics, a system of particles can be described in terms of an "energy functional" or Hamiltonian, which will measure the energy of any proposed...

 algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

. The distinguishing features of Galerkin's method were the following: he did not associate the method, developed by him, with any variational problem direct solution, but considered it to be common for solving differential equations. He interpreted it, using the probable displacements principle. These ideas showed to be very productive, not only in structural mechanics
Structural mechanics
Structural mechanics or Mechanics of structures is the computation of deformations, deflections, and internal forces or stresses within structures, either for design or for performance evaluation of existing structures. It is one subset of structural analysis...

, but for mathematical physics
Mathematical physics
Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...

 at large.

The Galerkin method
Galerkin method
In mathematics, in the area of numerical analysis, Galerkin methods are a class of methods for converting a continuous operator problem to a discrete problem. In principle, it is the equivalent of applying the method of variation of parameters to a function space, by converting the equation to a...

 (or Bubnov-Galerkin method) with Galerkin's (or "weak
Weak formulation
Weak formulations are an important tool for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations...

") differential equations problem statement form are known all over the world. Nowadays they provide a foundation for algorithms in the fields of mechanics
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....

, thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...

, electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

, hydrodynamics and many others.

In January 1919, Galerkin became a professor in the 2nd (formerly Women's) Polytechnical Institute, remaining a teacher of structural mechanics in the 1st Polytechnical Institute (at that time the Polytechnical Institute was named so) mechanical department. In March 1920, a professor chair in structural mechanics was established at the department, and Boris Grigoryevich won it in a competition. In Summer 1921, S.P. Belzetskiy, a famous scientist in the field of structural mechanics and theory of elasticity, who was holding a similar chair at the civil engineering
Civil engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works like roads, bridges, canals, dams, and buildings...

 faculty, emigrated to Poland
Poland
Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...

. Galerkin took part in a competition for his chair and in the beginning of 1922 he left the mechanical faculty for the civil engineering faculty, which was nearer to him in his scientific and engineering activities.

However his talent at that time was not wanted by anyone and he could concentrate his attention towards scientific problems. Before, in 1917-1919 Galerkin published a series of works on rectangular and triangular plates curving in scientific periodicals, mentioned above, and in the "Russian Academy of Sciences Transactions". Later he had a break in publications, and only in 1922 he began publishing again, but only in foreign magazines (in Soviet Russia
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....

 there was not enough paper for scientific literature).

In December 1923 Galerkin was elected dean
Dean (education)
In academic administration, a dean is a person with significant authority over a specific academic unit, or over a specific area of concern, or both...

 of the Polytechnical Institutes civil engineering faculty. It happened during a very important period of the institute's history, when a group of deans resigned from their posts, protesting from unceremonious intervention of so called "student' representatives", controlled by the trade-unions and the Communist party committees, into the educational process. Galerkin showed to be a talented leader of the faculty. He managed to neutralize too active "assistants", who were appointed against his will, and he did not hurry to fulfill the orders of incompetent leaders, who were conducting infinite experiments in the higher school at that time. In 1924 - 1929 Galerkin was also a professor in the Railway Engineers Institute and in the St. Petersburg University. In 1924 he made his last trip abroad - he participated in the Congress on applied mechanics in the Netherlands
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...

.

In spring 1926 Galerkin learned that Narkompros (Ministry of education) had adopted a decision to close the road-making section at his faculty. This decision was prepared and adopted secretly from the dean by the institute Communist party committee in the connection with the company on elimination of parallel specialities. Meanwhile, there were no other faculties in the country, training specialists in the construction of electrified railways, urban railways and subways (the faculty had worked on this since 1907). Galerkin managed to cancel this rash decision by Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...

. During the period of Galerkin at the dean post, the first laboratory at the faculty was created. He also managed to receive governmental approval of the idea to built some other big laboratories for the faculty (the Hydrotechnical Research Institute was later established on their base).

In January 1928 Galerkin was appointed as a corresponding member-elected at the USSR Academy of sciences. His candidature was nominated by academicians A.F. Yoffe (Abram Ioffe
Abram Ioffe
Abram Fedorovich Ioffe was a prominent Russian/Soviet physicist. He received the Stalin Prize , the Lenin Prize , and the Hero of Socialist Labor . Ioffe was an expert in electromagnetism, radiology, crystals, high-impact physics, thermoelectricity and photoelectricity...

), A.N. Krylov, P.P. Lazarev. In October 1929 he left the dean's post. After this the civil engineering faculty was divided into two parts: the hydrotechnical
Hydromechanics
The history of fluid mechanics, the study of how fluids move and the forces on them, dates back to the Ancient Greeks.-Archimedes:The fundamental principles of hydrostatics were given by Archimedes in his work On Floating Bodies, around 250 BC. In it, Archimedes develops the law of buoyancy, also...

 and irrigation
Irrigation
Irrigation may be defined as the science of artificial application of water to the land or soil. It is used to assist in the growing of agricultural crops, maintenance of landscapes, and revegetation of disturbed soils in dry areas and during periods of inadequate rainfall...

 sections became the water industry
Water industry
The water industry provides drinking water and wastewater services to residential, commercial, and industrial sectors of the economy. The water industry includes manufacturers and suppliers of bottled water...

 faculty, and the rest that became a part of the civil engineering faculty. was soon left out of the Polytechnical Institute and became the Civil and Industrial Engineering Institute, which however does not exist anymore. The water industry
Water industry
The water industry provides drinking water and wastewater services to residential, commercial, and industrial sectors of the economy. The water industry includes manufacturers and suppliers of bottled water...

 faculty soon became the Hydrotechnical institute. Galerkin was a professor at both institutes.

By the 1920s, Galerkin was already a world-famous scientist. He had had become an authority among engineers-designers. He was often recruited as a consultant to the designing and construction of serious industrial objects in the north-west Russia (heat power plants, Volkhov hydro power plant, Kondopoga
Kondopoga
Kondopoga is a town and the administrative center of Kondopozhsky District of the Republic of Karelia, Russia, situated on the coast of the Kondopozhskaya Gulf of Lake Onega, near the mouth of the Suna River and Kivach Nature Reserve, about from Petrozavodsk...

 pulp
Pulp mill
A pulp mill is a manufacturing facility that converts wood chips or other plant fibre source into a thick fibre board which can be shipped to a paper mill for further processing. Pulp can be manufactured using mechanical, semi-chemical or fully chemical methods...

 and paper mill
Paper mill
A paper mill is a factory devoted to making paper from vegetable fibres such as wood pulp, old rags and other ingredients using a Fourdrinier machine or other type of paper machine.- History :...

 and others). He was a member of the technical Councils of the designing institutes Gipromez and Giprotsvetmet, a member of the academic councils in the research institutes: Irrigation Institute (later - Hydrotechnical Research Institute), Institute of Structures. After the end of the Dnieper Hydroelectric Station
Dnieper Hydroelectric Station
The Dnieper Hydroelectric Station is the largest hydroelectric power station on the Dnieper River, placed in Zaporizhia, Ukraine.- Early Plans :In the lower current of the Dnieper River there were almost 100 km long part of the river filled with rapids...

 construction Boris Grigoryevich also became a member of the governmental commission.

In 1934, Galerkin got two doctoral degrees in technics
Technics
Technics may refer to:* Technics turntables, no longer in production.* Technics , a brand name of the Panasonic Corporation* An anglicization of the Ancient Greek term techne, used primarily in media theory...

 and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 and the Honoured Worker in Science and Engineering title. In the beginning of 1936 he was elected a member of the USSR Academy of sciences. He also became a member of the highest Certifying Commission in the State Committee on higher technical education, a chairman of the technical mechanics group in the USSR Academy of sciences technical section, the headmaster of the USSR Academy of sciences Institute of Mechanics, the chairman of the Civil engineers scientific society and its Leningrad
Saint Petersburg
Saint Petersburg is a city and a federal subject of Russia located on the Neva River at the head of the Gulf of Finland on the Baltic Sea...

 section. In April 1936 according to a governmental order Galerkin was appointed chairman of the Governmental Commission for the examination of the Moscow Palace of Soviets
Palace of Soviets
The Palace of the Soviets was a project to construct an administrative center and a congress hall in Moscow, Russia, near the Kremlin, on the site of the demolished Cathedral of Christ the Saviour...

 steel frame walls and overlappings initial project.

Though having so many titles, Galerkin remained a professor of the structural mechanics and theory of elasticity department at the hydrotechnical faculty (the Hydrotechnical Institute was returned to the Polytechnical
Institute of technology
Institute of technology is a designation employed in a wide range of learning institutions awarding different types of degrees and operating often at variable levels of the educational system...

 (at that time - Industrial) Institute as a faculty in 1934). Mostly he taught the course of the theory of elasticity, which was very difficult for the students of that time, who had a very weak training in mathematics. Students were visiting his lectures to look at the "real academician", but he disappointed them. He was short, puny, had a weak voice. His image did not correspond to the status of serious scientist with big authority, received from the government. At one time the academician was even pulled out of a tram by other well-grown passengers, and after this "accident" the institute administration applied to the authorities for a car.

War times and death

Galerkin drew in general
General
A general officer is an officer of high military rank, usually in the army, and in some nations, the air force. The term is widely used by many nations of the world, and when a country uses a different term, there is an equivalent title given....

s uniform
Uniform
A uniform is a set of standard clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are worn by armed forces and paramilitary organizations such as police, emergency services, security guards, in some workplaces and schools and by inmates...

 in 1939, when the VITU of Navy
Military Engineering-Technical University
The Saint Petersburg Military Engineering-Technical University , previously known as the Saint Petersburg Nikolaevsky Engineering Academy, was established in 1810 under Alexander I...

, previously was known as the Nikolaevsky Engineering Academy (now Military engineering-technical university
Military Engineering-Technical University
The Saint Petersburg Military Engineering-Technical University , previously known as the Saint Petersburg Nikolaevsky Engineering Academy, was established in 1810 under Alexander I...

, Russian: Военный инженерно-технический университет), was revival on the base of Civil and Industrial Engineering Institute, as the head of its structural mechanics department and the academician became a lieutenant general
Lieutenant General
Lieutenant General is a military rank used in many countries. The rank traces its origins to the Middle Ages where the title of Lieutenant General was held by the second in command on the battlefield, who was normally subordinate to a Captain General....

. Boris Grigoryevich had never been in the army before, but had to wear the generals uniform. He was shy and when someone salute
Salute
A salute is a gesture or other action used to display respect. Salutes are primarily associated with armed forces, but other organizations and civil people also use salutes.-Military salutes:...

d to him he usually got frightened and waved his hands.

In the summer of 1941 after the beginning of the war the Commission on the defensive installations construction was created by the city government. Some academicians and prominent scientists became members (almost everyone was from the Polytechnical Institute), but only Boris Grigoryevich was involved with construction engineering. Practically he became the supervisor of the work for the Commission. Simultaneously Boris Grigoryevich was the city engineering defence department experts group head.

Later he was evacuated to Moscow, where he joined the military engineering commission of the Academy of Sciences of the USSR. Hard non-stop work was undermining the scientist's health. Not long after the Great Victory, on July 12, 1945 Galerkin died in Moscow.

Mathematical contributions

Galerkins name is forever attached to the finite element method
Finite element method
The finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...

, which is a way to numerically
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

 solve partial differential equations

Galerkin methods include:
  • The Galerkin method
    Galerkin method
    In mathematics, in the area of numerical analysis, Galerkin methods are a class of methods for converting a continuous operator problem to a discrete problem. In principle, it is the equivalent of applying the method of variation of parameters to a function space, by converting the equation to a...

     - A method for approximating the solution to a problem in weak form
    Weak formulation
    Weak formulations are an important tool for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations...

    . Most well known in the finite element method
    Finite element method
    The finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...

    .
  • The Petrov-Galerkin method
  • The Streamline upwind Petrov-Galerkin method (SUPG)
  • The Discontinuous Galerkin method
    Discontinuous Galerkin method
    Discontinuous Galerkin methods in mathematics form a class of numerical methods for solving partial differential equations. They combine features of the finite element and the finite volume framework and have been successfully applied to hyperbolic, elliptic and parabolic problems arising from a...


External links

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