Accuracy and stability of finite quadratic serendipity elements in dynamic wave propagation problems

Abstract eng:
Accuracy and stability analysis of mass matrix lumping schemes applicable to wave propagation is carried out. To this end, a variable parameter, x, is defined for the 8node serendipity element whose role is to distribute total mass between the elements corner and midside nodes. Several previously developed methods are included as special cases, for instance, the diagonal scaling method by Hinton-Rock-Zienkiewicz (HRZ) can be mentioned. Using stability and dispersion theorems as vehicles, dispersive properties of different lumped matrices with variable mass distribution are discussed. It is shown that the HRZ mass ratio, x = 0.21, is not the best both in terms of dispersion and numerical stability. Instead, x = 0.23 is proposed and quantitative conclusions drawn. As a by-product, Fried’s theorem on eigenvalue bounds is numerically verified.

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