A Parametric Investigation Into Modeling of Unbounded Doamin Using Perfectly Matched Layer

One approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs wave propagating outwards from the domain interior. A perfectly matched layer (PML) is an unphysical absorbing layer model for linear wave equations that absorbs almost perfectly outgoing waves of all non-tangential angle-of-incidence and all non-zero frequencies. In this thesis different modeling procedure of unbounded domain and their merits and demerits ha been discussed. Detailed description of PML theory has been presented. A seven-step process to implement a PML element in a finite element model is proposed with a special reference to Opensees. Opensees is an object-oriented, open source framework developed by University of California, Berkeley which gives an advanced computational tool to simulate nonlinear soil and structure response and provides facility to add new material and elements. In this thesis, a new material code named PML material and a new element code named PML element has been written in C++ in Opensees compatible format using polymorphism and inheritance property of C++. A new material class named as soil has also been added to Opensees framework which can take care of Kelvin-Voigt damping (most common type of damping for soil). A shallow foundation model is considered for verifying coding results. Different boundary conditions are considered for modeling of unbounded domain and results are compared to perfectly matched layer modeling procedure. Numerical experiments were carried out to study effects of length of linear part, thickness of PML layer and different parameters involved in modeling PML layer. On the basis of these results, a set of guidelines has been presented for good modeling practices using perfectly matched layer. The effect of different ranges of frequency on PML modeling has been studied and found that PML modeling of unbounded domain is not significantly affected by the variation of frequency. Finally, the seismic response of a 2-D soil-pile model using PML model has been studied.