  A multi-resolution hexahedron element and method is presented with a new
multi-resolution analysis (MRA) framework. The MRA framework is formulated out
of a mutually nesting displacement subspace sequence, whose basis functions are
constructed of scaling and shifting on the element domain of a basic node shape
function. The basic node shape function is constructed from extending to other
seven quadrants around a specific node of a node isoparametric shape function.
The MRA endows the proposed element with the resolution level (RL) to adjust
the element node number, thus modulating structural analysis accuracy
accordingly. As a result, the traditional 8-node hexahedron element and method
is a mono-resolution one and also a special case of the proposed element and
method. The accuracy of a structural analysis is actually determined by the RL,
not by the mesh. The simplicity and clarity of shape function construction with
the Kronecker delta property and the rational MRA enable the proposed element
method to be more rational, easier and efficient in its implementation than the
conventional mono-resolution solid element method or other MRA methods. The
multi-resolution hexahedron element is more adapted to dealing with the
accurate computation of structural problems.
