Performance of old and new mass-lumped triangular finite elements for wavefield modelling

Finite elements with mass lumping allow for explicit time stepping when modelling wave propagation and can be more efficient than finite differences in complex geological settings. In two dimensions on quadrilaterals, spectral elements are the obvious choice. Triangles offer more flexibility for meshing, but the construction of polynomial elements is less straightforward. The elements have to be augmented with higher-degree polynomials in the interior to preserve accuracy after lumping of the mass matrix. With the classic accuracy criterion, triangular elements suitable for mass lumping up to a polynomial degree 9 were found. With a newer, less restrictive criterion, new elements were constructed of degree 5–7. Some of these are more efficient than the older ones. To assess which of all these elements performs best, the acoustic wave equation is solved for a homogeneous model on a square and on a domain with corners, as well as on a heterogeneous example with topography. The accuracy and runtimes are measured using either higher-order time stepping or second-order time stepping with dispersion correction. For elements of polynomial degree 2 and higher, the latter is more efficient. Among the various finite elements, the degree-4 element appears to be a good choice.