Boris Galerkin

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Galerkin, Boris Grigor’evich

 

Born Feb. 20 (Mar. 4), 1871, in Polotsk; died July 12, 1945, in Leningrad. Soviet engineer and scientist in the field of elasticity theory; became an academician of the Academy of Sciences of the USSR in 1935 (corresponding member in 1928). Lieutenant general of the engineers. Graduated from the St. Petersburg Technological Institute in 1899. In 1906 he was sentenced to 18 months’ imprisonment for participation in the revolutionary movement. He began to teach in 1909.

Galerkin’s works on problems of structural mechanics and elasticity theory facilitated the introduction of modern methods of mathematical analysis into research on the operation of structures and machines. He developed efficient methods of accurate and approximate integration of equations in elasticity theory. Galerkin was one of the creators of the theory of flexure of plates. He investigated the effect of the shape of a plate on the distribution of stresses in it, the effect of distribution of local pressure, and the effect of elasticity of an index contour. The form of the solution of equations of elastic equilibrium proposed by Galerkin in 1930, which consists of three biharmonic functions, made possible the effective resolution of many important spatial problems of elasticity theory. In his works on shell theory, Galerkin shunned conventional hypotheses concerning the character of changes in displacements in thickness and introduced other assumptions that provided greater accuracy and possibilities to extend this theory to shells of medium thickness.

Galerkin was a consultant during the planning and construction of the large Volkhovges, Dneproges, and Dzorages hydroelectric power plants and the Krasnyi Oktiabr’ and Dubrovskaia steam power plants. He was awarded the State Prize of the USSR (1942) and two Orders of Lenin.

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REFERENCES

Krylov, A. N. [et al.]. “Akademik B. G. Galerkin (K 70-letiiu so dnia rozhdeniia).” Vestnik AN SSSR, 1941, no. 4.
Sokolovskii, V. V. “O zhizni i nauchnoi deiatel’nosti akademika B. G. Galerkina.” Izvestiia AN SSSR: Otdelenie tekhnicheskikh nauk, 1951, no. 8.
References in periodicals archive ?
The newly developed software package named EDGE, for Extreme-Scale Discontinuous Galerkin Environment, can fully exploit the latest generation of Intel processors.
Using the Galerkin weighted residual method, he finds the solution of the eigen value problem, derives stability criteria for stationary and oscillating convection, and plots graphs to study the effects of various parameters on stationary and oscillating convection.
Various studies have been developed using different methods, such as extended finite element method (XFEM) [1], boundary element method (BEM) [2] , element free Galerkin method (EFGM) [3], and other methods [4, 5].
By avoiding the explicit integration of the shape functions that span the discrete space and introducing an innovative construction of the stiffness matrixes, the VEM acquires very interesting properties and advantages with respect to more standard Galerkin methods, yet still keeping the same coding complexity.
The mixed finite element methods presently available employ either the Streamline Upwind Petrov Galerkin (SUPG) method of Marchai and Crochet [15] or the discontinuous Galerkin (DG) method of Fortin [16].
But specifically in the Finite Element Method, the Galerkin method is known to present excellent numerical precision with low computational time for pure diffusion problems or diffusion-reaction [18-20]; however the same cannot happen with dominant convection problems [1, 21] and in the analysis of flows [22].
A different class of space-time methods based on a discontinuous Galerkin discretization using space-time elements has been developed in the finite element community; see [43, 44].
There are several other methods in use, such are collocation method, Galerkin method, Ritz method and finite element method.
2013) applied a technique based on the interpolating scaling functions and Galerkin method to numerically solve the Klein- Gordon equation.
During the last decades, several numerical and analytical techniques have been utilized to approximate the solutions of FIDEs such as the neural networks [3], comparison of Adomian decomposition with wavelet Galerkin [4], Differential transform [5], finite differences [6-7], comparison of finite elements and finite difference [8], sinc method [9], Tau method [10-11] and Galerkin method with hybrid functions [12].
The proposed method may often be used instead of the Galerkin method in the case of approximate determination of the equilibrium state in the post-critical state, recommended by Vlasov in his monograph [19].