Inverse Problems in Finite Element Method Using Automatic Differentiation

The progress of computer and numerical technique in recent years allows us not only complex numerical simulation but also resolution of inverse problems. It is important to pursue higher and higher quality of gradient computation (it is called sensitivity analysis) in inverse problem and this is the most bone-crushing point. In this study, the authors will propose the forward mode automatic differentiation as a new approach to the parameter identification problems. Forward mode automatic differentiation computes the partial derivatives according to the differentiation rules of a composite function whenever basic operation is performed. INTRODUCTION The Reynolds number is named after Osborne Reynolds (1842-1912) who conducted an experimental study to see how and when laminar and turbulent flows occur through a pipe. The Reynolds number is a dimensionless parameter and is defined as