Fast BE-FE method for poroelastic wave propagation phenomena

Wave propagation phenomena in porous media are of great interest in a lot of areas in engineering. There are many applications in soil mechanics where the physical effect of waves in porous media are used, e.g., the exploration of oil- and gas reservoirs or the identification of different layers with seismological methods. Further, improved knowledge on the propagation of disturbances, which are essentially waves, due to traffic or more dramatically due to earthquakes is required to ensure the safety of buildings, e.g., of a dam-reservoir system. In such problems like the dam-reservoir system, the domain of interest consists of areas governed by different sets of differential equations and the domain can even be unbounded, i.e., it is a multifield problem. All unbounded domains with a linear description are effectively treated by the Boundary Element Method, whereas all non-linear bounded domains are treated well by the Finite Element Method. That is why often a coupled approach of both methodologies is used. In this project, two aspects of such a coupling algorithm especially for poroelastic continua will be studied. First, using Mortar methods a very flexible coupling will be established. With this method different mesh sizes and different physical domains, e.g., a poroelastic domain and a fluid domain, can be coupled effectively. Second, the poroelastic Boundary Element formulation developed by Martin Schanz will be improved with fast methods like Fast Multipol Method, H-matrices, or Adaptive Cross Approximation. As a third part of this proposal, a cheap alternative to the coupling of Finite and Boundary Elements the so-called infinite elements will be extended to wave propagation in poroelastic continua and tested against the coupled approach with respect to efficiency and accuracy.

Wave propagation phenomena in porous media are of great interest in a lot of areas in engineering. There are many applications in soil mechanics where the physical effect of waves in porous media are used, e.g., the exploration of oil- and gas reservoirs or the identification of different layers with seismological methods. Further, improved knowledge on the propagation of disturbances, which are essentially waves, due to traffic or more dramatically due to earthquakes is required to ensure the safety of buildings, e.g., of a dam-reservoir system. In such problems like the dam-reservoir system, the domain of interest consists of areas governed by different sets of differential equations and the domain can even be unbounded, i.e., it is a multifield problem. All unbounded domains with a linear description are effectively treated by the Boundary Element Method, whereas all non-linear bounded domains are treated well by the Finite Element Method. That is why often a coupled approach of both methodologies is used. In this project, two aspects of such a coupling algorithm especially for poroelastic continua will be studied. First, using Mortar methods a very flexible coupling will be established. With this method different mesh sizes and different physical domains, e.g., a poroelastic domain and a fluid domain, can be coupled effectively. Second, the poroelastic Boundary Element formulation developed by Martin Schanz will be improved with fast methods like Fast Multipol Method, H-matrices, or Adaptive Cross Approximation. As a third part of this proposal, a cheap alternative to the coupling of Finite and Boundary Elements the so-called infinite elements will be extended to wave propagation in poroelastic continua and tested against the coupled approach with respect to efficiency and accuracy.