View full-textĪn unstructured finite element method for the transient solution of the 2D and 3D compressible Navier-Stokes equations using triangular respectively tetrahedral elements is presented. Detailed description of the deformation based grid generation, a least square finite element (LSFEM) solver for the underlying div-curl system, and a fast div-curl solver approximating the LSFEM solution using inverse filtering, along with several 2D and 3D experimental results are presented. Secondly, since no regularization term is introduced in the functional to be optimized, the resultant deformation field is highly flexible that large deformation frequently experienced in inter-patient or image-atlas registration tasks can be accurately estimated. Nevertheless, the regularity (no mesh folding) of the resultant deformation is theoretically guaranteed by controlling the Jacobian determinant of the transformation. In particular, there is no weight to balance the regularization functional and the similarity functional as commonly required in many non-rigid image registration methods. Thus, no regularization functional is required in this method. Firstly, the functional to be optimized consists of only one term, a similarity measure. Based on it, we have successfully developed a new non-rigid image registration method, which has many advantages. positive monitor function describing the anticipated grid density in the computational domain. The deformation based grid generation method is able to generate a grid with desired grid density distribution which is free from grid folding. In this paper, we present the latest results of the development of a novel non-rigid image registration method (NiRuDeGG) using a well-established mathematical framework known as the deformation based grid generation.

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