NEA-0443 FEM-2D.

1. NAME OR DESIGNATION OF PROGRAM:  FEM-2D.

3. NATURE OF PHYSICAL PROBLEM SOLVED

FEM-2D solves the two-dimensional diffusion equation in x-y geometry. This is done by the finite elements method.

4. METHOD OF SOLUTION

FEM-2D uses triangular elements with first and second order Lagrange approximations. The systems equations are formulated in multigroup form and solved by Cholesky procedure which operates only on nonzero elements. Various acceleration techniques are available for the outer iteration. Fluxes along various lines and rates in arbitrary zones may be output.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The code uses variable dimensioning. Thus, the problem size is restricted by the largest array which usually is the systems matrix. Fluxes of all groups are kept in memory. This might become another restrictive data set for a large number of groups. The validity of the results is restricted by the approximations used. FEM-2D requires a finite element net which allows the approximation of fluxes by at most parabolas. The node distribution should be more dense in areas of heavy flux changes (near absorbers or the reflector).

6. TYPICAL RUNNING TIME

The running time is determined by the number of elements, the number of nodes and the approximation used. Due to  the source and rate calculations, the number of nodes is the least important factor. Typical running times on a CDC 6600 for a two group problem are

------------------------------------------------------
nodes  elements  approximation   time/iteration (sec)
------------------------------------------------------
177    301       first order     0.26
654    1204      first order     0.70
501    228       second order    0.48
654    301       second order    0.61
746    345       second order    0.70

7. UNUSUAL FEATURES: UNUSUAL FEATURES OF THE PROGRAM

8. RELATED AND AUXILIARY PROGRAMS:  RSIMK simulates parts of the RSYST modular system.

- H.P. Franke and F.A.R. Schmidt:
FEM2D - Program for Solving the Two-Dimensional Diffusion Equation by the
Method of Finite Elements
Progress Report of Research Task RB 78 I
July 1, 1974, Report Number 4-25 (ORNL-tr-2971)
- F.A.R. Schmidt and H.P. Franke:
Power Reactor Calculation with the Finite Elemen Program FEM 2D
Technical Notes (Reprint from Nucl. Sci. & Eng. 56, 431-433
- F.A.R. Schmidt:
FEM-2D - Input Description and Performance
March 1975, ike 4-43

11. MACHINE REQUIREMENTS

CDC 6600 - use of disks for multigroup problems. Use of extended core storage for BLOCK DATA.

13. OPERATING SYSTEM OR MONITOR UNDER WHICH PROGRAM IS EXECUTED:  SCOPE.

14. ANY OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

FEM-2D is written in overlay mode.
It uses the following COMPASS routines

VEKMSKA - multiplies a vector by a SCALAR
VEKMVEK - multiplies a vector by a vector.
UTYLITY - transfers data array to the disk without using a buffer area.

15. NAME AND ESTABLISHMENT OF AUTHOR

    Institut fuer Kernenergetik
    University of Stuttgart
    7000 Stuttgart 80
    Pfaffenwaldring 31
    Germany, F.R.

File name	File description	Records
NEA0443_01.001	INFORMATION	5
NEA0443_01.002	'RSIMK' - SOURCE PROGRAM (F4+COMPASS)	539
NEA0443_01.003	SOURCE PROGRAM (F4,COMPASS)	4987
NEA0443_01.004	SAMPLE PROBLEM INPUT DATA	62
NEA0443_01.005	SAMPLE PROBLEM PRINTED OUTPUT	490