zbMATH — the first resource for mathematics

A flexible C++ framework for the partitioned solution of strongly coupled multifield problems. (English) Zbl 1361.65086
Summary: In this work, we present a flexible and generic C++ framework for the numerical solution of strongly coupled multifield problems, based on a partitioned approach. Coupled problems occur in a wide range of engineering applications, and their numerical treatment has recently gained much attention. We advocate a partitioned solution approach that enables the use of different discretization schemes and different solvers for the individual fields. Highly optimized, existing solvers can thus be reused – which enhances modularity, reusability, and performance. However, depending on the problem at hand, appropriate measures must be taken to stabilize the solution process and accelerate its convergence. In addition, the field quantities of interest need to be transferred between the solvers. To this end, we developed the software framework comana, which facilitates the implementation of different coupling strategies for a vast range of multifield problems. Interaction with the solvers is achieved through a uniform interface to the solvers’ databases. Interfaces for solvers for which there is no interface available yet can be implemented with minimum effort.

65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65Y15 Packaged methods for numerical algorithms
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
Full Text: DOI
[1] (Bungartz, H.-J.; Schäfer, M., Fluid-Structure Interaction, Lecture Notes in Computational Science and Engineering, vol. 53, (2006), Springer Berlin, Heidelberg)
[2] (Bungartz, H.-J.; Mehl, M.; Schäfer, M., Fluid Structure Interaction II, Lecture Notes in Computational Science and Engineering, vol. 73, (2010), Springer Munich, Darmstadt) · Zbl 1213.74110
[3] Bazilevs, Y.; Takizawa, K.; Tezduyar, T. E., Computational fluid-structure interaction: methods and applications, (2013), John Wiley & Sons · Zbl 1286.74001
[4] Bergheau, J.-M., Thermo-mechanical industrial processes: modeling and numerical simulation, (2014), John Wiley & Sons
[5] Park, K., Stabilization of partitioned solution procedure for pore fluid-soil interaction analysis, Internat. J. Numer. Methods Engrg., 19, 1669-1673, (1983) · Zbl 0519.76095
[6] Zienkiewicz, O.; Paul, D.; Chan, A., Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems, Internat. J. Numer. Methods Engrg., 26, 1039-1055, (1988) · Zbl 0634.73110
[7] Farhat, C.; Park, K. C.; Dubois-Pelerin, Y., An unconditionally stable staggered algorithm for transient finite element analysis of coupled thermoelastic problems, Comput. Methods Appl. Mech. Engrg., 85, 3, 349-365, (1991) · Zbl 0764.73081
[8] Armero, F.; Simo, J., A new unconditionally stable fractional step method for non-linear coupled thermomechanical problems, Internat. J. Numer. Methods Engrg., 35, 737-766, (1992) · Zbl 0784.73085
[9] Felippa, C.; Park, K.; Farhat, C., Partitioned analysis of coupled mechanical systems, Comput. Methods Appl. Mech. Engrg., 190, 3247-3270, (2001) · Zbl 0985.76075
[10] Küttler, U.; Wall, W. A., Fixed-point fluid-structure interaction solvers with dynamic relaxation, Comput. Mech., 43, 61-72, (2008) · Zbl 1236.74284
[11] Joppich, W.; Kürschner, M., Mpcci-a tool for the simulation of coupled applications, Concurr. Comput.: Pract. Exper., 18, 2, 183-192, (2006)
[12] Valcke, S., The OASIS3 coupler: a European climate modelling community software, Geosci. Model Dev., 6, 373-388, (2013)
[13] S. Slattery, P. Wilson, R. Pawlowski, The Data Transfer Kit: A geometric rendezvous-based tool for multiphysics data transfer, in: International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, 2013, pp. 5-9.
[14] Heroux, M. A.; Bartlett, R. A.; Howle, V. E.; Hoekstra, R. J.; Hu, J. J.; Kolda, T. G.; Lehoucq, R. B.; Long, K. R.; Pawlowski, R. P.; Phipps, E. T.; Salinger, A. G.; Thornquist, H. K.; Tuminaro, R. S.; Willenbring, J. M.; Williams, A.; Stanley, K. S., An overview of the trilinos project, ACM Trans. Math. Software, 31, 3, 397-423, (2005), doi: http://doi.acm.org/10.1145/1089014.1089021 · Zbl 1136.65354
[15] S. Sicklinger, T. Wang, Enhanced multi physics interface research engine (empire), 2016. http://empire-multiphysics.com.
[16] Bungartz, H.-J.; Lindner, F.; Gatzhammer, B.; Mehl, M.; Scheufele, K.; Shukaev, A.; Uekermann, B., Precice-A fully parallel library for multi-physics surface coupling, Comput. & Fluids, (2016) · Zbl 1390.76004
[17] Erbts, P.; Düster, A., Accelerated staggered coupling schemes for problems of thermoelasticity at finite strains, Comput. Math. Appl., 64, 2408-2430, (2012) · Zbl 1268.74016
[18] Runge, C., Über empirische funktionen und die interpolation zwischen äquidistanten ordinaten, Z. Math. Phys., 46, 224-243, (1901) · JFM 32.0272.02
[19] Degroote, J.; Bathe, K.-J.; Vierendeels, J., Performance of a new partitioned procedure versus a monolithic procedure in fluid-structure interaction, Comput. Struct., 87, 793-801, (2009)
[20] Gallinger, T., Effiziente algorithmen zur partitionierten Lösung Stark gekoppelter probleme der fluid-struktur-wechselwirkung, (2010), Technische Universität München München, (Ph.D. thesis)
[21] Ericson, C., Real-time collision detection, (2004), CRC Press
[22] Buhmann, M., Radial basis functions: theory and implementations, (2003), Cambridge University Press · Zbl 1038.41001
[23] Küttler, U.; Wall, W. A., Vector extrapolation for strong coupling fluid-structure interaction solvers, Comput. Mech., 76, 1-7, (2009)
[24] Irons, B.; Tuck, R., A version of the aitken accelerator for computer implementation, Internat. J. Numer. Methods Engrg., 1, 275-277, (1969) · Zbl 0256.65021
[25] MacLeod, A., Acceleration of vector sequences by multidimensional \(\Delta^2\) methods, Commun. Appl. Numer. Methods, 1, 3-20, (1986)
[26] Yamada, T.; Yoshimura, S., Line search partitioned approach for fluid-structure interaction analysis of flapping wing, Comput. Model. Eng. Sci., 24, 1, 51-60, (2008) · Zbl 1232.74134
[27] Beazley, D. M., Swig: an easy to use tool for integrating scripting languages with C and C++, (Proceedings of the 4th Conference on USENIX Tcl/Tk Workshop, Vol. 4, (1996), USENIX Association Berkeley, CA, USA)
[28] IEEE754-1985: IEEE standard for binary floating-point arithmetic, 1985.
[29] ISO/IEC 1539-1:2004 Information technology-Programming languages-Fortran-Part 1: Base language, 2004.
[30] M. Bauer, M. Abdel-Maksoud, A 3d potential based boundary element method for the modelling and simulation of marine propeller flows, in: 7th Vienna Conference on Mathematical Modelling, Vienna, Austria, 2012.
[31] B. Uekermann, H.J. Bungartz, B. Gatzhammer, M. Mehl, A parallel, black-box coupling algorithm for fluid-structure interaction, in: Proceedings of the 5th International Conference on Computational Methods for Coupled Problems in Science and Engineering, Ibiza, Spain, 2013, pp. 1-12.
[32] P. Erbts, S. Rothe, A. Düster, S. Hartmann, Energy-conserving data transfer in the partitioned treatment of thermo-viscoplastic problems, in: Proceedings in Applied Mathematics and Mechanics, Vol. 13, 2013, pp. 211-212.
[33] Komech, A.; Komech, A., Principles of partial differential equations, (2009), Springer New York · Zbl 1275.35001
[34] Hron, J.; Turek, S., Proposal for numerical benchmarking of fluid-structure interaction between elastic object and laminar incompressible flow, (Bungartz, H.; Schäfer, M., Fluid-Structure Interaction, Modelling, Simulation and Optimisation, Lecture Notes in Computational Science and Engineering, vol. 53, (2006), Springer), 146-170 · Zbl 1323.76049
[35] Weller, H. G.; Tabor, G.; Jasak, H.; Fureby, C., A tensorial approach to computational continuum mechanics using object-oriented techniques, Comput. Phys., 12, 6, (1998)
[36] Düster, A.; Bröker, H.; Rank, E., The \(p\)-version of the finite element method for three-dimensional curved thin walled structures, Internat. J. Numer. Methods Engrg., 52, 673-703, (2001) · Zbl 1058.74079
[37] Geller, S.; Tölke, J.; Krafczyk, M., Lattice Boltzmann methods on quadree-type grids for fluid-structure interaction, (Bungartz, H.; Schäfer, M., Fluid-Structure Interaction, Modelling, Simulation and Optimisation, Lecture Notes in Computational Science and Engineering, vol. 53, (2006), Springer), 270-293 · Zbl 1323.76079
[38] Kollmannsberger, S.; Geller, S.; Düster, A.; Tölke, J.; Sorger, C.; Krafczyk, M.; Rank, E., Fixed-grid fluid-structure interaction in two dimensions based on a partitioned lattice Boltzmann and \(p\)-FEM approach, Internat. J. Numer. Methods Engrg., 79, 817-845, (2009) · Zbl 1171.74340
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.