Fast three-dimensional temperature reconstruction

The work presented here deals with the reconstruction of the thermal field inside a three-dimensional structure when only some pointwise temperature measurements along a time interval [0, T] are available. The model-based reconstruction procedure builds upon optimal control theory applied to the determination of the unknown boundary conditions. The proposed dual approach enables one to reduce the on-line computational cost so that the resulting algorithm can be part of a real-time process. The complexity of the resulting algorithm does not depend on geometry. The paper details a novel methodology that enables to implement the reconstruction procedure using standard finite element tools, despite the difficulty to define the pointwise values of a three-dimensional field in the usual functional spaces where finite element methods converge.