Validation and further development of the perfectly matched layer technique for the numerical treatment of elastodynamic boundary value problems

• Applicant: Professor Dr.-Ing. Stavros A. Savidis
• Subject Area: Geotechnics, Hydraulic Engineering
• Term: from 2014 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 255685298

The analysis of wave propagation in elastic media is even in simple systems a difficult task. For some boundary value problems there are analytical solutions, but generally for the computation of dynamic soil-structure-interaction problems the application of numerical methods is standard.The base for all numerical methods is the discretization of soil and structure. Thereby the choice of appropriate boundary conditions is the key to obtain realistic results of the numerical computation because they have to be able to simulate the propagation of waves to infinite without reflections at the artificial boundary. So far, there are two techniques to simulate the wave propagation in infinite media, the boundary-element-method and a form of local transmitting boundaries. A relatively new approach is the perfectly matched layer (PML) method, which is common in the computation of electromagnetic fields. It combines the advantages of the two techniques mentioned above.When using PML in elastodynamics, a material layer will be attached to the artificial boundary, which is designed to simulate almost perfect wave propagation to infinity. But because the material is not entirely based on physical principles, it is not possible to make mechanically reasonable statements to the numerical quality of a PML formulation. Also, there is a lack of mathematical-theoretical research to the convergence of PML formulations if it is taken beyond simple boundary value problems. Hence, the quality of a chosen PML formulation cannot be forecasted which is why the technique is almost unused in elastodynamic fields.Because of these specific properties of PML, the usage of statistical methods is obvious. Thus, in the submitted research project sensitivity analysis methods are applied to qualitatively and quantitatively identify the factors of influence, which have an impact on the numerical solutions of boundary value problems solved with PML. By this way, the gap between the mathematically-artificially properties and the underlying physical differential equation of the PML can be closed, to create a tool, to handle complex dynamic soil-structure-interaction-problems. This newly developed procedure will be validated on practical questions.

• DFG Programme: Research Grants