Fast Time Domain Boundary Element Formulation for Partially Saturated Porous Media

In many engineering applications, the simulation of waves in unbounded domains is required. One example is soil- structure-interaction. In these multiphysical problems several computational methods have to be used and it is well known that a correct model for the radiation of waves in the unbounded domain is necessary. The Boundary Element Method (BEM) in time domain is the method of choice for this part of the problem. In case of, e.g., soil, the material behavior may be modeled by a linear three phase poroelastic model. In this project, a three phase poroelastic model based on the mixture theory is used. The fundamental solutions necessary for the BEM can be derived in Laplace domain and are implemented in a Convolution Quadrature based BEM. To obtain an efficient method this time domain BE formulation is accelerated by employing fast techniques. The Adaptive Cross Approximation and the Panel Clustering will be applied. Unfortunately, the efficiency of both methods decreases with frequency. But, the Panel clustering can be improved for larger frequencies by using a directional clustering. Hence, the behavior of both techniques in the low and higher frequency regime will be compared and presumably a combination of both will result in an efficient method.

In the project, the development of a Boundary Element (BEM) formulation for partial saturated materials as, e.g. soil, was under study. A time domain formulation based on the convolution quadrature method has been established. This is the first available time domain formulation for partial saturated continua. First steps to improve the efficiency of the BEM with so-called fast methods have successfully been realized.The main motivation for such a BE formulation is to simulate waves in unbounded domains. An example is the computation of waves during earthquakes in the soil. The main advantage is the correct modelling of the radiation of the waves in the unbounded domain, which avoids artificial reflections at the computing boundaries. Such reflections are a major problem in Finite Element Methods. The material behavior has been modeled by a linear three phase poroelastic model based on the mixture theory. The fundamental solutions necessary for the BEM has been derived in Laplace domain and were implemented in a convolution quadrature based BEM. To obtain an efficient BE formulation fast methods have to be used. Fortunately, the convolution quadrature based BEM allows to employ the fast techniques known from elliptic problems. Here, the fast multipole method (FMM) with a kernel decomposition using a Chebyschev interpolation is used. This method has been implemented and tested for poroelastodynamics in Laplace domain. The published results are promising. The extension to the partial saturated case is close to be finished, where first results are promising as well. For the application within the convolution quadrature a robust method for higher frequencies is still an open point.