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95/105= 0.91


1,1

Relation between accuracy and computational time for boundary element method applied to Laplace equation

doi: 10.6062/jcis.2013.04.02.0072(Free PDF)

Authors

Olavo H. Menin and Vanessa Rolnik

Abstract

The aim of this paper is to report a relation observed between accuracy and computational time to the boundary element method (BEM) applied to solve the Laplace equation. For this purpose, the BEM was implemented in C language and the program was tested for boundary value problems with known analytical solution. Moreover, the results show that the program is reliable, accurate and fast.

Keywords

boundary value problem, elliptic partial differential equations, numerical methods, computational cost.

References

[1] BREBBIA CA. 1978. The boundary element method for engineers, Pentech Press, Plymonth.

[2] BREBBIA CA & DOMINGUEZ J. 1989. Boundary elements: an introductory course,WIT Press, Southampton.

[3] ONYANGO TTM, INGHAM DB & LESNIC D. 2009. Applied Mathematics and Computation, 207: 569–575.

[4] MARTIN TJ & DULIKRAVICH GS. 1998. Transactions of the ASME, 120: 328–334.

[5] MENIN OH & ROLNIK V. 2011. International Journal of Modern Physics C, 22: 825–839.

[6] MENIN OH, ROLNIK V & MARTINEZ AS. 2013. Revista Brasileira de Ensino de F´ısica, 34: 2304.

[7] XU Y, DONG F & TAN C. 2010. Engineering Analysis with Boundary Elements, 34: 876–883.

[8] RIBEIRO GO, RIBEIRO TSA, JORGE AB & CRUSE TA. 2009. J. of the Braz. Soc. of Mech. Sci. & Eng., XXXXI: 261–268.

[9] KIRKUP SM & HENWOOD DJ. 1994. Appl. Math. Modelling, 18: 32–38.

[10] ANGWT. 2007.A beginner’s course in boundary element methods, Universal Publishers, Boca Raton.

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