# Solving a parameter estimation problem in a three-dimensional conical tube on a parallel and distributed software infrastructure.

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## Abstract

A parameter estimation problem arising from a three-dimensional computational fluid dynamics problem is formulated. The goal is to estimate the inflow velocity of a fluid flowing through a conical measuring cell from actual nuclear magnetic resonance measurements of the velocity in a certain region of the flow field. The flow is described by the incompressible Navier-Stokes equations and numerically solved by the parallel adaptive finite element package DROPS. Three different optimization algorithms for the solution of the parameter estimation problem are compared from within the EFCOSS environment. In this distributed component-based software architecture, one can access various optimization algorithms without the need to manually adapt the interfaces between the parallel flow solver DROPS and the different serial optimization software packages. Numerical experiments on a cluster consisting of Xeon-based quad-core processors connected by an InfiniBand network are reported. The results demonstrate a successful estimation of the inflow velocity by different optimization algorithms and a reduction of the time to evaluate the objective of the parameter estimation by a factor of roughly 27 using 40 processes.