Abstract
INMOST (Integrated Numerical Modeling Object-oriented Supercomputing Technologies) is an open-source platform for fast development of efficient and flexible parallel multi-physics models. In this paper we review capabilities of the platform and present two INMOST-based applications for parallel simulations of multi-phase flow in porous media and clot formation in blood flow. For a more detailed description we refer to [1].
The finite volume (FV) method is the popular approach to spatial discretizations on general meshes (i.e. meshes composed of general polyhedral cells), especially for geophysical and biomedical applications where local mass conservation is vital. INMOST provides a complete set of tools for development of FV discretizations for linear and nonlinear problems: automatic differentiation tool for assembly of the nonlinear residual and corresponding Jacobian and Hessian matrices, iterative solvers of nonlinear systems arising from PDEs discretization, parallel solvers for sparse linear algebraic systems.
The platform also provides a technology for development of numerical models on general unstructured grids. It includes parallel mesh data structures, low-level infrastructure for reading, writing, creating, manipulating and partitioning of distributed general meshes.
The synergy of INMOST platform and efficient FV discretizations for systems of PDEs on general meshes produces a powerful tool for supercomputing simulations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Vassilevski, Y., Terekhov, K., Nikitin, K., Kapyrin, I.: Parallel Finite Volume Computation on General Meshes. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-030-47232-0
Vassilevski, Y., Konshin, I., Kopytov, G., Terekhov, K.: INMOST - Program Platform and Graphic Environment for Development of Parallel Numerical Models on General Meshes. Moscow University Publishing, Moscow (2013). (in Russian)
Boman, E.G., Çatalyürek, Ü.V., Chevalier, C., Devine, K.D.: The Zoltan and Isorropia parallel toolkits for combinatorial scientific computing: partitioning, ordering and coloring. Sci. Program. 20(2), 129–150 (2012)
Karypis, G., Schloegel, K., Kumar, V.: Parmetis. Parallel graph partitioning and sparse matrix ordering library. Version, 2 (2003)
Hartigan, J.A., Manchek, A.W.: Algorithm as 136: a k-means clustering algorithm. J. Roy. Stat. Soc. Ser. C (Appl. Stat.) 28, 100–108 (1979)
Sleijpen, G.L., Fokkema, D.R.: BiCGStab (l) for linear equations involving unsymmetric matrices with complex spectrum. Electron. Trans. Numer. Anal. 1(11), 2000 (1993)
Olschowka, M., Neumaier, A.: A new pivoting strategy for Gaussian elimination. Linear Algebra Appl. 240, 131–151 (1996)
Cuthill, E., McKee, J.: Reducing the bandwidth of sparse symmetric matrices. In: Proceedings of the 1969 24th National Conference, pp. 157–172 (1969)
Karypis, G., Kumar, V.: Metis-unstructured graph partitioning and sparse matrix ordering system, version 2.0 (1995)
Soules, G.W.: The rate of convergence of Sinkhorn balancing. Linear Algebra Appl. 150, 3–40 (1991)
Kaporin, I.E.: Scaling, reordering, and diagonal pivoting in ILU preconditionings. Russ. J. Numer. Anal. Math. Model. 22(4), 341–375 (2007)
Li, N., Saad, Y., Chow, E.: Crout versions of ILU for general sparse matrices. SIAM J. Sci. Comput. 25(2), 716–728 (2003)
Kaporin, I.E.: High quality preconditioning of a general symmetric positive definite matrix based on its \(U^tU+ U^tR+ R^tU\)-decomposition. Numer. Linear Algebra Appl. 5(6), 483–509 (1998)
Bollhöfer, M., Saad, Y.: Multilevel preconditioners constructed from inverse-based ILUs. SIAM J. Sci. Comput. 27(5), 1627–1650 (2006)
Anderson, D.G.: Iterative procedures for nonlinear integral equations. J. ACM (JACM) 12(4), 547–560 (1965)
Evans, C., Pollock, S., Rebholz, L.G., Xiao, M.: A proof that Anderson acceleration improves the convergence rate in linearly converging fixed-point methods (but not in those converging quadratically). SIAM J. Numer. Anal. 58(1), 788–810 (2020)
Sterck, H.D.: A nonlinear GMRES optimization algorithm for canonical tensor decomposition. SIAM J. Sci. Comput. 34(3), A1351–A1379 (2012)
Lipnikov, K., Svyatskiy, D., Vassilevski, Y.: Anderson acceleration for nonlinear finite volume scheme for advection-diffusion problems. SIAM J. Sci. Comput. 35(2), 1120–1136 (2013)
Chen, Z., Huan, G., Ma, Y.: Computational Methods for Multiphase Flows in Porous Media. SIAM, Philadelphia (2006)
Norne - the full Norne benchmark case, a real field black-oil model for an oil field in the Norwegian Sea. https://opm-project.org/?page_id=559
Lacroix, S., Vassilevski, Y., Wheeler, J., Wheeler, M.: Iterative solution methods for modeling multiphase flow in porous media fully implicitly. SIAM J. Sci. Comput. 25(3), 905–926 (2003)
Bouchnita, A.: Mathematical modelling of blood coagulation and thrombus formation under flow in normal and pathological conditions. PhD thesis, Universite Lyon 1 - Claude Bernard; Ecole Mohammadia d’Ingenieurs - Universite Mohammed V de Rabat - Maroc. (2017)
Bouchnita, A., Terekhov, K., Nony, P., Vassilevski, Y., Volpert, V.: A mathematical model to quantify the effects of platelet count, shear rate, and injury size on the initiation of blood coagulation under venous flow conditions. PLOS ONE 15(7), e0235392 (2020). https://doi.org/10.1371/journal.pone.0235392
Shen, F., Kastrup, C.J., Liu, Y., Ismagilov, R.F.: Threshold response of initiation of blood coagulation by tissue factor in patterned microfluidic capillaries is controlled by shear rate. Arterioscler. Thromb. Vasc. Biol. 28(11), 2035–2041 (2008)
Acknowledgements
This work has been supported by the RAS Research program No. 26 “Basics of algorithms and software for high performance computing” and RFBR grant 18-31-20048 “Mathematical models of coronary blood flows and thrombogenic processes in cardiac pathologies”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Terekhov, K., Nikitin, K., Vassilevski, Y. (2020). INMOST Platform for Parallel Multi-physics Applications: Multi-phase Flow in Porous Media and Blood Flow Coagulation. In: Voevodin, V., Sobolev, S. (eds) Supercomputing. RuSCDays 2020. Communications in Computer and Information Science, vol 1331. Springer, Cham. https://doi.org/10.1007/978-3-030-64616-5_20
Download citation
DOI: https://doi.org/10.1007/978-3-030-64616-5_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-64615-8
Online ISBN: 978-3-030-64616-5
eBook Packages: Computer ScienceComputer Science (R0)