Skip to main content
Erschienen in: The Journal of Supercomputing 8/2018

01.08.2018

Performance of preconditioned iterative solvers in MFiX–Trilinos for fluidized beds

verfasst von: V. M. Krushnarao Kotteda, Vinod Kumar, William Spotz

Erschienen in: The Journal of Supercomputing | Ausgabe 8/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

MFiX, a general-purpose Fortran-based suite, simulates the complex flow in fluidized bed applications via BiCGStab and GMRES methods along with plane relaxation preconditioners. Trilinos, an object-oriented framework, contains various first- and second-generation Krylov subspace solvers and preconditioners. We developed a framework to integrate MFiX with Trilinos as MFiX does not possess advanced linear methods. The framework allows MFiX to access advanced linear solvers and preconditioners in Trilinos. The integrated solver is called MFiX–Trilinos, here after. In the present work, we study the performance of variants of GMRES and CGS methods in MFiX–Trilinos and BiCGStab and GMRES solvers in MFiX for a 3D gas–solid fluidized bed problem. Two right preconditioners employed along with various solvers in MFiX–Trilinos are Jacobi and smoothed aggregation. The flow from MFiX–Trilinos is validated against the same from MFiX for BiCGStab and GMRES methods. And, the effect of the preconditioning on the iterative solvers in MFiX–Trilinos is also analyzed. In addition, the effect of left and right smoothed aggregation preconditioning on the solvers is studied. The performance of the first- and second-generation solver stacks in MFiX–Trilinos is studied as well for two different problem sizes.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Arabnia HR, Oliver MA (1986) Fast operations on raster images with SIMD machine architectures. Comput Graph Forum 5(3):179–188CrossRef Arabnia HR, Oliver MA (1986) Fast operations on raster images with SIMD machine architectures. Comput Graph Forum 5(3):179–188CrossRef
2.
Zurück zum Zitat Arabnia HR, Taha TR (1998) A parallel numerical algorithm on a reconfigurable multi-ring network. Telecommun Syst 10(1):185–202CrossRef Arabnia HR, Taha TR (1998) A parallel numerical algorithm on a reconfigurable multi-ring network. Telecommun Syst 10(1):185–202CrossRef
3.
Zurück zum Zitat Arnoldi WE (1951) The principle of minimized iterations in the solution of the matrix eigenvalue problem. Q Appl Math 9(1):17–29MathSciNetCrossRefMATH Arnoldi WE (1951) The principle of minimized iterations in the solution of the matrix eigenvalue problem. Q Appl Math 9(1):17–29MathSciNetCrossRefMATH
4.
Zurück zum Zitat Axelsson O, Farouq S, Neytcheva M (2016) Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems. Numer Algorithms 73(3):631–663MathSciNetCrossRefMATH Axelsson O, Farouq S, Neytcheva M (2016) Comparison of preconditioned Krylov subspace iteration methods for PDE-constrained optimization problems. Numer Algorithms 73(3):631–663MathSciNetCrossRefMATH
5.
Zurück zum Zitat Axelsson O, Lukáš D (2018) Preconditioners for time-harmonic optimal control eddy-current problems. In: Lirkov I, Margenov S (eds) Large-scale scientific computing. Springer, Cham, pp 47–54CrossRef Axelsson O, Lukáš D (2018) Preconditioners for time-harmonic optimal control eddy-current problems. In: Lirkov I, Margenov S (eds) Large-scale scientific computing. Springer, Cham, pp 47–54CrossRef
7.
Zurück zum Zitat Axelsson O, Neytcheva M, Ahmad B (2014) A comparison of iterative methods to solve complex valued linear algebraic systems. Numer Algorithms 66(4):811–841MathSciNetCrossRefMATH Axelsson O, Neytcheva M, Ahmad B (2014) A comparison of iterative methods to solve complex valued linear algebraic systems. Numer Algorithms 66(4):811–841MathSciNetCrossRefMATH
8.
Zurück zum Zitat Babich I, Moulijn J (2003) Science and technology of novel processes for deep desulfurization of oil refinery streams: a review. Fuel 82(6):607–631CrossRef Babich I, Moulijn J (2003) Science and technology of novel processes for deep desulfurization of oil refinery streams: a review. Fuel 82(6):607–631CrossRef
9.
Zurück zum Zitat Baker CG, Heroux MA (2012) Tpetra, and the use of generic programming in scientific computing. Sci Program 20(2):115–128 Baker CG, Heroux MA (2012) Tpetra, and the use of generic programming in scientific computing. Sci Program 20(2):115–128
10.
Zurück zum Zitat Balay S, Gropp WD, McInnes LC, Smith BF (1997) Efficient management of parallelism in object oriented numerical software libraries. In: Arge E, Bruaset AM, Langtangen HP (eds) Modern software tools in scientific computing. Birkhäuser Press, Basel, pp 163–202CrossRef Balay S, Gropp WD, McInnes LC, Smith BF (1997) Efficient management of parallelism in object oriented numerical software libraries. In: Arge E, Bruaset AM, Langtangen HP (eds) Modern software tools in scientific computing. Birkhäuser Press, Basel, pp 163–202CrossRef
11.
Zurück zum Zitat Barrett R, Berry MW, Chan TF, Demmel J, Donato J, Dongarra J, Eijkhout V, Pozo R, Romine C, Van der Vorst H (1994) Templates for the solution of linear systems: building blocks for iterative methods, vol 43. SIAM, PhiladelphiaCrossRefMATH Barrett R, Berry MW, Chan TF, Demmel J, Donato J, Dongarra J, Eijkhout V, Pozo R, Romine C, Van der Vorst H (1994) Templates for the solution of linear systems: building blocks for iterative methods, vol 43. SIAM, PhiladelphiaCrossRefMATH
12.
Zurück zum Zitat Bavier E, Hoemmen M, Rajamanickam S, Thornquist H (2012) Amesos2 and Belos: direct and iterative solvers for large sparse linear systems. Sci Program 20(3):241–255 Bavier E, Hoemmen M, Rajamanickam S, Thornquist H (2012) Amesos2 and Belos: direct and iterative solvers for large sparse linear systems. Sci Program 20(3):241–255
13.
14.
Zurück zum Zitat Castaeda LC, Muoz JA, Ancheyta J (2014) Current situation of emerging technologies for upgrading of heavy oils. Catal Today 220–222:248–273CrossRef Castaeda LC, Muoz JA, Ancheyta J (2014) Current situation of emerging technologies for upgrading of heavy oils. Catal Today 220–222:248–273CrossRef
15.
Zurück zum Zitat Cheng Y, Jae J, Shi J, Fan W, Huber GW (2011) Production of renewable aromatic compounds by catalytic fast pyrolysis of lignocellulosic biomass with bifunctional Ga/ZSM-5 catalysts. Angew Chem 124(6):1416–1419CrossRef Cheng Y, Jae J, Shi J, Fan W, Huber GW (2011) Production of renewable aromatic compounds by catalytic fast pyrolysis of lignocellulosic biomass with bifunctional Ga/ZSM-5 catalysts. Angew Chem 124(6):1416–1419CrossRef
16.
Zurück zum Zitat Chisnall D (2013) The challenge of cross-language interoperability. Commun ACM 56(12):50–56CrossRef Chisnall D (2013) The challenge of cross-language interoperability. Commun ACM 56(12):50–56CrossRef
17.
Zurück zum Zitat Crowe C (1993) Research needs in fluids engineering: basic research needs in fluid–solid multiphase flows. J Fluids Eng 115(3):341–342CrossRef Crowe C (1993) Research needs in fluids engineering: basic research needs in fluid–solid multiphase flows. J Fluids Eng 115(3):341–342CrossRef
18.
Zurück zum Zitat Davidson JF, Clift R, Harrison D (1985) Fluidization. Academic Press, Orlando Davidson JF, Clift R, Harrison D (1985) Fluidization. Academic Press, Orlando
19.
Zurück zum Zitat Drgnescu A, Saraswat J (2016) Optimal-order preconditioners for linear systems arising in the semismooth newton solution of a class of control-constrained problems. SIAM J Matrix Anal Appl 37(3):1038–1070MathSciNetCrossRefMATH Drgnescu A, Saraswat J (2016) Optimal-order preconditioners for linear systems arising in the semismooth newton solution of a class of control-constrained problems. SIAM J Matrix Anal Appl 37(3):1038–1070MathSciNetCrossRefMATH
20.
Zurück zum Zitat Edwards HC, Trott CR, Sunderland D (2014) Kokkos: enabling manycore performance portability through polymorphic memory access patterns. J Parallel Distrib Comput 74(12):3202–3216CrossRef Edwards HC, Trott CR, Sunderland D (2014) Kokkos: enabling manycore performance portability through polymorphic memory access patterns. J Parallel Distrib Comput 74(12):3202–3216CrossRef
21.
Zurück zum Zitat Falgout RD, Yang UM (2002) Hypre: A library of high performance preconditioners. In: International Conference on Computational Science. Springer, pp 632–641 Falgout RD, Yang UM (2002) Hypre: A library of high performance preconditioners. In: International Conference on Computational Science. Springer, pp 632–641
22.
Zurück zum Zitat Freund RW (1993) A transpose-free quasi-minimal residual algorithm for non-hermitian linear systems. SIAM J Sci Comput 14(2):470–482MathSciNetCrossRefMATH Freund RW (1993) A transpose-free quasi-minimal residual algorithm for non-hermitian linear systems. SIAM J Sci Comput 14(2):470–482MathSciNetCrossRefMATH
23.
Zurück zum Zitat Gaidamour J, Hu J, Siefert C, Tuminaro R (2012) Design considerations for a flexible multigrid preconditioning library. Sci Program 20(3):223–239 Gaidamour J, Hu J, Siefert C, Tuminaro R (2012) Design considerations for a flexible multigrid preconditioning library. Sci Program 20(3):223–239
24.
Zurück zum Zitat Gee MW, Siefert CM, Hu JJ, Tuminaro RS, Sala MG (2006) ML 5.0 smoothed aggregation users guide. Technical report, SAND2006-2649, Sandia National Laboratories Gee MW, Siefert CM, Hu JJ, Tuminaro RS, Sala MG (2006) ML 5.0 smoothed aggregation users guide. Technical report, SAND2006-2649, Sandia National Laboratories
25.
Zurück zum Zitat Gel A, Hu J (2015) Modernizing a legacy open source CFD code by leveraging scalable parallel preconditioners and linear equation solvers. In: 27th International Conference on Parallel Computational Fluid Dynamics. McGill University, Montreal, pp 1–2 Gel A, Hu J (2015) Modernizing a legacy open source CFD code by leveraging scalable parallel preconditioners and linear equation solvers. In: 27th International Conference on Parallel Computational Fluid Dynamics. McGill University, Montreal, pp 1–2
26.
Zurück zum Zitat Gel A, Hu J, Ould-Ahmed-Vall E, Kalinkin AA (2017) Modernization and optimization of a legacy open-source CFD code for high-performance computing architectures. Int J Comput Fluid Dyn 31(2):122–133MathSciNetCrossRef Gel A, Hu J, Ould-Ahmed-Vall E, Kalinkin AA (2017) Modernization and optimization of a legacy open-source CFD code for high-performance computing architectures. Int J Comput Fluid Dyn 31(2):122–133MathSciNetCrossRef
27.
Zurück zum Zitat Gel A, Pannala S, Syamlal M, O’Brien T, Gel ES (2007) Comparison of frameworks for a next-generation multiphase flow solver, MFIX: a group decision-making exercise. Concurr Comput 19(5):609–624CrossRef Gel A, Pannala S, Syamlal M, O’Brien T, Gel ES (2007) Comparison of frameworks for a next-generation multiphase flow solver, MFIX: a group decision-making exercise. Concurr Comput 19(5):609–624CrossRef
28.
Zurück zum Zitat Ghai A, Lu C, Jiao X (2016) A comparison of preconditioned Krylov subspace methods for nonsymmetric linear systems. arXiv preprint arXiv:1607.00351 Ghai A, Lu C, Jiao X (2016) A comparison of preconditioned Krylov subspace methods for nonsymmetric linear systems. arXiv preprint arXiv:​1607.​00351
29.
Zurück zum Zitat Gupta CK, Sathiyamoorthy D (1998) Fluid bed technology in materials processing. CRC Press, Boca RatonCrossRef Gupta CK, Sathiyamoorthy D (1998) Fluid bed technology in materials processing. CRC Press, Boca RatonCrossRef
30.
Zurück zum Zitat Gupta R (2017) 6 Fluid bed granulation and drying. In: Pandey P, Bharadwaj R (eds) Predictive modeling of pharmaceutical unit operations. Woodhead Publishing, Sawston, pp 137–158CrossRef Gupta R (2017) 6 Fluid bed granulation and drying. In: Pandey P, Bharadwaj R (eds) Predictive modeling of pharmaceutical unit operations. Woodhead Publishing, Sawston, pp 137–158CrossRef
31.
Zurück zum Zitat Heroux M, Bartlett R, Hoekstra VHR, Hu J, Kolda T, Lehoucq R, Long K, Pawlowski R, Phipps E, Salinger A, Thornquist H, Tuminaro R, Willenbring J, Williams A, Stanley K (2005) An overview of the Trilinos project. ACM Trans Math Softw 31(3):397–423MathSciNetCrossRefMATH Heroux M, Bartlett R, Hoekstra VHR, Hu J, Kolda T, Lehoucq R, Long K, Pawlowski R, Phipps E, Salinger A, Thornquist H, Tuminaro R, Willenbring J, Williams A, Stanley K (2005) An overview of the Trilinos project. ACM Trans Math Softw 31(3):397–423MathSciNetCrossRefMATH
32.
Zurück zum Zitat Heroux MA (2009) Software challenges for extreme scale computing: going from petascale to exascale systems. Int J High Perform Comput Appl 23(4):437–439CrossRef Heroux MA (2009) Software challenges for extreme scale computing: going from petascale to exascale systems. Int J High Perform Comput Appl 23(4):437–439CrossRef
33.
Zurück zum Zitat Heroux MA, Willenbring JM (2012) A new overview of the Trilinos project. Sci Program 20(2):83–88 Heroux MA, Willenbring JM (2012) A new overview of the Trilinos project. Sci Program 20(2):83–88
34.
Zurück zum Zitat Jönsthövel TB, van Gijzen MB, MacLachlan S, Vuik C, Scarpas A (2012) Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials. Comput Mech 50(3):321–333MathSciNetCrossRefMATH Jönsthövel TB, van Gijzen MB, MacLachlan S, Vuik C, Scarpas A (2012) Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials. Comput Mech 50(3):321–333MathSciNetCrossRefMATH
35.
Zurück zum Zitat Ketterhagen WR (2011) Modeling the motion and orientation of various pharmaceutical tablet shapes in a film coating pan using dem. Int J Pharm 409(1–2):137–149CrossRef Ketterhagen WR (2011) Modeling the motion and orientation of various pharmaceutical tablet shapes in a film coating pan using dem. Int J Pharm 409(1–2):137–149CrossRef
36.
Zurück zum Zitat Kotteda VMK, Chattopadhyay A, Kumar V, Spotz W (2016) A framework to integrate MFiX with Trilinos for high fidelity fluidized bed computations. In: 2016 IEEE High Performance Extreme Computing Conference (HPEC). IEEE, pp 1–6 Kotteda VMK, Chattopadhyay A, Kumar V, Spotz W (2016) A framework to integrate MFiX with Trilinos for high fidelity fluidized bed computations. In: 2016 IEEE High Performance Extreme Computing Conference (HPEC). IEEE, pp 1–6
37.
Zurück zum Zitat Kotteda VMK, Chattopadhyay A, Kumar V, Spotz W (2017) Next-generation multiphase flow solver for fluidized bed applications. In: ASME 2017 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, p V01CT16A013 Kotteda VMK, Chattopadhyay A, Kumar V, Spotz W (2017) Next-generation multiphase flow solver for fluidized bed applications. In: ASME 2017 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, p V01CT16A013
38.
Zurück zum Zitat Kunii D, Levenspiel O (1991) Fluid Eng. Butterworth-Heinemann, Boston Kunii D, Levenspiel O (1991) Fluid Eng. Butterworth-Heinemann, Boston
39.
Zurück zum Zitat Lanczos C (1950) An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. United States Government, Press Office, Los AngelesMATH Lanczos C (1950) An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. United States Government, Press Office, Los AngelesMATH
40.
Zurück zum Zitat Lin P, Bettencourt M, Domino S, Fisher T, Hoemmen M, Hu J, Phipps E, Prokopenko A, Rajamanickam S, Siefert C, Kennon S (2014) Towards extreme-scale simulations for low Mach fluids with second-generation Trilinos. Parallel Process Lett 24(04):1442005MathSciNetCrossRef Lin P, Bettencourt M, Domino S, Fisher T, Hoemmen M, Hu J, Phipps E, Prokopenko A, Rajamanickam S, Siefert C, Kennon S (2014) Towards extreme-scale simulations for low Mach fluids with second-generation Trilinos. Parallel Process Lett 24(04):1442005MathSciNetCrossRef
42.
Zurück zum Zitat Lin PT, Shadid JN, Sala M, Tuminaro RS, Hennigan GL, Hoekstra RJ (2009) Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling. J Comput Phys 228(17):6250–6267MathSciNetCrossRefMATH Lin PT, Shadid JN, Sala M, Tuminaro RS, Hennigan GL, Hoekstra RJ (2009) Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling. J Comput Phys 228(17):6250–6267MathSciNetCrossRefMATH
43.
Zurück zum Zitat Minchener AJ (2005) Coal gasification for advanced power generation. Fuel 84(17):2222–2235CrossRef Minchener AJ (2005) Coal gasification for advanced power generation. Fuel 84(17):2222–2235CrossRef
44.
Zurück zum Zitat Pannala S, D’Azevedo E, Syamlal M (2003) Hybrid (OpenMP and MPI) parallelization of MFIX: a multiphase CFD code for modeling fluidized beds. In: Proceedings of the 2003 ACM Symposium on Applied Computing, ACM, pp 199–206 Pannala S, D’Azevedo E, Syamlal M (2003) Hybrid (OpenMP and MPI) parallelization of MFIX: a multiphase CFD code for modeling fluidized beds. In: Proceedings of the 2003 ACM Symposium on Applied Computing, ACM, pp 199–206
45.
Zurück zum Zitat Parks ML, De Sturler E, Mackey G, Johnson DD, Maiti S (2006) Recycling Krylov subspaces for sequences of linear systems. SIAM J Sci Comput 28(5):1651–1674MathSciNetCrossRefMATH Parks ML, De Sturler E, Mackey G, Johnson DD, Maiti S (2006) Recycling Krylov subspaces for sequences of linear systems. SIAM J Sci Comput 28(5):1651–1674MathSciNetCrossRefMATH
46.
Zurück zum Zitat Parks ML, Soodhalter KM, Szyld DB (2016) A block recycled GMRES method with investigations into aspects of solver performance. arXiv preprint arXiv:1604.01713 Parks ML, Soodhalter KM, Szyld DB (2016) A block recycled GMRES method with investigations into aspects of solver performance. arXiv preprint arXiv:​1604.​01713
47.
Zurück zum Zitat Perini F, Galligani E, Reitz RD (2014) A study of direct and krylov iterative sparse solver techniques to approach linear scaling of the integration of chemical kinetics with detailed combustion mechanisms. Combust Flame 161(5):1180–1195CrossRef Perini F, Galligani E, Reitz RD (2014) A study of direct and krylov iterative sparse solver techniques to approach linear scaling of the integration of chemical kinetics with detailed combustion mechanisms. Combust Flame 161(5):1180–1195CrossRef
48.
Zurück zum Zitat Rantanen J, Khinast J (2015) The future of pharmaceutical manufacturing sciences. J Pharm Sci 104(11):3612–3638CrossRef Rantanen J, Khinast J (2015) The future of pharmaceutical manufacturing sciences. J Pharm Sci 104(11):3612–3638CrossRef
49.
Zurück zum Zitat Ruiz J, Jurez M, Morales M, Muoz P, Mendvil M (2013) Biomass gasification for electricity generation: review of current technology barriers. Renew Sustain Energy Rev 18:174–183CrossRef Ruiz J, Jurez M, Morales M, Muoz P, Mendvil M (2013) Biomass gasification for electricity generation: review of current technology barriers. Renew Sustain Energy Rev 18:174–183CrossRef
51.
52.
Zurück zum Zitat Saad Y, Schultz MH (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7(3):856–869MathSciNetCrossRefMATH Saad Y, Schultz MH (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7(3):856–869MathSciNetCrossRefMATH
53.
54.
Zurück zum Zitat Stanislaus A, Marafi A, Rana MS (2010) Recent advances in the science and technology of ultra low sulfur diesel (ULSD) production. Catal Today 153(1):1–68CrossRef Stanislaus A, Marafi A, Rana MS (2010) Recent advances in the science and technology of ultra low sulfur diesel (ULSD) production. Catal Today 153(1):1–68CrossRef
55.
Zurück zum Zitat Syamlal M, Rogers W, OBrien TJ (1993) MFIX documentation: theory guide. Technical note DOE/METC-95/1013 and NTIS/DE95000031, National Energy Technology Laboratory, Department of Energy Syamlal M, Rogers W, OBrien TJ (1993) MFIX documentation: theory guide. Technical note DOE/METC-95/1013 and NTIS/DE95000031, National Energy Technology Laboratory, Department of Energy
56.
Zurück zum Zitat Syamlal M et al (1998) MFIX documentation: numerical technique. Technical note no. DOE/MC31346-5824, National Energy Technology Laboratory, Department of Energy Syamlal M et al (1998) MFIX documentation: numerical technique. Technical note no. DOE/MC31346-5824, National Energy Technology Laboratory, Department of Energy
57.
Zurück zum Zitat Thapliyal H, Arabnia HR, Srinivas MB (2009) Efficient reversible logic design of BCD subtractors. Springer, Berlin, pp 99–121 Thapliyal H, Arabnia HR, Srinivas MB (2009) Efficient reversible logic design of BCD subtractors. Springer, Berlin, pp 99–121
58.
Zurück zum Zitat Thapliyal H, Jayashree HV, Nagamani AN, Arabnia HR (2013) Progress in reversible processor design: a novel methodology for reversible carry look-ahead adder. Springer, Berlin, pp 73–97 Thapliyal H, Jayashree HV, Nagamani AN, Arabnia HR (2013) Progress in reversible processor design: a novel methodology for reversible carry look-ahead adder. Springer, Berlin, pp 73–97
59.
Zurück zum Zitat Trottenberg U, Oosterlee CW, Schuller A (2000) Multigrid. Academic Press, LondonMATH Trottenberg U, Oosterlee CW, Schuller A (2000) Multigrid. Academic Press, LondonMATH
60.
Zurück zum Zitat Tuminaro RS, Heroux M, Hutchinson SA, Shadid JN (1999) Official Aztec user’s guide, version 2.1. Technical report, Sandia National Laboratories, Albuquerque Tuminaro RS, Heroux M, Hutchinson SA, Shadid JN (1999) Official Aztec user’s guide, version 2.1. Technical report, Sandia National Laboratories, Albuquerque
61.
Zurück zum Zitat S̆ibanc R, Turk M, Dreu R (2018) An analysis of the mini-tablet fluidized bed coating process. Chem Eng Res Des 134:15–25CrossRef S̆ibanc R, Turk M, Dreu R (2018) An analysis of the mini-tablet fluidized bed coating process. Chem Eng Res Des 134:15–25CrossRef
62.
Zurück zum Zitat Van der Vorst HA (1992) Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J Sci Stat Comput 13(2):631–644MathSciNetCrossRefMATH Van der Vorst HA (1992) Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J Sci Stat Comput 13(2):631–644MathSciNetCrossRefMATH
63.
Zurück zum Zitat Van der Vorst HA (2003) Iterative Krylov methods for large linear systems, vol 13. Cambridge University Press, CambridgeCrossRefMATH Van der Vorst HA (2003) Iterative Krylov methods for large linear systems, vol 13. Cambridge University Press, CambridgeCrossRefMATH
64.
Zurück zum Zitat Xie KC (2015) Coal gasification. Springer, Berlin, pp 181–241 Xie KC (2015) Coal gasification. Springer, Berlin, pp 181–241
65.
Zurück zum Zitat Yates JG, Lettieri P (2016) Introduction. Springer, Cham, pp 1–21 Yates JG, Lettieri P (2016) Introduction. Springer, Cham, pp 1–21
Metadaten
Titel
Performance of preconditioned iterative solvers in MFiX–Trilinos for fluidized beds
verfasst von
V. M. Krushnarao Kotteda
Vinod Kumar
William Spotz
Publikationsdatum
01.08.2018
Verlag
Springer US
Erschienen in
The Journal of Supercomputing / Ausgabe 8/2018
Print ISSN: 0920-8542
Elektronische ISSN: 1573-0484
DOI
https://doi.org/10.1007/s11227-018-2415-5

Weitere Artikel der Ausgabe 8/2018

The Journal of Supercomputing 8/2018 Zur Ausgabe