Rapid identification of material properties of the interface tissue in dental implant systems using reduced basis method. (English) Zbl 1300.92047
Summary: This paper proposes a rapid inverse analysis approach based on the reduced basis (RB) 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 RB approximation is then established by using a proper orthogonal decomposition-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 RB 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.
MSC:
| 92C55 | Biomedical imaging and signal processing |
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 62H25 | Factor analysis and principal components; correspondence analysis |
Keywords:
second-order hyperbolic partial differential equations; reduced basis method; inverse analysis; Levenberg-Marquardt-Fletcher algorithm; material characterization; POD-Greedy algorithmReferences:
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