Dr Liviu Marin, Research Fellow at the University of Nottingham, Department of Mechanical Engineering, recently visited Ashurst Lodge to lecture on BEM Applied to Inverse Problems in Isotropic Linear Electricity.
Liviu graduated in Applied Mathematics at the University of Bucharest and completed a PhD at the University of Leeds under Professor Derek Ingham before taking his current appointment at Nottingham.
Two important classes of inverse problems occurring in isotropic linear elasticity were analysed, namely inverse boundary value and parameter identification problems. The first class of inverse problems in elasticity consists of the retrieval of both the displacement and the traction vectors on a part of the boundary from over-specified boundary measurements available on the remaining boundary. This is a classical example of an inverse problem, also known as the Cauchy problem. Both regular and singular Cauchy problems are solved numerically by employing an iterative alternating algorithm in conjunction with a regularizing stopping criterion. The latter class of inverse problems deals with the recovery of the elastic constants (the Poisson ratio and the shear modulus) from boundary measurements. Two cases were considered, namely (i) when measurements are possible on the whole boundary of the solution domain, and (ii) when measurements are available only on a part of the boundary (Cauchy data). The aforementioned parameter identification problems were tackled by minimising a BEM based objective function in order to retrieve the material constants and the unknown boundary data.
Liviu presented the following conclusions:
- Non-singular and singular Cauchy problems can be solved using an alternating iterative algorithm.
- Identification of the material constant is possible from incomplete boundary measurements using constrained minimisation techniques, as well as the alternating iterative algorithm.
- The stopping Morozov’s discrepancy principle was satisfactorily applied.
- Convergent and stable numerical solutions with respect to refining the mesh size and by decreasing the amount of noise. (DOES THIS MAKE SENSE?)
The Seminar ended with a lively discussion.