Numerical Recovery of Material Parameters in Euler-Bernoulli Beam Models
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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A fully Sinc-Galerkin method for recovering the spatially varying stiffness parameter in fourth-order time dependent problems with fixed and cantilever boundary conditions is presented. The forward problems are discretized with a sinc basis in both the spatial and temporal domains. This yields an approximate solution which converges exponentially and is valid on the infinite time interval. When the forward methods are applies to parameter recovery problems, the resulting inverse problems are ill-posed. Tikhonov regularization is applied and the resulting minimization problems are solved via a quasi-Newtontrust region algorithm. The L-curve is used to determine an appropriate value of the regularization parameter. Numerical results which highlight the method are given for problems with both fixed and cantilever boundary conditions.
- Numerical Mathematics