ODU Homepage

[access count]
  

              
   Duc Thai Nguyen

    
Professor, Ph.D.
Director, Multidisciplinary Parallel-Vector Computing Center

B.S.C.E., Northeastern University
M.S.C.E., University of California, Berkeley
Ph.D., University of Iowa

Office) Room 1310, Engineering and Computation Building
Phone) 757.683.3761
Fax) 757.683.5354
e-mail) nguyen@cee.odu.edu

  Research Interests


  1. Finite element analysis and optimal design
  2. Parallel computational mechanics
  3. Linear & nonlinear design optimization theories
  4. Design sensitivity analysis
  5. Nonlinear finite element algorithms
  6. Iterative solvers with pre_conditioning
  7. Parallel domain decomposition
  8. Parallel-vector equation (sparse, dense, symmetrical, unsymmetrical, real/complex numbers, positive/negative/indefinite matrix, incore/out-of-core with/without pivoting) solvers
  9. Eigen_solvers
  10. Structural dynamics

  Recent and Current Research Projects


  1. D.T. Nguyen, Principal Investigator, "Parallel Domain Decomposition Formulation and Software for Large-Scale Sparse/Unsymmetrical 3D Aeroacoustics Applications", NASA Langley Research Center, $ 135,000, January 15'2001 - Jan. 15'2004.

  2. "An Out-of-Core Revised Simplex algorithm for Large-Scale Linear Programming Problems," NASA LaRC GSRP award (with M.S. Student: Mr. Kevin Gould), NASA Langley Research Center, $22,000 + $22,000 + $22,000 (August 1, 1999-August 1, 2002)

  3. "Finite Element Analysis of Reverberation Chambers",$193,509,Co-PI. (with Dr. Bunting), NASA LaRC, Hampton, VA, January 1, 1998 - December 30, 2000.

  4. "Finite Element Analysis of 2-D Field and Structural Problems", $16,000, Co-PI (with Ms. Vanessa Hill, through Prof. Tiwari's ICAM budget), NASA LaRC, Hampton, VA, Jan. "98 - Dec. '98, also $6000 (NASA-ODU/ICAM, Jan.'99 - May'99).

  5. "Linear Programming and Equation Solver Algorithms for Thermal-Structural Analysis and Design Application", $21,864, Principal Investigator, NASA LaRC,Hampton, VA, October 1, 1997 - September 30, 1998.

  6. "New Parallel Algorithms for Structural Analysis and Design of Aerospace Structures," $160,000, Principal Investigator, NASA LaRC, Hampton, VA, November 1, 1995 - June 30, 1998.

  7. "Finite Element Software for Multidisciplinary Design Optimization," $20,000, Principal Investigator, NASA LaRC, Hampton, VA, February 1, 1995 - November 30, 1995.

  8. "Computational Mechanics on High-Performance Computers," $60,000, PI, NASA LaRC, Hampton, VA, October 1, 1994 - October 1, 1995.

  9. "Development of Concurrent Procedures for Large-Scale Integrated Structural Analysis and Optimization," $250,000, Principal Investigator, NASA LaRC, Hampton, VA, October 1, 1991 - October 1, 1994.

  10. "CSI-Design Code on High-Performance Computers," $26,000, Principal Investigator, NASA LaRC, Hampton, VA, January 1, 1993 - December 30, 1993.

  11. "Parallel-Vector Control Structure Integrated Methodology for General Dynamic Loads," $25,000, PI, NASA LaRC, Hampton, VA, August 1, 1992 - August 1, 1993.

  12. "Analysis and Design of Large-Scaled Pyramidal Truss Core Panels", The Jonathan Corp., Virginia Power Co., and Center of Innovative Technology (CIT), July 1, 1992-June 30'93, $184,000 (P.I. = Prof. Gene HOU, Co-PIs = D.T. Nguyen, and others)

  13. "Parallel-Vector Computations for CSI Design Code," $15,000, Principal Investigator, NASA LaRC, Hampton, VA, October 1, 1991 - October 1, 1992.

  14. "Parallel-Vector Algorithms for Nonlinear Finite Element Analysis," $20,355, Principal Investigator, AFOSR, Albuquerque, NM, August 1, 1991 - September 30, 1993.

  15. "Parallel-Vector Finite Element Analysis for the CSM Testbed," $58,458, PI, NASA LaRC, Hampton, VA, October 1, 1990 - October 1, 1991.

  16. "Parallel-Vector Computation for Controls-Structures Interaction Code," $21,931, PI, NASA LaRC, Hampton, VA, October 1, 1990 - October 1, 1991.

  17. Co-P.I. (with P.I. Dr. Ishibashi), NSF Grant No. MSS-8920878, "Development of Hybrid Discrete Element/Finite Element Model for Large Deformation Geotechnical Engineering Problems," $75,514 August 15, 1990 to August 14, 1992.

  18. NASA Minority Graduate Grants (for Mr. Kevin R. Pullen, and Mr. James E. Demby, Jr.), NASA Headquarters, Washington, D.C., $44,000, August 1990 - August 1991.

  19. "Parallel-Vector Processing For Nonlinear Finite Element Analysis," PI, $37,996 (including $18,000 cost-sharing from ODU for NCUBE parallel computer), AFOSR (January 1, 1990 - December 31, 1990).

  20. NASA Minority Graduate Grant (for Mr. Kevin R. Pullen, ODU Student), $18,000 per year, NASA Headquarters, Washington, D.C., August 1989 - August 1990.

  21. "Parallel Nonlinear Unconstrained Optimization," PI, $12,998, NASA LaRC, Hampton, VA, June 15, 1989 - June 15, 1990.

  22. "Substructuring Formulation and Domain Decomposition In a Parallel TestBed Environment" $27,800, Principal Investigator, NASA LaRC, Hampton, VA, April 1, 1989 - April 1, 1990.

  23. "Parallel Procedures For Statics, Eigenvalue Analysis and Struct. Dynamics," $21,188, NASA Langley Research Center, Hampton, VA, March 1, 1988 to February 28, 1989.

  24. "Simplified Procedures for Dynamic Anal. of Complex Structures," $61,000, Newport News Shipbuilding and Drydock Company, and Center for Innovative Technology Engr. Clinic, One of the PIs (with Dr. Jean W. Hou), November 20, 1986 to August 20, 1987.

  25. "An Element-By-Element Algorithm for Large Scale Structural Dynamics," $3,700 (out of which $500 was used to buy the computer equipment for the CE Department), Principal Investigator. Old Dominion University Research Foundation, Summer 1986.

  26. Recipient of Travel Support Grant (July 1983, sponsored by NSF and IFIF, $1,000, to Copenhagen, Denmark).

  Publications


  • Books & Editors

    1. Nguyen,Duc T., "Parallel/Sparse Finite Element Methods -
      Volume 1: Linear Statics and Eigen-Solutions"
      Volume 2: Nonlinear Dynamics Solutions"
      Volume 3: Sensitivity Analysis and Optimum Solutions"
      (Expected date of completion for Volume 1: December 31, 2004)

    2. Nguyen,Duc T.,"Parallel-Vector Equation Solvers for Finite Element Engr. Applications" Published in October'2001 (Copyright'2002), by Kluwer/Plenum Academics Publisher, ISBN # 0-306-46640-6. (http://www.wkap.nl/book.htm/0-306-46640-6)

    3. Storaasli,O.O., Housner,J.M., and Nguyen, D.T., Guest Editors, Special Issue: "Parallel Computational Methods for Large-Scale Structural Analysis and Design".Computing Systems in Engineering, An Inter. Journal, Vol. 4, Nos. 4-6 (August/October/December 1993), Pergamon.
    
    
    
    
  • Journal Articles

      In The Areas of SENSITIVITY & OPTIMIZATION:

    1. S.D. Rajan and D.T. Nguyen,Design Optimization of Discrete Structural Systems Using MPI-enabled Genetic Algorithm, Journal of Structural and Multidisciplinary Optimization, 27, 1-9, 2004.

    2. S.D. Rajan, and D.T. Nguyen, "Design Optimization of Discrete Structural Systems Using MPI-enabled Genetic Algorithm", Accepted to appear in STRUCTURAL OPTIMIZATION Research Journal

    3. S.D. Rajan, D.T. Nguyen, M.D. Deshpande and L. Harrell, "Optimal Design of Engineering Systems Using MPI-enabled Genetic Algorithm", Computer Assisted Mechanics and Engineering Sciences (CAMES) Journal, 11(2-3), 2004.

    4. Nguyen, D.T., Bai, Yu, Qin, J., and Hu, Yusong, "Computational Aspects of Linear programming Simplex Method" Advances In Engineering Software, Volume 31, Nos. 8-9, pages 539-546 (August-Sept.'2000)

    5. Nguyen, D.T., Tang, W.H., Tung, H.K. and Runesha, H.B.,"Nonlinear Constrained Optimizer and Parallel Processing for Golden Block Line Search," in COMPUTER ASSISTED MECHANICS and ENGINEERING SCIENCES Journal (CAMES Journal, Vol. 6, no. 3-4, 1999, pages 469-477).

    6. Nguyen, D.T., Runesha, H., Belegundu, A.D., and Chandrupatla, T.R, "Interior Point Method and Indefinite Sparse Solver for Linear Programming Problems", Advances in Engineering Software, Vol. 29, No. 3-6, pp. 409-414 (1998).

    7. Qin, J. and Nguyen, D.T., "Generalized Exponential Penalty Function for Nonlinear Pro- gramming," Computers & Structures Journal, Vol. 50, No. 4, (Feb. 1994), pp. 509-514.

    8. Nguyen, D.T., "Multilevel Structural Sensitivity Analysis," Computers & Structures Journal, Vol. 25, No. 2, pp. 191-202, April 1987.

    9. Nguyen, D.T. and Rogers, J.L., Jr., "Optimal Design of Structures with Multiple Design Variables Per Group and Multiple Loading Conditions on the Personal Computer," Computers & Structures, Vol. 22, No. 2, pp. 179-184, April 1986.

    10. Nguyen, D.T.,Arora, J.S.,and Belegundu, A.D., "Design Optimization Codes for Structures: DOCS Computer Program," Journal of Aircraft, Vol. 2, No. 9, pp. 817-824, September 1983.
    
    
    
    
      In The Areas of STRUCTURAL DYNAMICS/EARTHQUAKES & VIBRATIONS:

    1. Nguyen, D.T., Bunting, C., Moeller, K.J., Runesha H.B., and Qin, J., "Subspace and Lanczos Sparse Eigen-Solvers for Finite Element Structural and Electromagnetic Applications" Advances In Engineering Software, Volume 31, Nos. 8-9, pages 599-606 (August-Sept.'2000)

    2. Qin, J. and Nguyen, D.T., "Structure/Load Dependent Vectors For Linear Structural Dynamics", Computers & Structures Journal, Vol. 50, No. 4 (February 1994), pp. 515-524.

    3. Zhang, Y. and Nguyen, D.T., "Parallel-Vector Design Sensitivity Analysis in Structural Dynamics," Computing Systems in Engr. Journal, Vol. 3, No. 1-4, pp. 365-378, (1992).

    4. Zhang, Y., Nguyen, D.T.and Hou, G.W., "An Alternative Formulation for Design Sensitivity on Linear Struct. Dynamic Systems," Computers & Structures Journal, Vol. 44, No. 3, pp. 689-692 (1992).
    
    
    
    
      In The Areas of ALGORITHMS/SOFTWARE For EQUATIONS & EIGEN-SOLUTIONS:

    1. D.T. Nguyen, W.R. Watson, S. Tungkahotara, and S.D. Rajan, "Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis", Journal of Computational and Applied Mechanics, Vol. 4, No. 2, pages 189-201 (2003),

    2. W.R. Watson, D.T. Nguyen, C.J. Reddy, V.N. Vatsa, and W.H. Tang, "Algorithms and Application of Sparse Matrix Assembly and Equation Solvers for Aeroacoustics", AIAA Journal, Volume 40, No. 4, pages 661-670 (April'2002)

    3. Nguyen, D.T., Qin, J., Sancer, M.I. and McClary, R., "Finite Element-Boundary Integral Methods in Electro-magnetics", March'02, pp. 391-400, Volume 38, No. 5, in Finite Elements in Analysis and Design, an International Journal (Elsevier Science publisher).

    4. Nguyen, D.T., Hou, Gene, Runesha, H. and Han, Bangfei,"Alternative approach for solving Sparse INDEFINITE Symmetrical system of Equations", Advances In Engineering Software, Volume 31, Nos. 8-9, pages 581-584 (August-Sept.'2000)

    5. Runesha, H.B., and Nguyen, D.T., "Vectorized Sparse UnSymmetrical Equation solver for Computational Mechanics" Advances In Engineering Software, Volume 31, Nos. 8-9, pages 563-570 (August-Sept.'2000)

    6. Chen, P. , Runesha, H., Nguyen, D.T., Tong, P. and Chang, T.Y.P., "Sparse Algorithms For Indefinite Systems of Linear Equations", in COMPUTATIONAL MECHANICS Journal, Vol. 25, No. 1, pages 33-42 (Feb. 2000).

    7. Qin, J. and Nguyen, D.T., "A Parallel-Vector Equation Solver for Distributed Memory Computers," Computing Systems in Engineering Journal, Vol. 5. No. 1, (1994).

    8. Qin, J., Agarwal, T.K., Storaasli, O.O., Nguyen, D.T. and Baddourah, M.A., "Parallel- Vector Out-of-Core Equation Solver for Computational Mechanics," Computing Systems in Engineering Journal, Vol. 4, No. 4-6, pp. 381-386 (1993).

    9. Nguyen, D.T. and Arora, J.S., "An Algorithm for Solution of Large Eigenvalue Problems," Computers & Structures, Vol. 24, No. 4, pp. 645-650, August 1986.

    10. Arora, J.S. and Nguyen, D.T., "Eigen-solution for Large Structural Systems with Substructures", International Journal for Numerical Methods in Engineering, Vol. 15, 1980, pp. 333-341.
    
    
    
    
      In The Areas of PARALLEL/VECTOR COMPUTATIONS:

    1. Qin, J. and Nguyen, D.T., "A Tridiagonal Solver for Massively Parallel Computers", Advances in Engineering Software, Vol. 29, No. 3-6, pp. 395-397 (1998).

    2. Nguyen, D.T., Qamar, R. and Runesha, H. "Automatic Differentiation for Design Sensitivity Analysis of Structural Systems Using Parallel-Vector Processors", Advances in Engineering Software, Vol. 29, No. 3-6, pp. 375-382 (1998).

    3. Qin, J., and Nguyen, D.T., "A Parallel-Vector Simplex Algorithm On Distributed Memory Computers," Structural Optimization Journal, Vol. 11, Nos. 3 & 4, pp. 260-264, (1996).

    4. Agarwal, T.K., Storaasli, O.O., and Nguyen, D.T., "A Parallel-Vector Algorithm For Rapid Structural Analysis on High Performance Computers," to appear (Technical Note) in Computers and Structures Journal.

    5. Qin, J., Gray, Jr., C.E., Mei, C. and Nguyen, D.T., "A Parallel-Vector Equation Solver for Unsymmetric Matrices on Supercomputers," Computing Systems in Engineering, An International Journal, Vol. 2, No. 2/3, September 1991 (Pergamon Press), pp.197-202.

    6. Baddourah, M.A., and Nguyen, D.T., "Parallel-Vector Processing for Linear Programming," Journal of Computers and Structures, Vol. 38, No. 3, 1991, pp.2 9-282.
    
    
    
    
      In The Areas of FINITE ELEMENT APPLICATIONS:

    1. Baddourah, M.A. and Nguyen, D.T., "Parallel-Vector Computations for Geometrically Nonlinear Finite Element Analysis," Computers & Structures Journal, Vol. 51, No. 6, (1994), pp. 785-789.

    2. Maker, B.N., Qin, J. and Nguyen, D.T., "Performance of NIKE3D with PVSOLVE On Vector and Parallel Computers," Computing Systems In Engineering Journal, Vol. 5, No. 4-6, pp. 363-368 (Aug./Oct./Dec.' 1994).

    3. Storaasli, O.O., Nguyen, D.T., Baddourah, M.A. and Qin, J., "Computational Mechanics Analysis Tools for Parallel-Vector Supercomputers", Computing Systems in Engineering Journal, Vol. 4, No. 4-6, pp. 349-354 (1993).

    4. Belvin, W.K., Maghami, P.G. and Nguyen, D.T., "Efficient Use of High Performance Computers for Integrated Controls and Structures Design," Computing Systems in Engineering Journal, Vol. 3, No. 1-4, pp. 181-188, (1992).

    5. Nguyen, D.T., Storaasli, O.O., Carmona, E.A., Al-Nasra, M., Zhang, Y., Baddourah, M.A., and Agarwal, T.K., "Parallel-Vector Computation for Linear Structural Analysis and Nonlinear Unconstrained Optimization Problems," Computing Systems in Engineering, An International Journal, Vol. 2, No. 2/3, September 1991, (Pergamon Press), pp. 175-182.

    6. Moayyad, M.A., and Nguyen, D.T.,"An Algorithm For Domain Decomposition in Finite Element Analysis," Journal of Computers and Structures, Vol. 39, (1-4), 1991, pp. 277-290.

    7. Storaasli, O.O., Nguyen, D.T., and Agarwal, T.K., "The Parallel Solution of Large-Scale Structural Analysis Problems on Supercomputers," AIAA Journal, Vol. 28, No.7, pp. 1211-1216 (July 1990).

    8. Nguyen, D.T. and Arora, J.S., "Fail-Safe Optimal Design of Complex Structures with Substructures," ASME Journal of Mechanical Design, Vol. 104, No. 4, October 1982.
    
    
    
    
    
    
  • Proceedings/Conference Papers

    1. D. Lau, S. Yu, A. Damle, J. St. Ville, A. D. Belegundu, D.T. Nguyen and S.D. Rajan, "Challenges in the Development of Distributed Processing Design Optimization Software System", OPTECH04, Breckenridge, CO, May 2004.

    2. D.T. Nguyen, S.D. Rajan, Sohui Yu, and James St. Ville, "Parallel Finite Element Domain Decomposition Applications: Free Vibration", Proceedings, 75-th Shock and Vibration Symposium, Virginia Beach, VA (October 18-22, 2004)

    3. D.T. Nguyen, S.D. Rajan, W.R. Watson, and S. Tungkahotara, "Parallel Finite Element Domain Decomposition Applications: Incore, Out-of-Core, Symmetrical and Unsymmetrical Cases", Proceedings, 10-th AIAA/ISSMO Multidisciplinary Analysis and Optimization (MAO) Conference, August 30 - Sept. 1'2004, Albany, New York

    4. S.D. Rajan, D.T. Nguyen, Sohui Yu, David Lau, and James St. Ville, "Challenges in the Development of Distributed Processing Design Optimization Software System", Proceedings, Optimization Technology Meeting'2004, May 10-12'2004, Breckenridge, Colorado

    5. D.T. Nguyen, M.D. Deshpande, S.D. Rajan", and L. Harrell "Optimal Design of Engineering Systems Using Genetic Algorithms," 9-th International Conference on Numerical Methods and Computational Mechanics (July 15-19'02, Univ. of Miskolc, Miskolc, Hungary)

    6. S. Tungkahotara, W.R. Watson, D.T. Nguyen and H.B. Runesha" "Simple and Efficient Parallel Dense Equation Solvers," 9-th International Conference on Numerical Methods and Computational Mechanics (July 15-19'02, Univ. of Miskolc, Miskolc, Hungary)

    7. Y. Hu, K.E. Gould" and D.T. Nguyen "Linear Programming Domain Decomposition Solutions Using Simplex and Interior Point Methods Under Parallel Computer Environments," 9-th International Conference on Numerical Methods and Computational Mechanics (July 15-19'02, Univ. of Miskolc, Miskolc, Hungary)

    8. D.T. Nguyen, W.R. Watson, S. Tungkahotara, and S.D. Rajan" "Domain Decomposition Formulation and Implementation for Finite Element Structural/Accoustic Analysis Under Parallel MPI/FORTRAN Computer Environments," 9-th International Conference on Numerical Methods and Computational Mechanics (July 15-19'02, Univ. of Miskolc, Miskolc, Hungary)

    9. Duc T. Nguyen and Siroj Tungkahotara, "Parallel-Vector/Cache Algorithms/Software for Large-Scale Computation", the 2002 Space Radiation Shielding Technology Workshop, NASA Langley Research Center, Hampton, VA (Thursday, April 4, 2002).

    10. Y. Hu, D.T. Nguyen and K. Gould, "Large-Scale Linear Programming Problems By Decomposition and Parallel Procedures", the 8-th AIAA/USAF/NASA/ASSMO Symposium on Multidisciplinary Optimization, Sept. 6-8'2000, Westin, Long Beach, CA.

    11. Nguyen, D.T., Hou, Gene, Runesha, H. and Han, Bangfei,"Alternative approach for solving Sparse INDEFINITE Symmetrical system of Equations", 5th national symposium on Large- Scale Analysis, Design and Intelligent Synthesis Environment, October 12-15, 1999, Williamsburg, VA.

    12. Nguyen, D.T., Bunting, C., Moeller, K.J., Runesha H.B., and Qin, J., "Subspace and Lanczos Sparse Eigen-Solvers for Finite Element Structural and Electromagnetic Applications, 5-th National Symposium on Large-scale Analysis, Design and Intelligent Synthesis Environment, October 12-15, 1999, Williamsburg, VA

    13. Nguyen, D.T., Bai, Yu, Qin, J., and Hu, Yusong, "Computational Aspects of Linear programming Simplex Method' 5th National Symposium on Large-Scale analysis, Design and Intelligent Synthesis Environment, October 12-15, 1999, Williamsburg, VA.

    14. Runesha, H.B., and Nguyen, D.T., "Vectorized Sparse UnSymmetrical Equation solver for Computational Mechanics" 5th National Symposium on Large-Scale analysis, Design and Intelligent Synthesis Environment, October 12-15, 1999, Williamsburg, VA.

    15. Nguyen, D.T., Tang, W.H., Tung, H.K. and Runesha, H.B.,"Nonlinear Constrained Optimizer and Parallel Processing for Golden Block Line Search," August 24-27, '98), Miskolc, Hungary.

    16. Nguyen, D.T., Runesha,H.B. and Qin, J.,"Parallel Finite Element Analysis on Inexpensive Clusters of Sun Workstations," Numerical Methods,and Computational Mechanics in Science and Engineering, (August 24-27 '98), Miskolc, Hungary.

    17. Qin, J. and Nguyen, D.T., "A Tridiagonal Solver for Massively Parallel Computers", Proceedings of the 4th NASA National Symposium on Large-Scale Applications on High- Performance Computers and Workstations, Williamsburg, VA (October 15-17, 1997).

    18. Nguyen, D.T., Qamar, R.and Runesha, H."Automatic Differentiation for Design Sensitivity Analysis of Structural Systems Using Parallel-Vector Processors",Proceedings of the 4th NASA National Symposium on Large-Scale Applications on High-Performance Computers and Workstations, Williamsburg, VA (October 15-17, 1997).

    19. Nguyen, D.T., Runesha, H.,Belegundu, A.D., and Chandrupatla, T.R,"Interior Point Method & Indefinite Sparse Solver for Linear Programming Problems",Proceedings of the 4th NASA National Symposium on Large-Scale Applications on High-Performance Computers and Workstations, Williamsburg, VA (October 15-17, 1997).

    20. Hu, Y., Qin, J., Nguyen, D.T. and Belvin, W.K., "An Out-of-Core Equation Solver for Computational Mechanics on Supercomputers", Proceedings of the 1993 International Conference on FEMCAD-CRASH, IITT-International, 94 Promenade A. Ballu, 93460 Gournay Sur Marnes (France), June 28-29, 1993, (Editors: Dr. A.B. Sabir and Dr. A. Niku-Lari).

    21. Nguyen, D.T., Qin, J., Sancer, M. and McClary, R., "Mixed Sparse-Dense Symmetrical- Unsymmetrical Equation Solvers for Finite Element - Boundary Integral Methods in Electromagnetics", Proceedings of the ICES `97 Conference, Costa Rica, May 4-9, 1997.

    22. Nguyen, D.T., Qin, J., Chang, T.Y.Paul, and Tong, P., "Efficient Sparse Equation Solver With Unrolling Strategies for Computational Mechanics", Proceedings of the ICES `97 Conference, Costa Rica, May 4-9, 1997.

    23. Runesha, H., Nguyen, D.T., Qin, J., Chang, T.Y.Paul and Tong, P. 'Subspace and Lanczos Iterations With Vectorized Sparse Strategies", Proceedings of the ICES `97 Conference, Costa Rica, May 4-9, 1997.

    24. Pu, C., Runesha, H., Nguyen, D.T., Chang, T.Y.Paul and Tong, P., "Sparse Algorithms for INDEFINITE System of Linear Equations", Proceedings of the ICES `97 Conference, Costa Rica, May 4-9, 1997.

    25. Qin, J. and Nguyen, D.T., "A Parallel-Vector Simplex Algorithm on Distributed Memory Computers," Proceedings of the ICES '95 (International Conference on Computational Engineering Science), the Ritz-Carlton Hotel, Mauna Lani, Big Island of Hawaii (July 30- August 3, 1995).

    26. Qin, J., and Nguyen, D.T., "A Tridiagonal Solver for Massively Parallel Computers," Proceedings of the ICES '95, the Ritz-Carlton Hotel, Mauna Lani, Big Island of Hawaii (July 30 - Aug. 3, 1995).

    27. Akan, A.O., Qin, J., Nguyen, D.T., and Basco, D.R., "Parallel Computation for Groundwater Flow," Proceedings of the International Groundwater Management Symposium, San Antonio, TX (August 1995).

    28. Pamujula, H., Nguyen, D.T., and Chandler,L.J.,"Finite Element Structural Analysis Using Loosely Coupled Processors",proceedings of the Intern. Conference on Computational Methods In Structural and Geotechnical Engineering, Hong Kong, (December 12-14, 1994).

    29. Qin, J. and Nguyen, D.T., "Generalized Exponential Penalty Function for Nonlinear Programming," presented at the 35th Structures, Structural Dynamics, and Material Conference, Hilton Head, SC, (April 18-20, 1994).

    30. Qin, J. and Nguyen, D.T., " A Vector Out-of-Core Lanczons Eigen-solver for Structural Vibration Problems," presented at the 35th Structures, Structural Dynamics,and Material Conference, Hilton Head, SC, (April 18-20, 1994).

    31. Storaasli, O.O., Nguyen, D.T., Qin, J. and Baddourah, M.A., "Computational Mechanics Analysis Tools for Parallel-Vector Supercomputers," AIAA/ASME/AHS 34th SDM Conference, LaJolla, CA (April 19-22, 1993).

    32. Qin, J. and Nguyen, D.T., "A New Parallel-Vector Finite Element Analysis Software on Distributed-Memory Computers," Proceedings of the AIAA/ASME/ASCE/AHS 34th SDM Conference, LaJolla, CA (April 19-22, 1993).

    33. Baddourah, M.A. and Nguyen, D.T., "Geometrically Nonlinear Design Sensitivity Analysis on Parallel-Vector High-Performance Computers," Proceedings of the AIAA/ASME/ASCE/AHS 34th SDM Conference, LaJolla, CA (April 19-22, 1993).

    34. Qin, J. and Nguyen, D.T., "A Parallel-Vector Equation Solver for Distributed Memory Computers: Proceedings of the 2nd Parallel Computational Methods for Large-Scale Structural Analysis and Design, sponsored by NASA LaRC, Marriott Hotel, Norfolk, VA (February 24-25, 1993).

    35. Belvin, W.K., Maghami, P.G. and Nguyen, D.T., "Efficient Use of High Performance Computers for Integrated Controls and Structures Design," Proceedings of the Symposium on High-Performance Computing for Flight Vehicles, Washington, D.C. (Dec. 7-9, 1992).

    36. Zhang, Y. and Nguyen, D.T., "Parallel-Vector Sensitivity Calculations in Linear Struct. Dynamics," Proceedings of the Symposium on High-Performance Computing for Flight Vehicles, Washington, D.C. (December 7-9, 1992).

    37. Qin, J. and Nguyen, D.T.,"Structure/Load Dependent Vectors for Linear Struct. Dynamics", Proceedings of the AIAA/ASME/ASCE/AHS 33rd SDM Conference, Dallas, TX (April 13-15, 1992).

    38. Qin, J., Nguyen, D.T. and Zhang,Y.,"Parallel-Vector Lanczos Eigen-Solver for Structural Vibration Problems," Proceedings of the 4th Intern. Conference on Recent Advances in Structural Dynamics, Institute of Sound and Vibration Research, Univ. of Southampton, Southampton, England (July 15-18, 1991).

    39. Baddourah, M.A., Storaasli, O.O., Carmona, E.A., and Nguyen, D.T., "A Fast Parallel Algorithm for Generation and Assembly of Finite Element Stiffness and Mass Matrices," Proceedings of the AIAA/ASME/ASCE AHS 32nd SDM Conference, Baltimore, MD (April 8- 10, 1991).

    40. Nguyen, D.T., Storaasli, O.O., Carmona, E.A., Al-Nasra, M., Zhang, Y., Baddourah, M.A., and Agarwal, T.K., "Parallel-Vector Computation for Linear Structural Analysis and Nonlinear Unconstrained Optimization Problems," Symposium on Parallel Methods on Large- Scale Struct. Analysis and Physics Applications, NASA LaRC, Hampton, VA (February 5-6, 1991).

    41. Qin, J., Gray, Jr., C.E., Mei, C. and Nguyen, D.T., "A Parallel-Vector Equation Solver for Unsymmetric Matrices on Supercomputers,"Symposium on Parallel Methods on Large-Scale Structural Analysis and Physics Applications, NASA LaRC, Hampton, VA (Feb 5-6, 1991).

    42. Agarwal, T.K., Storaasli,O.O., and Nguyen, D.T., "A Parallel-Vector Algorithm for Rapid Structural Analysis on High Performance Computers," Proceedings of the AIAA/ASME/ASCE/AHS 31th SDM Conference, Long Beach, CA (April 2-4, 1990), AIAA paper # 90-1149.

    43. Nguyen, D.T. and Razzaq,Z.,"Recent Research Activities In Parallel Computational Struct. Mechanics," presented at the Sixth Conference on computing in Civil Engineering, sponsored by the ASCE's TCCP, Atlanta, GA, September 11-13, 1989.

    44. Nguyen, D.T. and Ninh, V.T., "Parallel Computation for Linear Programming," ASCE Structures Congress, San Francisco, CA, May 1-5, 1989, pp. 152-157.

    45. Nguyen, D.T., Agarwal, T.K., Benten, M.S., and Lin, C., "A Portable Parallel Equation Solver for Finite-Element Based Structural Analysis-Synthesis Codes," ASCE Structures Congress, San Francisco, CA, May 1-5, 1989, pp. 158-167.

    46. Storaasli, O.O., Nguyen, D.T., and Agarwal, T.K., "The Parallel Solution of Large-Scale Structural Analysis Problems on Supercomputers," AIAA/ASME/ASCE/AHS 30th SDM Conference, Mobil, AL, April 3-5, 1989, pp. 859-867.

    47. Nguyen, D.T., Shim, J.S., and Zhang, Y., "The Component Mode Method in a Parallel Computer Environment," Proceeding of the AIAA/ASME/ASCE/AHS/ASC 29th SDM Conference, Williamsburg, VA, April 18-20, 1988, AIAA Paper #88-2438, pp. 1705-1710.

    48. Nguyen, D.T. and Niu, K.T., "Structural Sensitivity Analysis on a Parallel Computer," Proceeding of 6th ASCE Structures Congress, Orlando, FL, August 17-20, 1987, pp. 98-112.

    49. Nguyen, D.T., "Practical Implementation of an Accurate Method for Multilevel Design Sensitivity Analysis," Proceeding of the AIAA/ASME/ASCE/AHS 28th SDM Conference, Monterey, CA, April 6-8, 1987.

    50. Nguyen, D.T. and Pollalis, S.N., "Struct. Optimization with Interactive Graphics on IBM Personal Computer," Proceeding of the International Conference on Engineering Software for Microcomputers, Venice, Italy, April 2-5, 1984.

    51. Nguyen, D.T. and Hadley, P.K., "Microcomputers in Structural Optimization," Proceeding of the First National Conference on Microcomputers in Civil Engineering, Orlando, FL, November 1-3, 1983.

    52. Nguyen, D.T. and Arora, J.S., "Optimal Geometry Modeling for Minimizing Weight of Plate Bending Structures with Substructures",Proceeding of the 11th IFIP Conference on System Modeling and Optimization, Copenhagen, Denmark, July 25-29, 1983. Appeared in lecture notes in control and information sciences. Edited by P. Thoft-Christensen, Springer- Verlag, Berlin Heidelberg, New York, Tokyo.

    53. Nguyen, D.T. and Arora, J.S., "Fail-Safe Optimal Design of Complex Structures with Substructures," presented at Design Automation Conference, Hartford, CT, September 20- 23, 1981. Appeared in "Progress in Engineering Optimization, 1981."

    54. Arora, J.S. and Nguyen, D.T., "Structural Dynamics with Substructures," Proceeding 7-th Conference on Electronic Computation, ASCE, St. Louis, MO, August, 1979, pp. 402-417.
    
    
    
  • Technical Reports

    1. D.T. Nguyen and P. Chen, "Automated Procedures For Obtaining Generalized Inverse For FETI Formulation", ODU/Structures Research Technical Note No. 03-19-2004, ODU, CEE Dept., 135 KAUF, Norfolk, VA 23529

    2. D.T. Nguyen, J. Qin and A. Tarafda, "Coupling of LAPACK, SCALAPACK Subroutines with MPI/FORTRAN ooc-Lanczos Code for Physics' Eigen-Solution", ODU/Structures Research Technical Note No. 2003-12-22, ODU, CEE Dept., 135 KAUF, Norfolk, VA 23529

    3. D.T. Nguyen, "Finite Element Domain Decomposition Implementation Under MPI/FORTRAN Parallel Computer Environments", ODU/Structures Research Technical Report No. 2002-08-28, ODU, CEE Dept., 135 KAUF, Norfolk, VA 23529

    4. D.T. Nguyen, "Coupling Between Genetic Algorithm (GA) and Finite Element Analysis (FEA) Codes", ODU/Structures Research Technical Note No. 2002-06-24, ODU, CEE Dept., 135 KAUF, Norfolk, VA 23529

    5. D.T. Nguyen, W.R. Watson, and H.B. Runesha, "Symmetrical/Sparse/Complex Number/ Assembly and LDL Solver Algorithms For Finite Element Acoustic Applications:
      (a1) SGI (lower triangular) sparse column formats
      (a2) SGI reordering algorithms
      (a3) SGI solver
      (b1) ODU (upper triangular) sparse row formats
      (b2) User Controled Options for ND, MMD, METIS, or Without Reordering Algorithms
      (b3) User Controled Options for Loop unrolling level 1, 2, or 8
      (b4) User Controled Options for Symbolic factorization only, or Numerical factorization only, or Forward/Backward only, or Complete solution"
      ODU/Structures Research Technical Note No. 2002-05-16, ODU, CEE Dept., 135 KAUF, Norfolk, VA 23529

    6. D.T. Nguyen, W.R. Watson, and H.B. Runesha, "Unsymmetrical Sparse Assembly and Solver Algorithms For Finite Element Engineering Applications", ODU/Structures Research Technical Note No. 2001-11-20, ODU, CEE Dept., 135 KAUF, Norfolk, VA 23529

    7. D.T. Nguyen,"Efficient Generation of Adjacency Arrays For METIS/MMD/ND Reordering Algorithms To Minimize Fill-In Terms", ODU/Structures Research Technical Note No. 2001-10-15, ODU, CEE Dept., 135 KAUF, Norfolk, VA 23529

    8. D.T. Nguyen, J. Qin, and W.R. Watson, "Automatically Generating NASA-ODU UNSYMMETRICAL/SYMMETRICAL K* Acoustic Data Files For Testing Complex-Number Equation and/or Eigen-Solvers", ODU/Structures Research Technical Note No. 2001-09-26, ODU, CEE Dept., 135 KAUF, Norfolk, VA 23529

    9. D.T. Nguyen, "Simple Explanation for Implementing Efficient Sparse Assembly in Finite Element Analysis" ODU/Structures Research Technical Note No. 2001-04-15, ODU, CEE Dept., 135 KAUF, Norfolk, VA 23529

    10. D.T. Nguyen, "Relationships Between Solving COMPLEX Versus REAL System of Symmetrical Equations", Structures Technical Report No. 2000-12-01, ODU, CEE Dept., 135 KAUF, Norfolk, VA 23529

    11. D.T. Nguyen, "A Convenient FORTRAN Software For Teaching Moment Distribution Method In Structural Analysis Course", Structural Technical Note No. 1999-06-22, ODU, CEE Dept., 135 KAUF, Norfolk, VA 23529

    12. D.T. Nguyen, and J. Qin, "Out-of-Core Sparse Equation and Eigen- Solvers: Modulars, Multiple RHS, Ranges of Eigenvalues, Shift and Consistent Mass Options", Structural Research Technical Note No. 1999-06-07, ODU, CEE Dept., 135 KAUF, Norfolk, VA 23529

    13. D.T. Nguyen, and Sethap Sethaboupha, "Simple Algorithms For Sparse Stiffness Matrix Assembly With Potential Parallel Applications In FEA and DSA", Structural Research Technical Note No. 1999-04-23, ODU, CEE Dept., 135 KAUF, Norfolk, VA 23529

    14. D.T. Nguyen, W.H. Tang, H.K. Tung, and H.B. Runesha, "Nonlinear Constrained Optimizer & Parallel Processing For Golden Block Line Search: Theories and Computer Program User Guide",ODU-Stuct. Tech. Report # 98-62, (Dec. 1, 1998)

    15. Nguyen, D.T.,"A Finite Element Computer Program For 2-D Field and Structural Problems", ODU Technical Note, No. 98-55 (October 12, 1998)

    16. Bunting, C.F., and Nguyen, D.T., "Finite Element Analysis of Reverberation Chambers", Year 1 Report submitted to NASA-LaRC (Nov. '98), NAG1-1982 (ODURF #180800).

    17. Nguyen, D.T., H. Runesha, J. Qin, Y.S. Hu and B. Hay, "Linear Programming and Equation Solver Algorithms For Thermal-Structural Analysis and Design",Final Report submitted to NASA-LaRC, Contract # NAS1-19858, Task 116 (Jan. 1999).

    18. Nguyen, D.T., "New Parallel Algorithms For Structural Analysis and Design of Aerospace Structures", Final Report submitted to NASA-LaRC, grant NAG1-858 (October 1998).

    19. Nguyen, D.T., and Hou, G., "Converting Symmetrical Indefinite Into Symmetrical Positive Definite System of Linear Equations," ODU Technical Note, No. 98-52 (June 26, 1998).

    20. Nguyen, D.T., "General Treatments of Lagrange Constraint Equations for Finite Element Static Analysis," ODU Technical Note, No. 98-51 (June 4, 1998).

    21. Nguyen, D.T., "Treatments of Non-zero Prescribed Boundary Conditions for Statics, Eigenvalue, and Structural Dynamic Problems," ODU Tech. Note, No. 97-51 (Aug. 18'97).

    22. Nguyen, D.T., "User Instructions for Incore Unsymmetrical Sparse Dense Equation Solver", Technical Report, Northrop-Grumman Corp., 1996.

    23. Nguyen, D.T., Runesha, H.B., and Bey,K.S.,"Incore and Out-of-Core Direct Sparse Solvers for hp Adaptive Discontinuous Galerkin Finite Element Analysis", NASA LaRC Tech. Report, Thermal Structures Branch (August 1997).

    24. Nguyen, D.T., "Enhancements to the CSI-Design Code for Integrated Design Optimization," NASA Technical Report, Master Contract NAS1-19858, Task 16, February 1995.

    25. Nguyen, D.T., Qin, J., Maker, B.N., "Parallel-Vector Algorithms for Nonlinear Finite Element Analysis," Final Report, Air Force Phillips Laboratory, Research Contract F24.650-91-W0945, May 1994.

    26. Ishibashi, I., Nguyen, D.T. and Wang, Y., "Hybrid Finite/Discrete Element Models for Large Deformation Geotechnical Engr. Problems," Report to NSF on Grant MSS-8920878, and also Geotechnical Engr. Report 93-3, Department of Civil and Environmental Engineering, Old Dominion University, April 1993.

    27. Nguyen, D.T., and Qin, J.,"Parallel-Vector Unsymmetric Eigen-solver on High Performance Computers," NASA Contractor Report #191417, Contract NAS1-18584, February 1993.

    28. Nguyen, D.T., "Parallel-Vector Computations for CSI-Design Code," NASA Technical Report, Master Contract NAS1-18584, Task 92, June 92.

    29. Storaasli, O.O., Nguyen, D.T. and Agarwal,T.K., "A Parallel-Vector Algorithm for Rapid Structural Analysis on High-Performance Computers," NASA TM 102614, March 1990, NASA LaRC.

    30. Nguyen, D.T., "Parallel-Vector Computation for Structural Analysis and Nonlinear Unconstrained Optimization Problems," Final Report for the period June 89 - June 90, Multidisciplinary Research Office, NASA LaRC, Hampton, VA.

    31. Nguyen, D.T. and E.A. Carmona, "Parallel and Vector Procedures for Systems of Nonlinear Equations," prepared for the AFOSR Air Force Summer 89 Faculty Research.

    32. Hou, G., Nguyen, D.T., Pai, F. and Zhang, H., "Simplified Procedures for Dynamics Anal. of Complex Structures," prepared for the Newport News Shipbuilding Co., Dept. E-10, Bldg. 600, 4101 Washington Avenue, Newport News, VA 23607 (September 1987).

    33. Nguyen, D.T., Belegundu, A.D. and Arora,J.S., "A System Manual for the Computer Program DOCS," Division of Materials Engr. The University of Iowa, Iowa City, IA, February 1982, Technical Report No. CAD-SS-82.10.

    34. Nguyen, D.T., Belegundu, A.D. and Arora,J.S.,"Sample solutions with DOCS," Tech. Report No. CAD-SS-82.9, Division of Materials Engr., The University of Iowa, Iowa City, IA, February 1982, prepared for the U.S. Army BRL.

    35. Nguyen, D.T., Arora, J.S., "Fail-Safe Optimal Design of Complex Structures with Substructures and Composite Materials," Tech. Report No. CAD-SS-82.3, Div. of Materials Engr., The University of Iowa, Iowa City, IA, February 1982, prepared for the U.S. Army ARRADCOM BRL.

    36. Arora, J.S., Nguyen, D.T., Belegundu, A.D. and Rajan, S.D., "Design Optimization Codes for Structures - DOCS," Tech. Report No. 71, Div. of Materials Engr., the University of Iowa, Iowa City, IA. August 1980, prepared for the U.S. Army BRL.

    37. Rajan, S.D., Nguyen, D.T., Belegundu, A.D. and Arora, J.S., "A User's Manual for the computer program DOCS: Level 1.0," Tech. Report No. 69, Div. of Materials Engr., the University of Iowa, Iowa City, IA, August 1980, prepared for the U.S. Army BRL.

    38. Nguyen, D.T. and Arora, J.S., "Damage-tolerant Design of Composite Structures with Substructuring," Tech. Report No. 67, Div. of Materials Engineering, the University of Iowa, Iowa City, IA, June 1980, prepared for the U.S. Army BRL.

    39. Arora, J.S. and Nguyen, D.T., "Dynamic Structural Analysis with Substructures," Tech. Report No. 46, Division of Materials Engineering. The University of Iowa, Iowa City, IA, December, 1978.

    40. Nguyen, D.T., Govil, A.K., Arora, J.S. and Haug, E.J., "Fail-Safe Optimal Design of Structures with Substructuring," Tech. Report No. 45, Div. of Materials Engr.. The Univ. of Iowa, Iowa City, IA, August, 1978, prepared for the U.S. Army BRL, Aberdeen Proving Ground, MD.

  • Published Abstracts

    1. Rajan, S.D., Nguyen, D.T., Yu, S.H., D. Lau and Ville, J. St., "Improving the Performance of Finite Element Computations Through Parallel Processing", pp. 2-3, Maui High Performance Computing Center, An Air Force Research Laboratory Center, Managed by the University of Hawaii, APPLICATION BRIEFS'2003

    2. Nguyen, D.T., "Genetic Algorithms and Computer Implementation For Electromagnetics Research Applications", NASA (LaRC)-ASEE Summer'2001 Faculty Fellowship Program, NASA Langley Research Center, Hampton, VA 23681

    3. D.T. Nguyen, and J.S. Shim "A Convenient FORTRAN Software For Teaching Moment Distribution Method In Structural Analysis Course", Structural Technical Note No. 1999-06-22, ODU, CEE Dept., 135 KAUF, Norfolk, VA 23529, educational paper (presented at the 2001 ASEE Conference, The Citadel, 171 Moultrie Street, Charleston, SC 29409, April 1-3'2001).

    4. S. Hans, S.Y. Bawab, A. Demuren and D.T. Nguyen "Initial Experience With Parallel Engineering Computation Under MPI/FORTRAN and LINUX PCs Computer Environments" VAS Conference, May 24-26'00, Radford University, Virginia

    5. Y. Hu, D.T. Nguyen and K. Gould "Decomposition Procedures For Linear Programming Problems: Sequential Computer Environments" VAS Conference, May 24-26'00, Radford University, Virginia

    6. W.R. Watson, V. Vatsa, S. Hans, P. Ayasit and D.T. Nguyen "Sparse Assembling Procedures For Structural Acoustics Finite Element Analysis" VAS Conference, May 24-26'00, Radford University, Virginia

    7. C. Bunting, T.X. Nguyen and D.T. Nguyen "Complex Sparse Lanczos Eigen-Solvers For Electro-magnetics Engineering Solutions" VAS Conference, May 24-26'00, Radford University, Virginia

    8. D.T. Nguyen, G. Hou, H. Runesha and Bangfei Han, "New Approach For Solving Large Indefinite System of Linear Equation", presented at VAS Conference, ODU, Norfolk, VA, (May 25-28, 1999)

    9. D.T. Nguyen, Yu Bai, J. Qin and YusongHu, "Computational Issues In the Revised Simplex Method For LP Problems", presented at Virginia Academy of Science (VAS) Conference, ODU, Norfolk, VA. (May 25- 28, 1999)

    10. Nguyen, D.T., Qin, J., and Qamar, R., "Automatic Differentiation for Design Sensitivity Analysis of Structural Systems Using Multiple Processors",presented at the ASME, AMD-MD Summer Meeting, UCLA (June 28-30, 1995).

    11. Storaasli, O.O. and Nguyen, D.T., "Parallel Computing Algorithms: Past, Present and Future", Proc. Society of Engr. Science 28th Annual Tech. Meeting, Univ. of Florida, Gainsville, FL (November 6-8, 1991).

    12. Storaasli, O.O. and Nguyen, D.T., "Parallel Structural Mechanics Algorithms with Applications to Structural Mechanics," First U.S. National Congress on Computational Mechanics, Chicago, IL (July 21-24, 1991).

    13. Carmona, E.A., Nguyen, D.T., Baddourah, M.A., and Agarwal, T.K., "Parallel-Vector Solution for Systems of Nonlinear Equations," accepted for presentation in the session Parallel Processing and Supercomputing of the 1990 ASCE Structures Congress, Baltimore, MD (April 30-May 3, 1990).

    14. Storaasli, O.O. and Nguyen, D.T., "A Portable Parallel Skyline Choleski Solver," CSM Compass, A newsletter about NASA Langley-sponsored CSM Research and Directions, Vol. 1, No. 7, pp. 5-6, July, 1988.

    15. Nguyen, D.T. and Mei, C., "Activities on Composites at Old Dominion Univ." presented at a conference at Virginia Polytechnic Institute, Blacksburg, VA, September 29, 1987.

    16. Nguyen, D.T. and Niu, K.T., "A Parallel Simplex Algorithm for Linear Programming" , presented at the Annual Meeting of Virginia Acad. of Science, Norfolk, VA, May 21'87.

    17. Nguyen, D.T. and Clark, S.B., "Structural Dynamics with Substructures: A Comparison Study", presented at Annual Meeting of the Virginia Acad. of Science, Norfolk, VA, May 21, 1987.

    18. Nguyen, D.T.,"Struct. Optimization by Decomposition Method with Reference to Sequential and Parallel Computers," presented at the 12th International Symposium on Mathematical Programming, M.I.T., Cambridge, MA, August 5-8, 1985.

    19. Nguyen, D.T., Yoon, C.Y. and Arora, J.S., "An Element-By-Element Procedure for Solution of Large Eigenvalue Problems," presented at the AIAA/ASME/ASCE/AHS 26th Structures, Structural Dynamics and Materials Conference, Orlando, FL, April 15-17, 1985, Work-In- Progress Session.

    20. Nguyen, D.T. and Rajan,S.D.,"MODES: Microcomputer-Based Optimal Design of Structures", presented at the 18th Midwestern Mechanics Conference, Iowa City, IA, May 16-18, 1983.

    21. Nguyen, D.T., Arora, J.S. and Belegundu, A.D., "A Computer Program for Damage-Tolerant Optimal Design of Complex Structures," AMMRC MS 82-5, the Army Symposium on Solid Mechanics, Cape Cod, MA, September 21-23, 1982.

    22. Nguyen, D.T., Belegundu, A.D. and Arora, J.S.,"Design Optimization Codes for Structures: DOCS Computer Program," presented at the Second JTCG/AS Workshop on Survivability and Computer Aided Design, Wright-Patterson AFB, OH, May 18-20, 1982.