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Mulder, W.A. (author)
When solving the wave equation with finite elements, mass lumping allows for explicit time stepping, avoiding the cost of a lower-upper decomposition of the large sparse mass matrix. Mass lumping on the reference element amounts to numerical quadrature. The weights should be positive for stable time stepping and preserve numerical accuracy....
journal article 2022
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Geevers, S. (author), Mulder, W.A. (author), van der Vegt, J.J.W. (author)
We present new and efficient quadrature rules for computing the stiffness matrices of mass-lumped tetrahedral elements for wave propagation modeling. These quadrature rules allow for a more efficient implementation of the mass-lumped finite element method and can handle materials that are heterogeneous within the element without loss of the...
journal article 2019
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Geevers, S. (author), Mulder, W.A. (author), van der Vegt, J. J.W. (author)
We analyse the dispersion properties of two types of explicit finite element methods for modelling acoustic and elastic wave propagation on tetrahedral meshes, namely mass-lumped finite element methods and symmetric interior penalty discontinuous Galerkin methods, both combined with a suitable Lax–Wendroff time integration scheme. The...
journal article 2018
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Shamasundara, R. (author), Mulder, W.A. (author)
Finite-element discretizations of the acoustic wave equation in the time domain often employ mass lumping to avoid the cost of inverting a large sparse mass matrix. For the second-order formulation of the wave equation, mass lumping on Legendre–Gauss–Lobatto points does not harm the accuracy. Here, we consider a first-order formulation of the...
journal article 2016
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Mulder, W.A. (author), Shamasundara, R. (author)
We consider isotropic elastic wave propagation with continuous mass-lumped finite elements on tetrahedra with explicit time stepping. These elements require higher-order polynomials in their interior to preserve accuracy after mass lumping and are only known up to degree 3. Global assembly of the symmetric stiffness matrix is a natural approach...
journal article 2016
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