New Continuous Mass-lumped Finite Elements for 3D Wave Propagation

Spectral elements with mass lumping allow for explicit time stepping and are therefore attractive for modelling seismic wave propagation. Their formulation on rectangular elements is straighforward, but for tetrahedra only elements up to degree 3 are known. To preserve accuracy after mass lumping, these elements require additional nodes that make them computationally more expensive. Here, we propose a new, less restrictive accuracy condition for the construction of these continuous mass-lumped elements. This enables us to construct several new tetrahedral elements. The new degree-2 and degree-3 elements require 15 and 32 nodes, while the existing ones have 23 and 50 nodes per element, respectively. We also developed degree-4 tetrahedral elements with 60, 61, or 65 nodes per element. Numerical examples confirm that the various mass-lumped elements maintain the optimal order of accuracy and show that the new elements are significantly more efficient in terms of accuracy versus compute time than the existing ones.