Hexahedral Edge Elements — Some 3D Applications

Abstract

Unlike 2D finite element calculations, in which classical problems are solved using well established formulations, 3D finite element application is still an open area in research. Although some formulations are already widely used, new numerical and physical approaches are still evolving. In fact, there are many difficulties and compromises involved in 3D calculations. Some of these are:

• The number of unknowns can vary from one to four per node of the mesh, depending on the formulation.

• Often, more than one formulation is used in the same problem, each formulation being used in different parts of the physical domain. These formulations must be properly coupled.

• Application of gauges in order to improve the condition of the system matrix (which is normally ill-conditioned). The application of these gauges allows faster convergence in the iterative solution of the system of equations but it also affects accuracy of results.

• The matrix solver itself. The ICCG method of solution (to be discussed later in this chapter) is the most commonly used method for solution of the system of equations. It is an iterative method and divergence can occur, depending on the problem and/or on the condition of the system of equations.