Wave propagation phenomena are mostly interesting in unbounded domains, e.g., in soil. Applications in visco- or poroelastic media can be found in geomechanics. As the Boundary Element Method (BEM) fulfills the radiation condition it is the preferred method. However, wave propagation problems should be treated in time domain to observe the waves as they evolve.
The usual BEM time stepping procedure requires to calculate and to store for every time step a matrix comparable to one static calculation. Especially, in inelastic problems there is no cutoff at some time. Hence, techniques must be developed to establish a data sparse matrix approximation of the overall matrix not only with respect to the spatial variable but also with respect to the time.
Unfortunately, both variables are connected in the retarded potentials of the governing integral equation. Further, aiming in the long-term perspective on poroelastic wave propagation the kernels are highly complicated and, therefore, a technique requiring an analytical kernel decomposition seems to be not promising. Here, the Adaptive Cross Approximation (ACA) and/or the so-called 'black box' Panel Clustering based on an interpolation of the kernel will be applied. Beside this sparse technique, a fast solution of the final equation system has to be explored, where either iterative solvers or hierarchical LU-solvers will be studied. Also an efficient preconditioner is essential for a fast solution.