A PARALLEL ALGORITHM FOR THE SOLUTION OF LARGE-SCALE NONCONFORMING FLUID-STRUCTURE INTERACTION PROBLEMS IN HEMODYNAMICS

doi:10.4208/jcm.1702-m2016-0630

In this work we address the numerical solution of large scale fluid-structure interaction problems when nonconforming grids and/or nonconforming finite elements discretizations are used at the interface separating the fluid and structure physical domains. To deal with nonconforming fluid-structure discretizations we use the INTERNODES method (INTERpolation for NOnconforming DEcompositionS) formerly introduced in [6] for the solution of elliptic PDEs on nonconforming domain decomposition. To cope with the high computational complexity of the three dimensional FSI problem obtained after spatial and temporal discretization, we use the block parallel preconditioner FaCSI [7]. A numerical investigation of the accuracy properties of INTERNODES applied to the nonconforming FSI problem is carried out for the simulation of the pressure wave propagation in a straight elastic cylinder. Finally, we study the scalability performance of the FaCSI preconditioner in the nonconforming case by solving a large-scale nonconforming FSI problem in a patient-specific arterial bypass.

Key words: Fluid-Structure Interaction, Domain decomposition, Nonconforming discretizations, INTERNODES, Biomechanics, Parallel preconditioners, High performance computing

CLC Number:

74F10
65M55

[1] P. Crosetto, S. Deparis, G. Fourestey, and A. Quarteroni, Parallel algorithms for fluid-structure interaction problems in haemodynamics. SIAM Journal on Scientific Computing, 33:4(2011), 1598-1622.

[2] M.W. Gee, U. Küttler, and W.A. Wall, Truly monolithic algebraic multigrid for fluid-structure interaction. International Journal for Numerical Methods in Engineering, 26(2010), 52-72.

[3] F. Nobile, Numerical approximation of fluid-structure interaction problems with application to haemodynamics. PhD Thesis, EPFL, 2001.

[4] Y. Bazilevs, K. Takizawa, and T. Tezduyar, Computational Fluid-Structure Interaction. Methods and Applications. Wiley Series in Computational Mechanics. Wiley, 2013.

[5] L. Formaggia, A. Quarteroni, and A. Veneziani, editors, Cardiovascular mathematics, volume 1 of MS&A. Modeling, Simulation and Applications. Springer-Verlag Italia, Milan. Modeling and simulation of the circulatory system, 2009.

[6] S. Deparis, D. Forti, P. Gervasio, and A. Quarteroni, INTERNODES:an accurate interpolationbased method for coupling the Galerkin solutions of PDEs on subdomains featuring nonconforming interfaces. Computers & Fluids, 141(2016) 22-41.

[7] S. Deparis, D. Forti, G. Grandperrin, and A. Quarteroni, FaCSI:a block parallel preconditioner for fluid-structure interaction problems in hemodynamics. Journal of Computational Physics, 327(2016), 700-718.

[8] S. Deparis, D. Forti, and A. Quarteroni, A Rescaled Localized Radial Basis Function Interpolation on Non-Cartesian and Nonconforming Grids. SIAM Journal on Scientific Computing, 36(2014), A2745-A2762.

[9] S. Deparis, D. Forti, and A. Quarteroni, A fluid-structure interaction algorithm using radial basis function interpolation between non-conforming interfaces. in Advances in Computational FluidStructure, Modeling and Simulation in Science, Engineering and Technology, accepted (2015).

[10] M.A. Fernández, and M. Moubachir, An exact block-Newton algorithm for solving fluid-structure interaction problems. C. R. Math. Acad. Sci. Paris, 336:8(2003), 681-686.

[11] C. Bernardi, Y. Maday, and A.T. Patera, Domain decomposition by the mortar element method. In Asymptotic and numerical methods for partial differential equations with critical parameters (Beaune, 1992), volume 384 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., pp. 269-286. Kluwer Acad. Publ., Dordrecht, (1993).

[12] C. Bernardi, Y. Maday, and A.T. Patera, A new nonconforming approach to domain decomposition:the mortar element method. In Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. XI (Paris, 1989-1991), volume 299 of Pitman Res. Notes Math. Ser., pp. 13-51. Longman Sci. Tech., Harlow, (1994).

[13] F.P.T. Baaijens, A fictitious domain/mortar element method for fluid-structure interaction. International Journal for Numerical Methods in Fluids, 35:7(2001), 743-761.

[14] A. Gerstenberger, and W.A. Wall, An extended finite element method/lagrange multiplier based approach for fluid-structure interaction. Computer Methods in Applied Mechanics and Engineering, 197:19(2008), 1699-1714.

[15] T. Klöppel, A. Popp, U. Küttler, W.A. and Wall, Fluid-structure interaction for non-conforming interfaces based on a dual mortar formulation. Computer Methods in Applied Mechanics and Engineering, 200(2011), 3111-3126.

[16] M. Mayr, T. Klöppel, W.A. Wall, and M.W. Gee, A temporal consistent monolithic approach to fluid-structure interaction enabling single field predictors. SIAM Journal on Scientific Computing, 37:1(2015), B30-B59.

[17] U.M. Mayer, A. Popp, A. Gerstenberger, and W.A. Wall, 3d fluidstructure-contact interaction based on a combined xfem fsi and dual mortar contact approach. Computational Mechanics, 46:1(2010), 53-67.

[18] A. Popp, M. Gitterle, M.W. Gee, and W.A. Wall, A dual mortar approach for 3d finite deformation contact with consistent linearization. International Journal for Numerical Methods in Engineering, 83:11(2010), 1428-1465.

[19] C. Farhat, M. Lesoinne, and P. Le Tallec, Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces:Momentum and energy conservation, optimal discretization and application to aeroelasticity. Computer Methods in Applied Mechanics and Engineering, 157:1(1998), 95-114.

[20] Y.S. Cho, S. Jun, S. Im, and H.G. Kim, An improved interface element with variable nodes for non-matching finite element meshes. Computer Methods in Applied Mechanics and Engineering, 194:27(2005), 3022-3046.

[21] A. De Boer, A.H. Van Zuijlen, and H. Bijl, Review of coupling methods for non-matching meshes. Computer Methods in Applied Mechanics and Engineering, 196:8(2007), 1515-1525.

[22] P.R. Amestoy, I.S. Duff, J. Koster, and J.Y. L'Excellent, A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM Journal on Matrix Analysis and Applications, 23:1(2001), 15-41.

[23] P.R. Amestoy, A. Guermouche, J.Y. L'Excellent, and S. Pralet, Hybrid scheduling for the parallel solution of linear systems. Parallel Computing, 32:2(2006), 136-156.

[24] C.M. Colciago, Reduced Order Fluid-Structure Interaction Models for Hemodynamics Applications. PhD Thesis, EPFL, Lausanne, 2014.

[1]	Guangbao Guo, Weidong Zhao. SCHWARZ METHOD FOR FINANCIAL ENGINEERING [J]. Journal of Computational Mathematics, 2021, 39(4): 538-555.
[2]	Wenbin Chen, Xuejun Xu, Shangyou Zhang. ON THE OPTIMAL CONVERGENCE RATE OF A ROBIN-ROBIN DOMAIN DECOMPOSITION METHOD [J]. Journal of Computational Mathematics, 2014, 32(4): 456-475.
[3]	F. Alouges, J. Bourguignon-Mirebeau, D. P. Levadoux. A SIMPLE PRECONDITIONED DOMAIN DECOMPOSITION METHOD FOR ELECTROMAGNETIC SCATTERING PROBLEMS [J]. Journal of Computational Mathematics, 2013, 31(1): 1-21.
[4]	Igor Boglaev , Matthew Hardy . A MONOTONE DOMAINDECOMPOSITION ALGORITHM FOR SOLVING WEIGHTED AVERAGE APPROXIMATIONS TO NONLINEAR SINGULARLY PERTURBED PARABOLIC PROBLEMS [J]. Journal of Computational Mathematics, 2008, 26(1): 76-97.
[5]	Ju-e Yang,De-hao Yu. DOMAIN DECOMPOSITION WITH NONMATCHING GRIDS FOR EXTERIORTRANSMISSION PROBLEMS VIA FEM AND DTN MAPPING [J]. Journal of Computational Mathematics, 2006, 24(3): 323-342.
[6]	Mei-qun Jiang,Pei-liang Dai. A PARALLEL NONOVERLAPPING DOMAIN DECOMPOSITION METHOD FOR TOKESPROBLEMS [J]. Journal of Computational Mathematics, 2006, 24(2): 209-224.
[7]	De Hao YU. NATURAL BOUNDARY INTEGRAL METHOD AND ITS NEW DEVELOPMENT [J]. Journal of Computational Mathematics, 2004, 22(2): 309-318.
[8]	Ping LUO,Guo Ping LIANG. DOMAIN DECOMPOSITION METHODS WITH NONMATCHING GRIDS FOR THE UNILATERAL PROBLEM [J]. Journal of Computational Mathematics, 2002, 20(2): 197-206.
[9]	Mo MU,Yun Qing HUANG. PARTITION PROPERLY OF DOMAIN DECOMPOSITION WITHOUT ELLIPTICITY [J]. Journal of Computational Mathematics, 2001, 19(4): 423-432.
[10]	Ping LUO,Guo Ping LIANG. GLOBAL SUPERCONVERGENCES OF THE DOMAIN DECOMPOSITION METHODS WITH NONMATCHING GRIDS [J]. Journal of Computational Mathematics, 2001, 19(2): 187-194.
[11]	Qi Ya HU,Guo Ping LIANG,Jin Zhao LIU. CONSTRUCTION OF A PRECONDITIONER FOR DOMAIN DECOMPOSITION METHODS WITH POLYNOMIAL LAGRANGIAN MULTIPLIERSS [J]. Journal of Computational Mathematics, 2001, 19(2): 213-224.
[12]	De Hao YU,Ji Ming WU. A NONOVERLAPPING DOMAIN DECOMPOSITION METHOD FOR EXTERIOR 3-D PROBLEM [J]. Journal of Computational Mathematics, 2001, 19(1): 77-86.
[13]	Jian Guo HUANG. On the domain decomposition method for Morley element-from weak overlap to nonoverlap [J]. Journal of Computational Mathematics, 1999, 17(6): 615-628.
[14]	Dao-qi Yang. A PARALLEL ITERATIVE DOMAIN DECOMPOSITION ALGORITHM FOR ELLIPTIC PROBLEMS [J]. Journal of Computational Mathematics, 1998, 16(2): 141-151.
[15]	Jin-sheng Gu,Xian-cheng Hu. SOME ESTIMATES WITH NONCONFORMING ELEMENTS IN DOMAIN DECOMPOSITIONANALYSIS [J]. Journal of Computational Mathematics, 1998, 16(1): 63-080.

Viewed

Full text

Abstract

A PARALLEL ALGORITHM FOR THE SOLUTION OF LARGE-SCALE NONCONFORMING FLUID-STRUCTURE INTERACTION PROBLEMS IN HEMODYNAMICS

扫码分享