New mass-lumped tetrahedral elements for 3D wave propagation modelling

Abstract (2019)

Authors

S. Geevers University of Twente
W.A. Mulder Shell, Applied Geophysics and Petrophysics - CEG
J.J.W. van der Vegt University of Twente
Research Group
Applied Geophysics and Petrophysics (CEG) (TU Delft)
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Published Date

2019

Language

English

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Faculty

Civil Engineering & Geosciences

Department

Geoscience and Engineering

Research Group

Applied Geophysics and Petrophysics

Abstract

We present a new accuracy condition for constructing mass-lumped finite elements. This new condition is less restrictive than the one that has been used for several decades and enabled us to construct new mass-lumped tetrahedral elements of degrees 2,3, and 4. The new degree-2 and degree-3 elements require 14 and 32 nodes, respectively, while the degree-2 and degree-3 elements currently available in the literature require 23 and 50 nodes, respectively. Mass-lumped tetrahedral elements of degree 4 had not been found until now. The resulting mass-lumped finite element method is suitable for 3D wave propagation problems, since it can accurately capture the effects of a complex geometry and since it results in a fully explicit time-stepping scheme. A dispersion analysis and several numerical tests illustrates the efficiency of this new method. In particular, they illustrate a significant reduction in degrees of freedom, number of time steps, and computation time for a given accuracy compared to other finite element methods, such as the previous mass-lumped finite element methods or the discontinuous Galerkin method.