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NEA-0443 FEM-2D.

FEM-2D, 2-D MultiGroup Diffusion in X-Y Geometry

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1. NAME OR DESIGNATION OF PROGRAM:  FEM-2D.
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2. COMPUTERS
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Program name Package id Status Status date
FEM-2D NEA-0443/01 Tested 01-JUL-1978

Machines used:

Package ID Orig. computer Test computer
NEA-0443/01 CDC CYBER 173 CDC CYBER 173
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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.
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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.
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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).
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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
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7. UNUSUAL FEATURES: UNUSUAL FEATURES OF THE PROGRAM
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8. RELATED AND AUXILIARY PROGRAMS:  RSIMK simulates parts of the RSYST modular system.
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9. STATUS
Package ID Status date Status
NEA-0443/01 01-JUL-1978 Tested at NEADB
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10. REFERENCES
NEA-0443/01, included references:
- 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
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11. MACHINE REQUIREMENTS

CDC 6600 - use of disks for multigroup problems. Use of extended core storage for BLOCK DATA.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NEA-0443/01 FORTRAN-IV
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13. OPERATING SYSTEM OR MONITOR UNDER WHICH PROGRAM IS EXECUTED:  SCOPE.
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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.
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15. NAME AND ESTABLISHMENT OF AUTHOR

    Institut fuer Kernenergetik
    University of Stuttgart
    7000 Stuttgart 80
    Pfaffenwaldring 31
    Germany, F.R.
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16. MATERIAL AVAILABLE
NEA-0443/01
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
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17. CATEGORIES
  • C. Static Design Studies

Keywords: Lagrange equations, diffusion equations, finite element method, power reactors, two-dimensional, x-y.