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1.4 Inquiries and verification

1.4.1 Inquiries

Preprocessor IMAGXX lists the contents of an arbitrary type D.S. It calls module IM DS corresponding to the D.S. under consideration (see [MODULEF User Guide - 2]).

Preprocessor INFOXX obtains, in particular, information about a mesh stored in a D.S. NOPO or GEOM. In the case of a NOPO type D.S., it calls module INFONO, described in chapter 4 of [MODULEF User Guide - 3]. In the case of a GEOM type D.S., it calls module INFOGE, described in the same chapter of [MODULEF User Guide - 3].

The information obtained is the following, depending on the options chosen:

for a D.S. NOPO, and for a D.S. GEOM.

When changing (using NOPGXX or GEONXX) from one type of D.S. to another, we can obtain one or the other type of information.

Preprocessor REFPXX calls module REFPOI (see [MODULEF User Guide - 3]) which lists the numbers of the points in a mesh with a given reference.

Preprocessor REFNXX calls module REFNOP (see [MODULEF User Guide - 3]) which lists the numbers of the elements in a mesh containing a face or edge with given reference.

1.4.2 Verification

Preprocessor QUALXX verifies that all the elements in a two-dimensional mesh have positive surfaces. It also ascertains the element quality of a mesh.

For the three-dimensional case, the verification for positiveness of the element volumes is done whereas the quality is only calculated for tetrahedral type elements.

The module called is QUALNO. The element computational subroutines are: MESELE for a triangle, MESELQ for a quadrilateral, and MESELT for a tetrahedron (MESELP and MESELH for a pentahedron and a hexahedron). These subroutines evaluates the element surface (volume). In essence, the formula to calculate the quality of a triangle is the following:

where is a normalization coefficient ( is set equal to in such a way that Q=1. for a equilateral triangle), h is the diameter of the element and is the radius of the inscribed circle. This formula can be expressed as:

where p is the semi-perimeter and S is the surface of the triangle. For simplicity, we use the same formula in the case of a quadrilateral (the result is not exact but the elements are compared with each other without difficulty. On could undoubtedly find better!). For a tetrahedron, the formula is analogous (and therefore exact) to that of the triangle.

Note that the higher the value of Q, the worse the element.

Remark: QUALXX
replaces GEODXX, which has been discarded.


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