Carrer, J. A. M.; Mansur, W. J. Time-domain BEM analysis for the 2D scalar wave equation: Initial conditions contributions to space and time derivatives. (English) Zbl 0880.73071 Int. J. Numer. Methods Eng. 39, No. 13, 2169-2188 (1996). Summary: The complete expressions corresponding to space and time derivatives of Volterra’s integral representation of the time-dependent scalar wave equation are presented. The concept of finite part of an integral is used in order to compute boundary kernels contributions. Time integration of boundary kernels is performed analytically for linear and constant time approximations for the potential and its normal derivative, respectively. The new integral representations presented are quite general, as contributions due to the initial conditions have also been included. Two examples are presented to assess the accuracy of the formulation. Cited in 11 Documents MSC: 74S15 Boundary element methods applied to problems in solid mechanics 74J10 Bulk waves in solid mechanics 74H45 Vibrations in dynamical problems in solid mechanics Keywords:time-dependent wave equation; finite part of integral; Volterra’s integral representation PDFBibTeX XMLCite \textit{J. A. M. Carrer} and \textit{W. J. Mansur}, Int. J. Numer. Methods Eng. 39, No. 13, 2169--2188 (1996; Zbl 0880.73071) Full Text: DOI References: [1] Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Dover Publications, New York, 1952. · Zbl 0049.34805 [2] Mansur, Eng. Anal. Boundary Elements 12 pp 283– (1993) · doi:10.1016/0955-7997(93)90055-P [3] Carrer, Eng. Anal. Boundary Elements 13 pp 67– (1994) · doi:10.1016/0955-7997(94)90008-6 [4] ’A time-stepping technique to solve wave propagation problems using the boundary element method’, Ph.D. Thesis, University of Southampton, England, 1983. [5] ’On the numerical evaluation of finite-part integrals involving an algebraic singularity’, Special Report WISK 179, National Research Institute for Mathematical Sciences, Pretoria, 1979. [6] Antes, Int. J. numer. methods eng. 31 pp 1151– (1991) · Zbl 0825.73813 · doi:10.1002/nme.1620310609 [7] Beskos, Appl. Mech. Rev. 40 pp 1– (1987) · doi:10.1115/1.3149529 [8] Dominguez, Int. J. numer. methods eng. 33 pp 635– (1992) · Zbl 0825.73906 · doi:10.1002/nme.1620330309 [9] and , Boundary Element Methods in Elastodynamics, Unwin Hyman Publishing Co., 1988. [10] Ness, Commun. numer. methods eng. 10 pp 661– (1994) · Zbl 0811.65082 · doi:10.1002/cnm.1640100809 [11] Belytschko, Int. J. numer. methods eng. 37 pp 91– (1994) · Zbl 0796.73056 · doi:10.1002/nme.1620370107 [12] Mansur, Earthquake Eng. Struct. Dyn. 21 pp 51– (1992) · doi:10.1002/eqe.4290210104 [13] and , Methods of Theoretical Physics, McGraw-Hill, New York, Toronto and London, 1953. [14] and , Theoretical Acoustics, McGraw-Hill, London, 1968. 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.