×

A linear \(\theta\) method applied to 2D time-domain BEM. (English) Zbl 0919.65064

This paper presents a boundary element method (BEM) for the wave equation in the time domain. An example is given to illustrate the instability of the usual time stepping. The authors propose an alternative method of time stepping. In order to take a time step \(\Delta t\), one first takes a longer time step with the usual method, followed by linear interpolation back to \(\Delta t\). The examples given indicate that this approach adds artificial viscosity and may result in a stable computation.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L05 Wave equation
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Beskos, Boundary element methods in dynamic analysis: Part II (1986-1996), Appl. Mech. Rev. 50 (3) pp 149– (1997)
[2] W. J. Mansur A time-stepping technique to solve wave propagation problems using the boundary element method 1983
[3] Cod, Boundary Elements XVIII (1996)
[4] Schanz, Boundary Elements XIX (1997)
[5] Siebrit, Boundary Elements XVII (1995)
[6] Mansur, Time discontinuous linear traction approximation in time-domain BEM scalar wave propagation analysis, Int. j. numer. methods eng. 42 pp 667– (1998) · Zbl 0904.73075
[7] Bath, Stability and accuracy analysis of direct integration methods, Earthq. eng. struct. dyn. 1 pp 283– (1973)
[8] Bathe, Finite Element Procedures in Engineering Analysis (1996)
[9] Manoli, Boundary Element Methods in Elastodynamics (1988)
[10] Domingue, Time domain boundary element method for dynamic stress intensity factor computations, Int. j. numer. methods eng. 33 pp 635– (1992) · Zbl 0825.73906
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.