NESC0612 QMESH,RENUM,QPLOT, 2

1. NAME OR DESIGNATION OF PROGRAM:  QMESH,RENUM,QPLOT, 2-d FEM mesh
generation

3. DESCRIPTION OF PROBLEM OR FUNCTION

A set of five programs which make up a self-organising mesh generation package. QMESH generates meshes having quadrilateral elements on arbitrarily-shaped, two-dimensional (planar or axisymmetric) bodies. It is designed for  use with two-dimensional finite element analysis applications. A flexible hierarchical input scheme is used to describe bodies to QMESH as collections of regions. A mesh for each region is developed independently, with the final assembly and bandwidth minimization performed by the independent program, RENUM or RENUM8. RENUM is applied when four-node elements are desired. Eight-node elements (with mid-side nodes) may be obtained with RENUM8., QPLOT and QPLOT8 are plot programs for meshes generated by the QMESH/RENUM and QMESH/RENUM8 program pairs, respectively. QPLOT and QPLOT8 automatically section the mesh into appropriately-sized sections for legible display of node and element numbers. An overall plot showing the position of the selected plot areas is produced.

4. METHOD OF SOLUTION

The mesh generating process for each individual region begins with the installation of an initial mesh which is a transformation of a regular grid on the unit square. The dimensions and orientation of the initial mesh may be defined by the user or, optionally, may be chosen by QMESH. Various smoothing algorithms may be applied to the initial mesh. Then, the mesh may be "restructured" using an iterative scheme involving "element pair restructuring", "acute element deletion", and smoothing. In element pair restructuring, the interface side between two elements is removed and placed between two different nodes belonging to the pair of elements, provided that the change produces an overall improvement in the shapes of the two elements. In acute element deletion, an element having one diagonal much shorter than the other is deleted by collapsing the short diagonal to zero length The exact order in which restructuring, element deletion, and smoothing are performed may be controlled by use of "scheme" input information. The scheme input provision also allows the user to control plotting and printing. The resulting mesh descriptions for individual regions are melded into an integrated mesh by the companion program, RENUM, which also performs bandwidth minimization using a modified Cuthill-McKee algorithm. RENUM8 performs essentially the same process as RENUM, then interpolates (linearly or by circular fit) to find mid-side node positions. It then relabels the entire mesh to maintain near-minimal bandwidth. QPLOT and QPLOT8 automatically plot meshes processed by RENUM and RENUM8,  respectively. Appropriate sections of the mesh for plotting are selected by an iterative techniques which determines the size and position of each section, so as to include the smallest as yet unlabelled element in each successive section.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

QMESH - Maxima of
1,000 nodes
400 lines
100 sides
70 regions
RENUM- Maxima of
15,000 nodes (Cray1,IBM3033)
10,000 elements (Cray1,IBM3033)
QPLOT - Maxima of
5,000 nodes
4,800 elements
RENUM8 - Maxima of
10,000 output nodes (Cray1,IBM3033)
5,000 input nodes
4,800 elements
Non-straight lines should have at least two intervals, as mid-side node placement is always done linearly for lines with only one interval. Corner lines should not be used, as circular interpolation on region boundaries could produce unreasonable results near the actual corner.
QPLOT8 - Maxima of
20,000 nodes (Cray1)
10,000 elements (Cray1)
5,000 nodes (IBM3033)
4,800 elements (IBM3033)

6. TYPICAL RUNNING TIME

Meshes of up to several hundred elements which do not require restructuring are handled by QMESH in a few seconds. Large meshes involving much restructuring and smoothing may require several minutes of execution time. RENUM and RENUM8 requires a few seconds at most. QPLOT and QPLOT8 usually run in a
fraction of the time required by QMESH on a nontrivial problem.

7. UNUSUAL FEATURES OF THE PROGRAM

The hierarchical input system used in QMESH is quite natural and allows inclusion of such structures as cracks  and sliding  interfaces.

8. RELATED AND AUXILIARY PROGRAMS

QMESH is a stand-alone mesh generation program intended for use with a variety of two- dimensional finite element analysis programs.

10. REFERENCES

- QMESH,RENUM,QPLOT, NESC No. 612.3033, QMESH,RENUM,QPLOT IBM
  Version Tape Description and Sample Problem Output, National
  Energy Software Center Note 92-29, November 15, 1991.
- QMESH,RENUM,QPLOT, NESC No. 612,CRA1, QMESH,RENUM,QPLOT Crayl
  Version Tape Description, Implementation Information, and Sample
  Problem Output, National Energy Software Center No. 92-28,
  November 15, 1991.
- Rondall E. Jones, The QMESH Mesh Generation Package, Association
  for Computing Machinery SIGNUM Newsletter, Vol. 10, No. 4, pp.
  31-34, December 1975.

- R. E. Jones:
  QMESH: A Self-Organizing Mesh Generation Program
  SLA-73-1088 (July 1974)
- R. E. Jones:
  Users Manual for QMESH-RENUM a Self-Organizing Mesh Generation
  Program
  SLA-74-0239 (July 1974)
- Nodal Coordinate Data File for SANCHO
  Format of the Output File from RENUM
  7-1/7-2
- R. E. Jones:
  QMESH: A Self-Organizing Mesh Generation Program
  SLA-73-1088 (July 1974)
- R. E. Jones:
  Users Manual for QMESH-RENUM a Self-Organizing Mesh Generation
  Program
  SLA-74-0239 (July 1974)
- Nodal Coordinate Data File for SANCHO
  Format of the Output File from RENUM
  7-1/7-2

11. MACHINE REQUIREMENTS

The available memory required to execute the  programs on a CDC CYBER175 and IBM3033, respectively is: 151,000 (octal) words and 360 Kbytes (QMESH); 240,000 (octal) words and 800  Kbytes (RENUM); 152,000 (octal) words and 400 Kbytes (QPLOT); 247,000 (octal) words and 430 Kbytes (RENUM8); and 217,000 (octal) words and 400 Kbytes (QPLOT8).

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:
COS (Crayl), NOS 2.2 (CDC CYBER175), MVS (IBM3033).

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

The mesh plotted by QMESH does not include any mid-side nodes, and RENUM8 input cannot refer to any mid-side nodes. Mid-side nodes appear only in QPLOT8 plots.
The Crayl version uses the SNLA-environment Graphics Compatibility System (GCS) library to generate graphics output. Suitable alternatives are required for graphics output in other environments. Calls to the plotting package can be eliminated if no P character is included in the scheme input.
The IBM3033 version produces graphical output using the proprietary  CalComp subroutines PLOT, PLOTS, NUMBER, and SYMBOL. Subroutines DATE, CLOCK, and ITIMER are written in Basic Assembler Language and  return the current date, current wall clock time, and elapsed CPU time, respectively.

15. NAME AND ESTABLISHMENT OF AUTHORS

   CRA1          R. E. Jones, Division 2642
                 Sandia Laboratories
                 P. O. Box 5800
                 Albuquerque, New Mexico  87115
   3033          A.F. Schkade
                 Sandia National Laboratories, Albuquerque
                 L.R. Eyberger
                 National Energy Software Center
                 Argonne National Laboratory

File name	File description	Records
NESC0612_02.001	Information file	134
NESC0612_02.002	QMESH Fortran-77 source	5785
NESC0612_02.003	RENUM Fortran-77 source	1067
NESC0612_02.004	QMESH sample input data	34
NESC0612_02.005	RENUM sample input data	3
NESC0612_02.006	JCL used at Data Bank (QMESH and RENUM)	19
NESC0612_02.007	Sample output (QMESH and RENUM)	9363

File name	File description	Records
NESC0612_03.001	Information file	47
NESC0612_03.002	JCL and control information	66
NESC0612_03.003	QMESH FORTRAN source	5779
NESC0612_03.004	RENUM FORTRAN source	1070
NESC0612_03.005	QMESH sample input data	34
NESC0612_03.006	RENUM sample input data	3
NESC0612_03.007	QMESH-RENUM sample output	919