  The request for high-quality solutions continually grows in a world where
more and more tasks are executed through computers. This also counts for fields
such as engineering, computer graphics, etc., which use meshes to solve their
problems. A mesh is a combination of some elementary elements, for which
hexahedral elements are a good choice thanks to their superior numerical
features. The solutions reached using these meshes depend on the quality of the
elements making up the mesh. The problem is that these individual elements can
take on a shape which prevents accurate computations. Such elements are
considered to be invalid. To allow users to get accurate results, the shape of
these elements must therefore be changed to be considered valid. In this work,
we combine the results of two papers to scan a mesh, identify possible invalid
elements and then change the shape of these elements to make them valid. With
this combination, we end up with a working algorithm. But there is room for
improvement, which is why we introduce multiple improvements to speed up the
algorithm as well as make it more robust. We then test our algorithm and
compare it to another approach. This work, therefore, introduces a new
efficient and robust approach to untangle invalid meshes.
