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Digitized by the Internet Archive 
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 http://archive.org/details/generalizedeleme946spee 
 
°' ' 'UIUCDCS-R-78-946 
 T 2 ^ 
 
 /r(<XA^_ 
 
 UILU-ENG 78 1738 
 C00-2383-0055 
 
 THE GENERALIZED ELEMENT METHOD 
 by 
 B. Speelpenning 
 
 November 1978 
 
UIUCDCS-R-78-946 
 
 THE GENERALIZED ELEMENT METHOD 
 by 
 B. Speelpenning 
 
 November 1978 
 
 DEPARTMENT OF COMPUTER SCIENCE 
 
 UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN 
 
 URBANA, ILLINOIS 61801 
 
 Supported in part by the U. S. Department of Energy, Grant US ENERGY/EY-76-S-02-2383 
 
PREFACE 
 
 This paper was written in 1973 to report on work that I did at the TNO-IBBC 
 institute for Applied Technological Research in Delft, the Netherlands, and 
 at the Delft University of Technology, also in Delft, the Netherlands. 
 The paper was privately circulated among people at the IBM Research Center 
 in Yorktown Heights, N.Y., and by them to others, but it was never published. 
 Because of a number of references made to this paper in the literature, it was 
 decided to make it available as a departmental report; no changes have been 
 made to the original, nor any attempts to bring it up to date: it is a direct 
 photographic reproduction of the 1973 paper. 
 
 The paper deals with the computational intricacies of assembling and solving 
 the linear system of equations that arise from applying the finite element 
 method to civil engineering structural analysis, but the method presented 
 can in principle be applied wherever a network obeys Kirchhoff's laws. 
 The "generalized element method" is an improvement over older methods of 
 solving stiffness matrix equations. It offers a clean, very general theoretical 
 basis, a very efficient algorithm that achieves the low operation counts 
 of linked list techniques without any of the overhead associated with those, 
 and great flexibility in setting up the equations. 
 
 The method has been used since 1973 in the DIANA system developed at TNO-IBBC 
 as a general purpose program for performing structural analysis and has indeed 
 proven to be very fast, flexible and reliable. It routinely deals with systems 
 containing 5000 equations and a "bandwidth" of up to about A00. 
 

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 FormAEC-427 U.S. ATOMIC ENERGY COMMISSION 
 
 aec 6 m3201 UNIVERSITY-TYPE CONTRACTOR'S RECOMMENDATION FOR 
 
 DISPOSITION OF SCIENTIFC AND TECHNICAL DOCUMENT 
 
 ( See Instructions on Reverse Side ) 
 
 1. AEC REPORT NO. 
 
 COO-2383-0055 
 
 2. TITLE 
 
 THE GENERALIZED ELEMENT METHOD 
 
 3. TYPE OF DOCUMENT (Check one): 
 
 (3 a- Scientific and technical report 
 
 I I b. Conference paper not to be published in a journal: 
 
 Title of conference 
 
 Date of conference 
 
 Exact location of conference 
 
 Sponsoring organization 
 
 □ c. Other (Specify! 
 
 4. RECOMMENDED ANNOUNCEMENT AND DISTRIBUTION (Check one): 
 
 Ixl a. AEC's normal announcement and distribution procedures may be followed. 
 
 I | b. Make available only within AEC and to AEC contractors and other U.S. Government agencies and their contractors. 
 ~2 c. Make no announcement or distrubution. 
 
 5. REASON FOR RECOMMENDED RESTRICTIONS: 
 
 6. SUBMITTED BY: NAME AND POSITION (Please print or type) 
 
 C. W. Gear 
 
 Professor and Principal Investigator 
 
 Organization 
 
 Department of Computer Science 
 University of Illinois U-C 
 Urbana, Illinois £1801 
 
 Signature f 
 
 Date 
 
 November 1978 
 
 FOR AEC USE ONLY 
 
 7. AEC CONTRACT ADMINISTRATOR'S COMMENTS, IF ANY. ON ABOVE ANNOUNCEMENT AND DISTRIBUTION 
 RECOMMENDATION: 
 
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 CD a. AEC patent clearance has been granted by responsible AEC patent group. 
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r; 
 
BIBLIOGRAPHIC DATA 
 SHEET 
 
 1. Report No. 
 
 UIUCDCS-R-78-946 
 
 3. Recipient's Accession No. 
 
 4. Title and Subtitle 
 
 THE GENERALIZED ELEMENT METHOD 
 
 5. Report Date 
 
 November 1978 
 
 7. Author(s) 
 
 B. Speelpenning 
 
 8- Performing Organization Rept. 
 
 No - R-78-946 
 
 9. Performing Organization Name and Address 
 
 Department of Computer Science 
 University of Illinois U-C 
 Urbana, Illinois 61801 
 
 10. Project/Task/Work Unit No. 
 
 11. Contract /Grant No. 
 
 US ENERGY/ 
 EY-76-S-02-2383 
 
 12. Sponsoring Organization Name and Address 
 
 U. S. Department of Energy 
 Chicago Operations Office 
 9800 South Cass Avenue 
 Argonne, Illinois 60439 
 
 13. Type of Report & Period 
 Covered 
 
 research 
 
 14. 
 
 15. Supplementary Notes 
 
 16. Abstracts 
 
 This paper presents a new method for solving large, sparse symmetric 
 equations derived from networks. The method is particularly suited 
 arising from using the finite element method. The main characterist 
 method are its homogeneity and efficiency. Homogeneity allows of au 
 substructuring, interrupt and restart facilities, all completely con 
 the elimination sequence of the nodes. For each elimination sequenc 
 operation count is achieved. The amount of I/O can be controlled to 
 extent. The generalized element method has evolved from a new inter 
 the wavefront method. It may be used adaptively in combination with 
 as the hypermatrix method to optimize the use of available core. 
 
 systems of 
 to networks 
 ics of the 
 tomatic 
 trolled by 
 e, minimal 
 
 a certain 
 pretation of 
 
 such methods 
 
 17. Key Words and Document Analysis. 17a. Descriptors 
 
 finite element method, sparse linear equations, superelements , computational 
 linear algebra, wavefront method, DIANA system, structural analysis, 
 stiffness matrix. 
 
 17b. Identif iers/Open-Knded Terms 
 
 17c. ( OSAT1 Field/Group 
 
 18. Availability Statement 
 
 unlimited 
 
 FORM NTIS-3B (10-70) 
 
 19. Security Class (This 
 Report) 
 
 UNCLASSIFIED 
 
 20. Security (lass (This 
 Page 
 
 UNCLASSIFIED 
 
 21. No. of Pages 
 11 
 
 22. Price 
 
 USCOMM-DC 40329-P7* 
 
Alia 1 !