Reduced Basis Approximation and Inverse Analyses for Dental Implant Problems

Abstract

This thesis proposes a rapid inverse analysis approach based on the reduced basis method and the Levenberg?Marquardt?Fletcher algorithm to identify the ?unknown? material properties: Young?s modulus and stiffness-proportional Rayleigh damping coefficient of the interfacial tissue between a dental implant and the surrounding bones. In the forward problem, a finite element approximation for a three-dimensional dental implant-bone model is first built. A reduced basis approximation is then established by using a Proper Orthogonal Decomposition (POD)?Greedy algorithm and the Galerkin projection to enable extremely fast and reliable computation of displacement responses for a range of material properties. In the inverse analysis, the reduced basis approximation for the dental implant-bone model are incorporated in the Levenberg?Marquardt?Fletcher algorithm to enable rapid identification of the unknown material properties. Numerical results are presented to demonstrate the efficiency and robustness of the proposed method.