Further improvement to the stability of the coupling BEM/FEM scheme for 2-D elastodynamic problems

 The stability of the coupling BEM/FEM scheme as applied in 2-D elastodynamic problems is studied further. The linear θ method, which is more stable than the standard BEM scheme (Mansur, 1983), makes the coupling BEM/FEM scheme more stable also. But due to the inter-influence of these two kinds of numerical methods – FEM and BEM, the coupling of BEM and FEM is less stable than both BEM algorithm and FEM algorithm. Unlike in FEM, any error in BEM scheme will affect all the later results, which makes the BEM procedure tends to be less stable. And even more, a procedure that is stable when only BEM is used can be unstable in the coupling BEM/FEM procedure due to the effect of the oscillations by FEM. The procedure used in this paper is to reduce such kind of oscillations caused by the FEM scheme, so that it will not cause instability problem to the BEM scheme and further maintain the stability of the coupling BEM/FEM scheme. Although little numerical damping will be introduced by the new method, the stability is greatly improved and the computer time is nearly the same.