NEA-0896 FINELM.

1. NAME OR DESIGNATION OF PROGRAM:  FINELM.

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.

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)

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

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED

CRAY        --> UNICOS
SUN         --> SUN-OS (UNIX)
VAX-STATION --> VMS
CDC         --> NOS

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)

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