NUMERICAL STABILITY OF MASS LUMPING SCHEMES FOR ...
NUMERICAL STABILITY OF MASS LUMPING SCHEMES FOR ... NUMERICAL STABILITY OF MASS LUMPING SCHEMES FOR ...
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12.07.2015
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Contents• Finite element dispersion errorbilinear versus serendipity elementsnumerical examples• Effect of time integrationexplicit and implicit schemesmass lumpingnumerical stability• Conclusions
Dispersion curvesAfter Newton, Kelvin, Born . . .mü i = k(u i−1 − 2u i + u i+1 )solution formu i = û sin K(x i − ct)wave numberK = 2π Λ = ω csolvability conditionc = function(ω)
- Page 4: Finite element method• Belytschko
- Page 7: frequency ωH/c 1 =0.5
- Page 11 and 12: Contents• Finite element dispersi
- Page 14 and 15: Mass matrix lumpingRow sum and Hint
- Page 16 and 17: Optimum mass distribution(central d
- Page 18 and 19: Numerical stability• Fried, I.: D
- Page 20: Conclusions• Threshold values of
Contents• Finite element dispersion errorbilinear versus serendipity elementsnumerical examples• Effect of time integrationexplicit and implicit schemesmass lumpingnumerical stability• Conclusions
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