000013191 001__ 13191
000013191 005__ 20161114160331.0
000013191 04107 $$aeng
000013191 046__ $$k2009-06-22
000013191 100__ $$aPlesek, J.
000013191 24500 $$aAccuracy and stability of finite quadratic serendipity elements in dynamic wave propagation problems

000013191 24630 $$n2.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013191 260__ $$bNational Technical University of Athens, 2009
000013191 506__ $$arestricted
000013191 520__ $$2eng$$aAccuracy 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.

000013191 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013191 653__ $$aWave Propagation, Dispersion Analysis, Serendipity Elements, Mass Lumping, Fried Theorem. Abstract. 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.

000013191 7112_ $$aCOMPDYN 2009 - 2nd International Thematic Conference$$cIsland of Rhodes (GR)$$d2009-06-22 / 2009-06-24$$gCOMPDYN2009
000013191 720__ $$aPlesek, J.$$iKolman, R.$$iGabriel, D.
000013191 8560_ $$ffischerc@itam.cas.cz
000013191 8564_ $$s741210$$uhttps://invenio.itam.cas.cz/record/13191/files/CD257.pdf$$yOriginal version of the author's contribution as presented on CD, section: Computational methods for waves - ii (MS).
000013191 962__ $$r13074
000013191 980__ $$aPAPER