Figure 14 also reports cross-sectional views of the four mesh types used: the pyramidal and prismatic (flatirons) meshes are both derived from the same o-grid scheme as the hexahedral mesh, by splitting the hexahedra either in two or in 6 child cells.

Cell Type Mesh 1 Mesh 2 Mesh 3 Hexahedra 14,400/0.39 52,200/0.25 98,400 / 0.20 Tetrahedra 12,800/0.80 47,207/0.49 98,557/0.38 Pyramids 14,400/0.52 52,920/0.33 98,124/0.27 Flatirons 13,770/0.63 50,688/0.41 99,180/0.33 Table 4.

Little is known about the conditions under which a Hamiltonian path exists in grids consisting of quadrilaterals or

hexahedra. An algorithm is given that might find a through-vertex Hamiltonian path in a quadrilateral or hexahedral grid, if one exists, and is likely to give a broken path with a small number of discontinuities, i.e., something close to a through-vertex Hamiltonian path.

Interacting sprays, characterized on the CALIST facility, are simulated inside a parallelepiped mesh of 800,000

hexahedra regular cells, representing a domain of 1.20 x 0.80 x 2 m.

The microorganisms themselves provided nucleation sites for the crystallization process with the crystals mainly being

hexahedra and oblique polyhedra and ellipsoids, indicating modulated growth.

The electric fields inside the

hexahedra are represented as [2,18]

For the finite element discretisation of (2.4), we are given a shape regular family {[[tau].sub.h]} of decomposition of [OMEGA] into d-simplices, quadrilaterals, or

hexahedra. The diameter of [KAPPA] will be denoted by [h.sub.[KAPPA]] and the mesh size parameter h is defined by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].

In 3D the mesh consists either of tetrahedra, of rectangular

hexahedra, or of rectangular pentahedra (i.e.

In two dimensions K can be triangles or quadrilaterals, in three dimensions the elements are tetrahedra,

hexahedra, prisms or pyramids.

In 3d the procedure is straight forward and is applicable to

hexahedra, tetrahedra, prisms and pyramids.

Approximation of De Rham's complex on

hexahedra. In this section we develop exact sequences of finite element spaces on unstructured hexahedral and quadrilateral grids.

Let [T.sup.[OMEGA].sub.h] be a regular triangulation made of elements that are tetrahedra with a maximum size h (the extension to the

hexahedra does not create any technical difficulty).