The solution of very large non-linear algebraic systems

Computers and Chemical Engineering

Volumn 33, Issue 10, 2009, Pages 1727-1734

  Manca, Davide ^a   Buzzi Ferraris, Guido ^a   Cuoci, Alberto ^a   Frassoldati, Alessio ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

Applied numerical analysis; Mixed CFD and detailed kinetics; Very large non linear algebraic systems

Indexed keywords

APPLIED NUMERICAL ANALYSIS; COMBUSTION DEVICE; COMPUTING DEVICES; CONVERGENCE TEST; DETAILED KINETICS; MICROPOLLUTANTS; MIXED CFD AND DETAILED KINETICS; NON LINEAR SYSTEM; NON-LINEAR; NON-LINEAR ALGEBRAIC SYSTEM; NUMERICAL CHALLENGES; NUMERICAL PROBLEMS; NUMERICAL SIMULATION; NUMERICAL SOLUTION; ORDERS OF MAGNITUDE; OUTPUT DATA; POST-PROCESSOR; REACTIVE SYSTEM; SPARSE SYSTEMS; VERY LARGE NON-LINEAR ALGEBRAIC SYSTEMS;

ALGEBRA; COMPUTER SIMULATION LANGUAGES; LINEAR SYSTEMS; NONLINEAR SYSTEMS; NUMERICAL ANALYSIS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 68549083489     PISSN: 00981354     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compchemeng.2009.04.010     Document Type: Article

References (38)

1. Barendregt S., van Goethem M., Risseeuw I., Frassoldati A., Faravelli T., Cuoci A., et al. The design of ultra-low NOx critical furnaces. Proceedings of the 8th European Conference on Industrial Furnaces and Boilers, Vilamoura, Portugal, March 25-28 (2008)
2. Barnes J.C.P. An algorithm for solving nonlinear equations based on the secant method. Computational Journal 8 (1965) 66
3. Broyden C.G. A class of methods for solving nonlinear simultaneous equations. Mathematics of Computation 21 (1965) 368
4. Broyden C.G. A new method of solving nonlinear simultaneous equations. Computational Journal 12 (1969) 94
5. Buzzi Ferraris G., and Manca D. BzzOde: A new C++ class for the solution of stiff and non-stiff ordinary differential equation system. Computers and Chemical Engineering 22 11 (1998) 1595-1621
6. Buzzi-Ferraris G. Scientific C++ (1993), Addison-Wesley, New York
7. Buzzi-Ferraris G., and Manca D. Large scale algebraic systems computer aided process and product engineering vol. 1 (2006), Wiley-VCH, Weinheim pp. 15-34
8. Buzzi-Ferraris G., and Mazzotti M. Orthogonal procedure for the updating of sparse Jacobian matrices. Computers and Chemical Engineering 8 (1984) 389
9. Buzzi-Ferraris G., and Tronconi E. BUNLSI-a Fortran program for solution of systems of nonlinear algebraic equations. Computers and Chemical Engineering 10 (1986) 129
10. Buzzi-Ferraris G., and Tronconi E. An improved convergence criterion in the solution of nonlinear algebraic equations. Computers and Chemical Engineering 17 (1993) 419
11. Cuoci A., Frassoldati A., Buzzi-Ferraris G., Faravelli T., and Ranzi E. The ignition, combustion and flame structure of carbon monoxide/hydrogen mixtures. Note 2. Fluid dynamics and kinetic aspects of syngas combustion. International Journal of Hydrogen Energy 32 (2007) 3486-3500
12. Curtis, A. R., Powell, M. J. D., & Reid, J. K. (1972). On estimation of sparse Jacobian Matrices, Report TP476, AERE, Harwell.
13. Deuflhard P. Newton methods for nonlinear problems (2005), Springer, New York
14. Eberhart J.G. Solving equations by successive substitution-the problems of divergence and slow convergence. Journal of Chemical Education 63 (1986) 576
15. Falcitelli M., Pasini S., and Tognotti L. An algorithm for extracting chemical reactor network models from CFD simulation of industrial combustion systems. Combustion Science and Technology 174 (2002) 22
16. Falcitelli M., Pasini S., Rossi N., and Tognotti L. CFD + reactor network analysis: An integrated methodology for the modelling and optimisation of industrial systems for energy saving and pollution reduction. Applied Thermal Engineering 22 (2002) 971
17. Frassoldati A., Frigerio S., Colombo E., Inzoli F., and Faravelli T. Determination of NOx emissions from strong swirling confined flames with an integrated CFD-based procedure. Chemical Engineering Science 60 (2005) 2851-2869
18. Frassoldati A., Cuoci A., Faravelli T., Ranzi E., Astesiano D., Valenza M., et al. Experimental and modeling study of low-NOx industrial burners. MPT Metallurgical Plant and Technology International 31 6 (2008) 44-46
19. Frassoldati A., Cuoci A., Faravelli T., Ranzi E., Colantuoni S., Di Martino P., et al. Experimental and modeling study of a low NOx combustor for aero-engine turbofan. Combustion Science and Technology 181 3 (2009) 1-13
20. Gupta Y.P. Bracketing method for on-line solution of low-dimensional nonlinear algebraic equations. Industrial and Engineering Chemistry Research 15 (1995) 239
21. Jsun Y.W. Multiple step method for solving nonlinear systems of equations. Computer Applications in Engineering Education 5 (1997) 121
22. Karr C.L., Weck B., and Freeman L.M. Solutions to systems of nonlinear equations via a genetic algorithm. Engineering Applications of Artificial Intelligence 11 (1998) 369
23. Manca D., and Buzzi-Ferraris G. BzzMath: An object oriented library for applied numerical analysis. ACS Reed Business Information, Milan, vol. 7 (2005) 209-218
24. Manca D., and Buzzi-Ferraris G. Numerical Solution of Dae Problems. Revista de Chimie 58 4 (2007) 410-414
25. Manca D., and Buzzi-Ferraris G. The solution of very large non-linear algebraic systems. In: Braunschweig B., and Joulia X. (Eds). Proceedings of ESCAPE-18, Elsevier (2008). 978-0-444-53227-5 587-592
26. Manca, D., Faravelli, T., Pennati, G., Buzzi-Ferraris, G., Ranzi, E. (1995). Numerical integration of large kinetic systems, ICheaP-2, ERIS, Milan, 115-121.
27. Novosselov I.V., and Malte P.C. Development and application of an eight-step global mechanism for CFD and CRN simulations of lean-premixed combustors. Proceedings of the ASME Turbo Expo 2007, vol. 2, Montreal, Canada (2007) 769-779
28. Novosselov I.V., Malte P.C., Yuan S., Srinivasan R., and Lee J.C.Y. Chemical reactor network application to emissions prediction for industrial DLE gas turbine. Proceedings of GT2006 ASME Turbo Expo 2006, vol. 1, Barcelona, Spain (2006) 221-235
29. Paloschi J.R. Bounded homotopies to solve systems of algebraic nonlinear equations. Computers and Chemical Engineering 19 (1995) 1243
30. Paterson W.R. A new method for solving a class of nonlinear equations. Chemical Engineering Science 41 (1986) 135
31. Powell M.J.D. In: Rabinowitz G. (Ed). A hybrid method for nonlinear equations in numerical methods for nonlinear algebraic equations (1970), Breach, London
32. Rice R.J. Numerical methods software and analysis (1993), Academic Press, London
33. Russo C., Mori G., Anisimov V.V., and Parente J. Micro gas turbine combustor emissions evaluation using the chemical reactor modelling approach. Proceedings of the ASME Turbo Expo 2007, vol. 2, Montreal, Canada (2007) 531-542
34. Schubert L.K. Modification of a Quasi-Newton method for nonlinear equations with a sparse Jacobian. Mathematics of Computation 24 (1970) 27
35. Shacham M., and Brauner N. Numerical solution of non-linear algebraic equations with discontinuities. Computers and Chemical Engineering 26 (2002) 1449
36. Skjøth-Rasmussen M.S., Holm-Christensen O., Østberg M., Christensen T.S., Johannessen T., Jensen A., et al. Post-processing of detailed chemical kinetic mechanism onto CFD simulations. Computers and Chemical Engineering 28 (2004) 2351-2361
37. Sundar S., Bhagavan B.K., and Prasad S. Newton preconditioned Krylov subspace solvers for system of nonlinear equations: A numerical experiment. Applied Mathematics Letters 14 (2001) 195
38. Wilhelm C.E., and Swaney R.E. Robust solution of algebraic process modeling equations. Computers and Chemical Engineering 18 (1994) 511