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NEA-0896 FINELM. (Abstract last modified 05-DEC-1990)


FINELM, MultiGroup Diffusion in 3-D by Finite Elements Method

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Abstract Table of Contents:

NAME | COMPUTER | PROBLEM | SOLUTION | RESTRICTIONS | CPU | FEATURES | AUXILIARIES | STATUS | REFERENCES | REQUIREMENTS | LANGUAGE | OPERATING SYSTEM | OTHER RESTRICTIONS | AUTHOR | MATERIAL | CATEGORIES |

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1. NAME OR DESIGNATION OF PROGRAM - FINELM. 


2. COMPUTER FOR WHICH PROGRAM IS DESIGNED AND OTHER MACHINE VERSION PACKAGES AVAILABLE -

To request or retrieve programs click on the one of the active versions below. A password and special authorization is required.

Explanation of the status codes.

Program-name         Package-ID  Status
FINELM               NEA-0896/01 Obsolete
FINELM               NEA-0896/02 Obsolete
FINELM               NEA-0896/03 Tested

Machines used:
Package-ID     Orig.Computer                       Test Computer
NEA-0896/03    Many Computers                      DEC VAX 8810

3. DESCRIPTION OF PROGRAM OR FUNCTION - FINELM solves multi-group diffusion theory eigenvalue (direct and adjoint) and source problems in 2- and 3-dimensional space. Geometries provided are x-y, x-y-z, r-z, r-theta, and r-theta-z. Triangular and rectangular Lagrangian elements are used. Distinct orders of approximations may be used along each axis for rectangles. For triangular elements, the appro- ximation in the plane must remain constant but can differ from the approximation in z. The coefficient matrices required for the chosen approximations are generated within the code. Both up- and down- scatterimg are provided. Group-dependent internal boundary conditions may also be considered. Albedos may range from zero to unity, both on internal and external boundaries. In addition, for internal boundary conditions, distinct albedos along each coordinate axis may be specified in order to model the total leakage more exactly and to compensate for the shape of the element. A very flexible choice of output point/element/zone flux normalization is available. A restart option has also been provided.


4. METHOD OF SOLUTION - A group by group direct solution method with Choleski decomposition of the system matrix is used. A series of smaller sub-problems may be defined using incomplete dissections should the in-core computer storage become a problem. The outer iterations are accelerated by the use of Lebedev (a variant of Chebyshev) accelerations in combination with coarse-mesh rebalancing of the space collapsing type.


5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM - The problem dimen- sions are all variable. The total problem size is limited only by on-line random access disc storage. Since most of the data is generated from very simple input, a rectangular mesh of elements is required. In the plane these are either right-triangular and/or rectangular meshes. Along the third axis a rectangular mesh is used. The degree of approximation along each axis need not necessarily be the same. Should the problem become too large to fit into core, the method of dissections may be implemented. In this manner, the problem is divided into a series of smaller linked sub-problems. It is suggested that the number of energy groups remain small as FINELM is a diffusion code. However, no built-in upper limit exists.


6. TYPICAL RUNNING TIME - Running time is a function of the number of nodes, the orders of approximation, the order of space, the number of energy groups, the width of the up- and down-scatter bands, the usage/non-usage of coarse-mesh rebalancing, the usage/non-usage of Lebedev acceleration, and the number and type of dissections.
The 2 energy group, 2-dimensional problem designated test case1 (an IAEA LWR benchmark, having 164 nodes/group, with no dissections and using both Lebedev accelerations and coarse-mesh rebalancing from the 9th iteration, required 17 seconds to model and assemble the input and Choleski system matrices; and 70 seconds to iterate 20 times to an eigenvalue convergence of 4.0E-6.
NEA 896/03: NEA-DB executed the test cases included in the package on a VAX 8810. The following CPU times were required: case 1A: 27 s; case 1B: 3m03s; case 2: 15s; case 3: 12s; case 4A: 3s; case 4B: 3s; case 5: 5s; case 6: 4s; case 7: 3s; case 8: 3s


7. UNUSUAL FEATURES OF THE PROGRAM - 
- Very simple user-friendly input. 
- Distinct approximation along each axis to minimize excessive allocation of nodes where the flux is relatively flat.
- Higher orders of approximation may be chosen. 
- Group-dependent internal boundary conditions. 
- Flexible choice of re-normalization of results. 
- Simple to use re-start option. 
- The ability to dissect the program into a sequence of smaller linked problems if fast core limits are reached.


8. RELATED AND AUXILIARY PROGRAMS - 
A postprocessor, REFINE, which uses the FINELM output point fluxes, may be used to arbitrarily sub-divide the meshes used by FINELM to produce refined average fluxes for follow-up calculations. Along an axis, the sub-divisions must be uniform, but may be distinct along each axis.
Operating instructions are distributed on the dispatched tape. 


9. STATUS
NEA-0896/01: 04-FEB-1988 Obsolete
NEA-0896/02: 28-SEP-1989 Obsolete
NEA-0896/03: 05-DEC-1990 Tested at NEADB


10. REFERENCES  - 
- D.M. Davierwalla: 
  "A Finite Element Solution to the Neutron Diffusion Equation in 
   Two Dimensions" 
  ISNM 37 (1977) 
- D.M. Davierwalla and C.E. Higgs: 
  Mathematical and Computational Meeting on Advances in Reactor 
  Computation, 28-31 March l983, Salt Lake City, U. S. A. 
  Poster Session Kiosk Address F 
- Workshop Seminar on Finite Element Multi-Dimensional Diffusion 
  Codes, 15-16 September 1983, Saclay, France 
  NEA Newsletter No. 30 (December 1983) 
NEA-0896/03:
- D.M. Davierwalla:
  FINELM: A Multigroup Finite Element Diffusion Code.
  Part I: X-Y Geometry and Dissections.
  EIR - Bericht Nr. 419  (December 1980)
- D.M. Davierwalla:
  FINELM: A Multigroup Finite Element Diffusion Code.
  Part II: R-Z Geometry and Numerical Accelerations.
  EIR - Bericht Nr. 428  (May 1981)
- C.E. Higgs and D.M. Davierwalla:
  FINELM: A Multigroup Finite Element Diffusion Code.
  Input Description, Program Description and Test Examples.
  EIR - Bericht Nr. 442  (June 1981)
- S. Pelloni, C. Higgs and D.M. Davierwalla:
  FINELM: A Multigroup Finite Element Diffusion Code.
  Part III: R-Theta Geometry and Internal Boundary Conditions.
  EIR - Bericht Nr. 459  (April 1982)
- J. Stepanek and D.M. Davierwalla:
  Chapters 3 and 5 of Draft FINELM Manual
- Comparison Tables for Two 3-Dim. Cases on CRAY, SUN and VAX


11. MACHINE REQUIREMENTS - 
- To date we have not exceeded 24 Mbytes of disc storage (for 3-dimensional x-y-z geometry, cubic approximation in the plane, quadratic in Z, 2-group 3-x dissectors, 2-y dissectors, almost 6000 nodes/group).
- A line printer or hard copy terminal with 132 characters/line would be advantageous.
- Restart file may be stored on tape. 
- The VAX 11/780 system clock is used. 

NEA-0896/03:

 NEA-DB executed the test cases on a VAX 8810 in 184k bytes of main storage. 


12. PROGRAMMING LANGUAGE(S) USED -
NEA-0896/03: FORTRAN-77 


13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED - 
CRAY        --> UNICOS 
SUN         --> SUN-OS (UNIX) 
VAX-STATION --> VMS 
CDC         --> NOS 

NEA-0896/03:

 VMS V5.3 (VAX 8810). 


14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS - 
CCCC structured format is used for interfaces files. 


15. NAME AND ESTABLISHMENT OF AUTHORS - 
         D.M. Davierwalla and C.E. Higgs 
         Paul Scherrer Institut 
         CH-5303 WUERENLINGEN (Switzerland) 


16. MATERIAL AVAILABLE -
NEA-0896/03:
NEA0896_03.001    Information file                                  117 records
NEA0896_03.002    FINELM.UPD   Source file                         9978 records
NEA0896_03.003    FINELM.VAX   VAX version source file            10036 records
NEA0896_03.004    UPDATE.FOR   Subsidiary program                   112 records
NEA0896_03.005    VAX.JOB      VAX test run procedure                93 records
NEA0896_03.006    CRAY.JOB     CRAY test run procedure              147 records
NEA0896_03.007    SUN.JOB      SUN test run procedure               120 records
NEA0896_03.008    CASE1A.DAT   Input data for test case 1A           31 records
NEA0896_03.009    CASE1B.DAT   Input data for test case 1B           71 records
NEA0896_03.010    CASE2.DAT    Input data for test case 2            26 records
NEA0896_03.011    CASE3.DAT    Input data for test case 3            20 records
NEA0896_03.012    CASE4A.DAT   Input data for test case 4A           22 records
NEA0896_03.013    CASE4B.DAT   Input data for test case 4B           20 records
NEA0896_03.014    CASE5.DAT    Input data for test case 5            17 records
NEA0896_03.015    CASE6.DAT    Input data for test case 6            16 records
NEA0896_03.016    CASE7.DAT    Input data for test case 7            16 records
NEA0896_03.017    CASE8.DAT    Input data for test case 8            16 records
NEA0896_03.018    XSLIB1.DAT   Cross-section library                 21 records
NEA0896_03.019    XSLIB2.DAT   Cross-section library                 36 records
NEA0896_03.020    XSLIB3.DAT   Cross-section library                 51 records
NEA0896_03.021    XSLIB4A.DAT  Cross-section library                 10 records
NEA0896_03.022    XSLIB4B.DAT  Cross-section library                 10 records
NEA0896_03.023    XSLIB5.DAT   Cross-section library                  4 records
NEA0896_03.024    FINOUT.DAT   VAX output obtained at NEADB        6859 records
NEA0896_03.025    OUTPUT.XMP   CRAY-XMP output                     7575 records
NEA0896_03.026    OUTPUT.SUN   SUN output                          6945 records


17. CATEGORIES  - 

- C.  Static Design Studies


Keywords: COARSE MESH, DIFFUSION, EIGENVALUES, FINITE ELEMENT METHOD, FINITE ELEMENTS, LAGRANGE EQUATIONS, MULTIGROUP, R-THETA, R-Z, RECTANGULAR, THREE-DIMENSIONAL, TRIANGULAR, TWO-DIMENSIONAL, X-Y, X-Y-Z

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