A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D
Abstract
Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.
- Authors:
-
- Idaho National Lab. (INL), Idaho Falls, ID (United States). Modeling and Simulation
- Univ. of Colorado, Boulder, CO (United States). Dept. of Computer Science
- Publication Date:
- Research Org.:
- Idaho National Lab. (INL), Idaho Falls, ID (United States)
- Sponsoring Org.:
- USDOE Office of Nuclear Energy (NE)
- OSTI Identifier:
- 1375242
- Alternate Identifier(s):
- OSTI ID: 1413567
- Report Number(s):
- INL/JOU-16-39081
Journal ID: ISSN 0021-9991; PII: S0021999117302383
- Grant/Contract Number:
- AC07-05ID14517
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 340; Journal Issue: C; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; isogeometric coarse mesh; Newton-Krylov-Schwarz; Nonlinear fluid-structure interaction; parallel software development; unstructured mesh
Citation Formats
Kong, Fande, and Cai, Xiao-Chuan. A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D. United States: N. p., 2017.
Web. doi:10.1016/j.jcp.2017.03.043.
Kong, Fande, & Cai, Xiao-Chuan. A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D. United States. https://doi.org/10.1016/j.jcp.2017.03.043
Kong, Fande, and Cai, Xiao-Chuan. Fri .
"A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D". United States. https://doi.org/10.1016/j.jcp.2017.03.043. https://www.osti.gov/servlets/purl/1375242.
@article{osti_1375242,
title = {A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D},
author = {Kong, Fande and Cai, Xiao-Chuan},
abstractNote = {Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.},
doi = {10.1016/j.jcp.2017.03.043},
journal = {Journal of Computational Physics},
number = C,
volume = 340,
place = {United States},
year = {Fri Mar 24 00:00:00 EDT 2017},
month = {Fri Mar 24 00:00:00 EDT 2017}
}
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Works referenced in this record:
Computational vascular fluid dynamics: problems, models and methods
journal, March 2000
- Quarteroni, Alfio; Tuveri, Massimiliano; Veneziani, Alessandro
- Computing and Visualization in Science, Vol. 2, Issue 4
Experimental and Computational Methods in Cardiovascular Fluid Mechanics
journal, January 2004
- Taylor, Charles A.; Draney, Mary T.
- Annual Review of Fluid Mechanics, Vol. 36, Issue 1
Open problems in computational vascular biomechanics: Hemodynamics and arterial wall mechanics
journal, September 2009
- Taylor, C. A.; Humphrey, J. D.
- Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 45-46
Fluid-structure interaction
journal, October 1980
- Belytschko, Ted
- Computers & Structures, Vol. 12, Issue 4
M ODELING OF F LUID -S TRUCTURE I NTERACTION
journal, January 2001
- Dowell, Earl H.; Hall, Kenneth C.
- Annual Review of Fluid Mechanics, Vol. 33, Issue 1
Numerical Methods for Fluid-Structure Interaction — A Review
journal, August 2012
- Hou, Gene; Wang, Jin; Layton, Anita
- Communications in Computational Physics, Vol. 12, Issue 2
Immersed Boundary Methods
journal, January 2005
- Mittal, Rajat; Iaccarino, Gianluca
- Annual Review of Fluid Mechanics, Vol. 37, Issue 1
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
journal, April 1998
- Farhat, C.; Lesoinne, M.; Le Tallec, P.
- Computer Methods in Applied Mechanics and Engineering, Vol. 157, Issue 1-2
Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity
journal, March 2006
- Farhat, Charbel; van der Zee, Kristoffer G.; Geuzaine, Philippe
- Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 17-18
Fluid–structure algorithms based on Steklov–Poincaré operators
journal, August 2006
- Deparis, Simone; Discacciati, Marco; Fourestey, Gilles
- Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 41-43
Stable loosely-coupled-type algorithm for fluid–structure interaction in blood flow
journal, October 2009
- Guidoboni, Giovanna; Glowinski, Roland; Cavallini, Nicola
- Journal of Computational Physics, Vol. 228, Issue 18
Scalable parallel methods for monolithic coupling in fluid–structure interaction with application to blood flow modeling
journal, February 2010
- Barker, Andrew T.; Cai, Xiao-Chuan
- Journal of Computational Physics, Vol. 229, Issue 3
Two-Level Newton and Hybrid Schwarz Preconditioners for Fluid-Structure Interaction
journal, January 2010
- Barker, Andrew T.; Cai, Xiao-Chuan
- SIAM Journal on Scientific Computing, Vol. 32, Issue 4
Isogeometric fluid-structure interaction: theory, algorithms, and computations
journal, August 2008
- Bazilevs, Y.; Calo, V. M.; Hughes, T. J. R.
- Computational Mechanics, Vol. 43, Issue 1
Isogeometric Fluid–structure Interaction Analysis with Applications to Arterial Blood Flow
journal, June 2006
- Bazilevs, Y.; Calo, V. M.; Zhang, Y.
- Computational Mechanics, Vol. 38, Issue 4-5
A Newton method using exact jacobians for solving fluid–structure coupling
journal, January 2005
- Fernández, Miguel Ángel; Moubachir, Marwan
- Computers & Structures, Vol. 83, Issue 2-3
A fully implicit domain decomposition based ALE framework for three-dimensional fluid–structure interaction with application in blood flow computation
journal, February 2014
- Wu, Yuqi; Cai, Xiao-Chuan
- Journal of Computational Physics, Vol. 258
Fluid–structure interaction using the particle finite element method
journal, March 2006
- Idelsohn, S. R.; Oñate, E.; Pin, F. Del
- Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 17-18
Unified Lagrangian formulation for elastic solids and incompressible fluids: Application to fluid–structure interaction problems via the PFEM
journal, March 2008
- Idelsohn, S. R.; Marti, J.; Limache, A.
- Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 19-20
A numerical method for solving the 3D unsteady incompressible Navier–Stokes equations in curvilinear domains with complex immersed boundaries
journal, August 2007
- Ge, Liang; Sotiropoulos, Fotis
- Journal of Computational Physics, Vol. 225, Issue 2
Immersed boundary technique for turbulent flow simulations
journal, May 2003
- Iaccarino, Gianluca; Verzicco, Roberto
- Applied Mechanics Reviews, Vol. 56, Issue 3
The immersed/fictitious element method for fluid-structure interaction: Volumetric consistency, compressibility and thin members: THE IMMERSED/FICTITIOUS ELEMENT METHOD FOR FSI
journal, September 2007
- Wang, Hongwu; Chessa, Jack; Liu, Wing K.
- International Journal for Numerical Methods in Engineering, Vol. 74, Issue 1
A finite element method for crack growth without remeshing
journal, September 1999
- Mo�s, Nicolas; Dolbow, John; Belytschko, Ted
- International Journal for Numerical Methods in Engineering, Vol. 46, Issue 1
An extended finite element method for modeling crack growth with frictional contact
journal, October 2001
- Dolbow, John; Moës, Nicolas; Belytschko, Ted
- Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 51-52
Lattice Boltzmann method for moving boundaries
journal, January 2003
- Lallemand, Pierre; Luo, Li-Shi
- Journal of Computational Physics, Vol. 184, Issue 2
An efficient framework for fluid-structure interaction using the lattice Boltzmann method and immersed moving boundaries
journal, August 2010
- Owen, D. R. J.; Leonardi, C. R.; Feng, Y. T.
- International Journal for Numerical Methods in Engineering, Vol. 87, Issue 1-5
Meshless methods: An overview and recent developments
journal, December 1996
- Belytschko, T.; Krongauz, Y.; Organ, D.
- Computer Methods in Applied Mechanics and Engineering, Vol. 139, Issue 1-4
Modelling and simulation of fluid structure interaction by meshfree and FEM
journal, May 2003
- Zhang, Lucy T.; Wagner, Gregory J.; Liu, Wing K.
- Communications in Numerical Methods in Engineering, Vol. 19, Issue 8
Scalable large-scale fluid-structure interaction solvers in the Uintah framework via hybrid task-based parallelism algorithms: UINTAH HYBRID TASK-BASED PARALLELISM ALGORITHMS
journal, July 2013
- Meng, Qingyu; Berzins, Martin
- Concurrency and Computation: Practice and Experience, Vol. 26, Issue 7
Parallel Algorithms for Fluid-Structure Interaction Problems in Haemodynamics
journal, January 2011
- Crosetto, Paolo; Deparis, Simone; Fourestey, Gilles
- SIAM Journal on Scientific Computing, Vol. 33, Issue 4
A coupled momentum method for modeling blood flow in three-dimensional deformable arteries
journal, August 2006
- Figueroa, C. Alberto; Vignon-Clementel, Irene E.; Jansen, Kenneth E.
- Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 41-43
Cardiovascular flow simulation at extreme scale
journal, December 2009
- Zhou, Min; Sahni, Onkar; Kim, H. Jin
- Computational Mechanics, Vol. 46, Issue 1
Added-mass effect in the design of partitioned algorithms for fluid–structure problems
journal, October 2005
- Causin, P.; Gerbeau, J. F.; Nobile, F.
- Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 42-44
Modular vs. non-modular preconditioners for fluid–structure systems with large added-mass effect
journal, September 2008
- Badia, Santiago; Quaini, Annalisa; Quarteroni, Alfio
- Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 49-50
A Highly Scalable Multilevel Schwarz Method with Boundary Geometry Preserving Coarse Spaces for 3D Elasticity Problems on Domains with Complex Geometry
journal, January 2016
- Kong, Fande; Cai, Xiao-Chuan
- SIAM Journal on Scientific Computing, Vol. 38, Issue 2
Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces
journal, November 1994
- Johnson, A. A.; Tezduyar, T. E.
- Computer Methods in Applied Mechanics and Engineering, Vol. 119, Issue 1-2
Mesh Moving Techniques for Fluid-Structure Interactions With Large Displacements
journal, January 2003
- Stein, K.; Tezduyar, T.; Benney, R.
- Journal of Applied Mechanics, Vol. 70, Issue 1
Analysis of fluid–structure interaction problems with structural buckling and large domain changes by ALE finite element method
journal, September 2001
- Zhang, Qun; Hisada, Toshiaki
- Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 48
Modelling of fluid–structure interactions with the space–time finite elements: Arterial fluid mechanics
journal, January 2007
- Tezduyar, Tayfun E.; Sathe, Sunil; Cragin, Timothy
- International Journal for Numerical Methods in Fluids, Vol. 54, Issue 6-8
Fluid–structure interaction simulation of aortic blood flow
journal, April 2011
- Crosetto, Paolo; Reymond, Philippe; Deparis, Simone
- Computers & Fluids, Vol. 43, Issue 1
Finite element modeling of blood flow in arteries
journal, May 1998
- Taylor, Charles A.; Hughes, Thomas J. R.; Zarins, Christopher K.
- Computer Methods in Applied Mechanics and Engineering, Vol. 158, Issue 1-2
A stabilized finite element method for the incompressible Navier-Stokes equations using a hierarchical basis
journal, January 2001
- Whiting, Christian H.; Jansen, Kenneth E.
- International Journal for Numerical Methods in Fluids, Vol. 35, Issue 1
Inexact Newton Methods
journal, April 1982
- Dembo, Ron S.; Eisenstat, Stanley C.; Steihaug, Trond
- SIAM Journal on Numerical Analysis, Vol. 19, Issue 2
Globally Convergent Inexact Newton Methods
journal, May 1994
- Eisenstat, Stanley C.; Walker, Homer F.
- SIAM Journal on Optimization, Vol. 4, Issue 2
Choosing the Forcing Terms in an Inexact Newton Method
journal, January 1996
- Eisenstat, Stanley C.; Walker, Homer F.
- SIAM Journal on Scientific Computing, Vol. 17, Issue 1
A Flexible Inner-Outer Preconditioned GMRES Algorithm
journal, March 1993
- Saad, Youcef
- SIAM Journal on Scientific Computing, Vol. 14, Issue 2
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
journal, January 1999
- Cai, Xiao-Chuan; Sarkis, Marcus
- SIAM Journal on Scientific Computing, Vol. 21, Issue 2
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
journal, July 1986
- Saad, Youcef; Schultz, Martin H.
- SIAM Journal on Scientific and Statistical Computing, Vol. 7, Issue 3
Parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere
journal, April 2011
- Yang, Chao; Cai, Xiao-Chuan
- Journal of Computational Physics, Vol. 230, Issue 7
A review of algebraic multigrid
journal, March 2001
- Stüben, K.
- Journal of Computational and Applied Mathematics, Vol. 128, Issue 1-2
Unstructured Geometric Multigrid in Two and Three Dimensions on Complex and Graded Meshes
journal, January 2013
- Brune, Peter R.; Knepley, Matthew G.; Scott, L. Ridgway
- SIAM Journal on Scientific Computing, Vol. 35, Issue 1
Parallel multigrid solvers for 3D unstructured finite element problems in large deformation elasticity and plasticity
journal, July 2000
- Adams, Mark F.
- International Journal for Numerical Methods in Engineering, Vol. 48, Issue 8
Optimal Coarsening of Unstructured Meshes
journal, April 1999
- Miller, Gary L.; Talmor, Dafna; Teng, Shang-Hua
- Journal of Algorithms, Vol. 31, Issue 1
Coarsening unstructured meshes by edge contraction
journal, January 2003
- Ollivier-Gooch, Carl
- International Journal for Numerical Methods in Engineering, Vol. 57, Issue 3
Two algorithms for constructing a Delaunay triangulation
journal, June 1980
- Lee, D. T.; Schachter, B. J.
- International Journal of Computer & Information Sciences, Vol. 9, Issue 3
Constrained delaunay triangulations
journal, June 1989
- Paul Chew, L.
- Algorithmica, Vol. 4, Issue 1-4
Laplacian smoothing and Delaunay triangulations
journal, November 1988
- Field, David A.
- Communications in Applied Numerical Methods, Vol. 4, Issue 6
Tetrahedral mesh improvement using swapping and smoothing
journal, November 1997
- Freitag, Lori A.; Ollivier-Gooch, Carl
- International Journal for Numerical Methods in Engineering, Vol. 40, Issue 21
A Parallel Algorithm for Mesh Smoothing
journal, January 1999
- Freitag, Lori; Jones, Mark; Plassmann, Paul
- SIAM Journal on Scientific Computing, Vol. 20, Issue 6
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journal, February 2018
- Kong, Fande; Wang, Yaqi; Schunert, Sebastian
- Numerical Linear Algebra with Applications, Vol. 25, Issue 3
Simulation of unsteady blood flows in a patient‐specific compliant pulmonary artery with a highly parallel monolithically coupled fluid‐structure interaction algorithm
journal, May 2019
- Kong, Fande; Kheyfets, Vitaly; Finol, Ender
- International Journal for Numerical Methods in Biomedical Engineering, Vol. 35, Issue 7
Numerical aerodynamic simulation of transient flows around car based on parallel Newton–Krylov–Schwarz algorithm
journal, July 2019
- Yan, Zhengzheng; Chen, Rongliang; Zhao, Yubo
- Applicable Analysis