×

zbMATH — the first resource for mathematics

Mechanical quadrature methods and their splitting extrapolations for solving boundary integral equations of axisymmetric Laplace mixed boundary value problems. (English) Zbl 1187.65135
Summary: The mechanical quadrature methods (MQM) and splitting extrapolation methods (SEM) are applied to the boundary integral equations (BIE) of axisymmetric mixed boundary value problems governed by Laplace’s equation. By ring potential theory, the double integral equations of axisymmetric Laplace problems can be converted into the single integral equations. For solving the BIE, the MQM based on the quadrature rules for computing the singular periodic functions are presented, which possesses a high order accuracy \(O(H^3_0)\) and low computing complexities. Moreover, using the SEM based on the multi-parameter asymptotic error expansion, we cannot only improve the accuracy order of approximation, but also give a posteriori error estimate. Several numerical examples show that the accuracy order of approximation is very high, and the SEM and a posteriori error estimate are also very effective.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
65D32 Numerical quadrature and cubature formulas
80A20 Heat and mass transfer, heat flow (MSC2010)
80M15 Boundary element methods applied to problems in thermodynamics and heat transfer
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] ()
[2] Liem, C.B.; Lü, T.; Shih, T.M., The splitting extrapolation method, (1995), World Scientific Singapore · Zbl 0875.65002
[3] Davis, P., Methods of numerical integration, (1984), Academic Press New York
[4] Geadshteyn, I.S.; Ryzhk, I.M., Table of integral, series, and products, (1980), Academic Press New York
[5] Jin, Huang; Tao, Lü, The mechanical quadrature methods and their splitting extrapolations for solving first-kind boundary integral equations on polygonal regions, Math numer sinica, 1, 51-60, (2004)
[6] Krutitskii, P.A., Method of boundary integral equations in the mixed problem for the Laplace equation with an arbitrary partition of the boundary, Diff equat, 37, 1, 78-89, (2001) · Zbl 1001.35028
[7] Lin, Q.; Lü, T., Splitting extrapolations for multi-dimensional problems, J comput math, 1, 45-51, (1983)
[8] Rüde U. Extrapolation and related techniques for solving elliptic equation. In: Berricht I-9135, Institute for Informatik, TU München; January 1991.
[9] Rüde, U.; Zhou, A., Multi-paratemeter extrapolation methods for boundary integral equations, Adv comput math, 9, 173-190, (1998) · Zbl 0922.65075
[10] Sidi, A.; Israrli, M., Quadrature methods for periodic singular Fredholm integral equation, J sci comput, 3, 201-231, (1988)
[11] Sidi, A., (), 359-374
[12] Sloan, I.H.; Spence, A., The Galerkin method for integral equations of the first kind with logarithmic kernel, IMA, J numer anal, V, 105-122, (1988) · Zbl 0636.65143
[13] Wrobel, L.C., Boundary element methods, vol. 1, (2002), Wiley New York
[14] Yan, Y., The collocation method for first-kind boundary integral equations on polygonal regions, Math comput, 54, 139-154, (1990) · Zbl 0685.65121
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.