Speeding up a mass-lumped tetrahedral finite-element method for wave propagation

Mass-lumped finite elements on tetrahedra offer more flexibility than their counterpart on hexahedra for the simulation of seismic wave propagation, but there is no general recipe for their construction, unlike as with hexahedra. Earlier, we found new elements up to degree 4 that have significantly less nodes than previously known elements by sharpening the accuracy criterion. A similar approach applied to numerical quadrature of the stiffness matrix provides a speed improvement in the acoustic case and an additional factor 1.5 in the isotropic elastic case. We present numerical results for a homogeneous and heterogeneous isotropic elastic test problem on a sequence of successively finer meshes and for elements of degrees 1 to 4. A comparison of their accuracy and computational efficiency shows that a scheme of degree 4 has the best performance when high accuracy is desired, but the one of degree 3 is more efficient at intermediate accuracy.