AUTOMATED SOFTWARE COMPLEX FOR DETERMINATION OF THE OPTIMAL PARAMETERS SET FOR THE WEIGHTED FINITE ELEMENT METHOD ON COMPUTER CLUSTERS
( Pp. 9-19)

More about authors
Rukavishnikov Viktor A. zaveduyuschiy laboratoriey, prof., d-r fiz.-mat. nauk
CC FEB RAS Maslov Oleg V. student
FESTU Mosolapov Andrey O. nauch. sotr.
CC FEB RAS Nikolaev Sergey G. nauch. sotr.
CC FEB RAS
For read the full article, please, register or log in
Abstract:
In the paper we present the automated software complex designed to search the optimal parameters values for weighted FEM for the mathematical models with singularity. The operation of the entire complex and its constituent components are described. In conclusion, we present the results delivered by the complex during numerical experiment for elasticity theory problem with singularity caused by the reentrant corner on the domain boundary
How to Cite:
Rukavishnikov V.A., Maslov O.V., Mosolapov A.O., Nikolaev S.G., (2015), AUTOMATED SOFTWARE COMPLEX FOR DETERMINATION OF THE OPTIMAL PARAMETERS SET FOR THE WEIGHTED FINITE ELEMENT METHOD ON COMPUTER CLUSTERS. Computational Nanotechnology, 1: 9-19.
Reference list:
Arroyo D., Bespalov A., Heuer N. On the finite element method for elliptic problems with degenerate and singular coefficients // Mathematics of Computation. 2007. Vol. 76. P. 509-537.
Assous F., Ciarlet, P. Jr., Segre J. Numerical Solution of the Time-Dependent Maxwell Equations in Two-Dimensional Singular Domain: The Singular Complement Method // J. Comp. Physics. 2000. Vol. 161. P. 218-249.
Costabel M., Dauge M., Schwab C. Exponential convergence of hp-FEM for Maxwell equations with weighted regularization in polygonal domains // Math. Models and Meth. in Appl. Sci. 2005. Vol. 15. P. 575-622.
Li H., Nistor V. Analysis of a modified Schr dinger operator in 2D: Regularity, index, and FEM // J. Comp. Appl. Math. 2009. Vol. 224. P. 320-338.
Rukavishnikov V. A. O vesovoy otsenke skhodimosti raznostnykh skhem // Dokl. AN SSSR. 1986. T. 288. № 5. S. 1058-1062.
Rukavishnikov V. A. Zadacha Dirikhle s nesoglasovannym vyrozhdeniem iskhodnykh dannykh // DAN. 1994. T. 337. №4. S. 447-449.
Rukavishnikov V. A. O zadache Dirikhle dlya ellipticheskogo uravneniya vtorogo poryadka s nesoglasovannym vyrozhdeniem iskhodnykh dannykh // Differentsial nye uravneniya. 1996. T. 32. №3. S. 402-408.
Rukavishnikov V. A. O edinstvennosti -obobshchennogo resheniya dlya kraevykh zadach s nesoglasovannym vyrozhdeniem iskhodnykh dannykh // DAN. 2001. T. 376. №4. S. 451-453.
Rukavishnikov V. A., Bespalov A. YU. Eksponentsial naya skorost skhodimosti metoda konechnykh elementov dlya zadachi Dirikhle s singulyarnost yu resheniya // DAN. 2000. T. 374. №6. S. 727-731
Rukavishnikov V. A., Rukavishnikova H. I. The Finite Element Method For Boundary Value Problem With Strong Singularity // Journal of Computational and Applied Mathematics. 2010. Vol. 234. №9. P. 2870-2882.
Rukavishnikov V. A., Mosolapov A. O. New numerical method for solving time-harmonic Maxwell equations with strong singularity // Journal of Computational Physics. 2012. Vol. 231. P. 2438-2448.
Rukavishnikov V. A., Nikolaev S.G. Vesovoy metod konechnykh elementov dlya zadachi teorii uprugosti s singulyarnost yu // DAN. 2013. T. 453. №4. S. 378-382.
Rukavishnikov V. A., Rukavishnikova H. I. On the Error Estimation of the Finite Element Method for the Boundary Value Problems with Singularity in the Lebesgue Weighted Space // Numerical Functional Analysis and Optimization. 2013. Vol. 34. №12. P.1328-1347.
Rukavishnikov V. A., Nikolaev S. G., Sarykov A. S. Programma dlya paketnogo modelirovaniya singulyarnykh zadach na vysokoproizvoditel nom klastere // Informatika i sistemy upravleniya. 2013. № 1(35). S. 99-107.
Rukavishnikov V. A., Nikolaev S. G. Proba IV - programma dlya chislennogo resheniya dvumernykh zadach teorii uprugosti s singulyarnost yu // Sv. 2013616248 Rossiyskaya Federatsiya, Programmy dlya EVM. Bazy dannykh. Topologii integral nykh mikroskhem. 2013. Byul. №3(84).
Keywords:
automated computer system, high performance computing, boundary value problem with a singularity, Rv-generalized solution, weighting finite element method.