메뉴 건너뛰기




Volumn 193, Issue 1, 2004, Pages 317-348

A fast solver for the Stokes equations with distributed forces in complex geometries

Author keywords

Cartesian grid methods; Double layer potential; Embedded domain methods; Fast multipole methods; Fast solvers; Fictitous domain methods; Immersed interface methods; Integral equations; Moving boundaries; Stokes equations

Indexed keywords

COMPUTATIONAL COMPLEXITY; GEOMETRY; INTEGRAL EQUATIONS; NUMERICAL METHODS; PARALLEL PROCESSING SYSTEMS; POISSON EQUATION; SINGULAR VALUE DECOMPOSITION;

EID: 0344981320     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2003.08.011     Document Type: Article
Times cited : (72)

References (57)
  • 1
    • 0009939172 scopus 로고    scopus 로고
    • A parallel multilevel method for adaptively refined Cartesian grids with embedded boundaries
    • 38th Aerospace Sciences Meeting and Exhibit, Reno, NV, January AIAA
    • M.J. Aftosmis, M.J. Berger, G. Adomavicius, A parallel multilevel method for adaptively refined Cartesian grids with embedded boundaries, in: 38th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 2000, AIAA.
    • (2000)
    • Aftosmis, M.J.1    Berger, M.J.2    Adomavicius, G.3
  • 2
    • 4043164825 scopus 로고    scopus 로고
    • A parallel dynamic-mesh Lagrangian method for simulation of flows with dynamic interfaces
    • Proceedings of Supercomputing 2000, ACM/IEEE, Dallas, TX
    • J.F. Antaki, G.E. Blelloch, O. Ghattas, I. Malčević, G.L. Miller, N.J. Walkington, A parallel dynamic-mesh Lagrangian method for simulation of flows with dynamic interfaces, in: Proceedings of Supercomputing 2000, ACM/IEEE, Dallas, TX, 2000.
    • (2000)
    • Antaki, J.F.1    Blelloch, G.E.2    Ghattas, O.3    Malčević, I.4    Miller, G.L.5    Walkington, N.J.6
  • 4
    • 0002515487 scopus 로고    scopus 로고
    • Efficient management of parallelism in object oriented numerical software libraries
    • E. Arge, A.M. Bruaset, H.P. Langtangen (Eds.), Birkhäuser Press, Basel
    • S. Balay, W.D. Gropp, L. Curfman McInnes, B.F. Smith, Efficient management of parallelism in object oriented numerical software libraries, in: E. Arge, A.M. Bruaset, H.P. Langtangen (Eds.), Modern Software Tools in Scientific Computing, Birkhäuser Press, Basel, 1997, pp. 163-202.
    • (1997) Modern Software Tools in Scientific Computing , pp. 163-202
    • Balay, S.1    Gropp, W.D.2    Curfman McInnes, L.3    Smith, B.F.4
  • 5
    • 0042410892 scopus 로고    scopus 로고
    • A method for computing nearly singular integrals
    • J. Thomas Beale, Ming-Chih Lai, A method for computing nearly singular integrals, SIAM Journal on Numerical Analysis 38 (6) (2001) 1902-1925.
    • (2001) SIAM Journal on Numerical Analysis , vol.38 , Issue.6 , pp. 1902-1925
    • Thomas Beale, J.1    Lai, M.-C.2
  • 6
    • 85030883233 scopus 로고    scopus 로고
    • The embedded boundary integral method for the incompressible Navier-Stokes equations
    • Proceedings of the International Association for Boundary Element Methods 2002 Symposium, CDROM, University of Texas at Austin, Austin TX
    • G. Biros, Lexing Ying, D. Zorin, The embedded boundary integral method for the incompressible Navier-Stokes equations, in: Proceedings of the International Association for Boundary Element Methods 2002 Symposium, CDROM, University of Texas at Austin, Austin TX, 2002.
    • (2002)
    • Biros, G.1    Ying, L.2    Zorin, D.3
  • 7
    • 85190253073 scopus 로고    scopus 로고
    • On finite element discretizations of the pure Neumann problem
    • Technical Report SAND2001-0733J, Sandia National Laboratories, Albuquerque, NM, 20001
    • P. Bochev, R.B. Lehoucq, On finite element discretizations of the pure Neumann problem, Technical Report SAND2001-0733J, Sandia National Laboratories, Albuquerque, NM, 20001.
    • Bochev, P.1    Lehoucq, R.B.2
  • 11
    • 85190291103 scopus 로고    scopus 로고
    • A second-order accurate symmetric discretization of the Poisson equation on irregular domains
    • Li-Tien Cheng, R.P. Fedkiw, F. Gibou, Myungjoo Kang, A second-order accurate symmetric discretization of the Poisson equation on irregular domains, Journal of Computational Physics 171 (2001) 205-227.
    • (2001) Journal of Computational Physics , vol.171 , pp. 205-227
    • Cheng, L.-T.1    Fedkiw, R.P.2    Gibou, F.3    Kang, M.4
  • 12
    • 0036207957 scopus 로고    scopus 로고
    • Evaluation of single layer potentials over curved surfaces
    • L. Farina, Evaluation of single layer potentials over curved surfaces, SIAM Journal on Scientific Computing 23 (1) (2001) 81-91.
    • (2001) SIAM Journal on Scientific Computing , vol.23 , Issue.1 , pp. 81-91
    • Farina, L.1
  • 13
    • 0016972792 scopus 로고
    • Hybrid finite element methods
    • G. Fix, Hybrid finite element methods, SIAM Review 18 (3) (1976) 460-484.
    • (1976) SIAM Review , vol.18 , Issue.3 , pp. 460-484
    • Fix, G.1
  • 14
    • 0034775815 scopus 로고    scopus 로고
    • Immersed interface methods for Neumann and related problems in two and three dimensions
    • A.L. Fogelson, J.P. Keener, Immersed interface methods for Neumann and related problems in two and three dimensions, SIAM Journal on Scientific Computing 22 (5) (2000) 1630-1654.
    • (2000) SIAM Journal on Scientific Computing , vol.22 , Issue.5 , pp. 1630-1654
    • Fogelson, A.L.1    Keener, J.P.2
  • 16
    • 0028035577 scopus 로고
    • A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations
    • R. Glowinski, T.W. Pan, J. Periaux, A fictitious domain method for external incompressible viscous flow modeled by Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering 112 (1-4) (1994) 133-148.
    • (1994) Computer Methods in Applied Mechanics and Engineering , vol.112 , Issue.1-4 , pp. 133-148
    • Glowinski, R.1    Pan, T.W.2    Periaux, J.3
  • 17
    • 0030675426 scopus 로고    scopus 로고
    • A multipole direct and indirect BEM for 2D cavity flow at low Reynolds number
    • J.E. Gómez, H. Power, A multipole direct and indirect BEM for 2D cavity flow at low Reynolds number, Engineering Analysis with Boundary Elements 19 (1997) 17-31.
    • (1997) Engineering Analysis With Boundary Elements , vol.19 , pp. 17-31
    • Gómez, J.E.1    Power, H.2
  • 18
    • 0001067436 scopus 로고
    • Laplace's equation and the Dirichlet-Neumann map in multiply connected domains
    • A. Greenbaum, L. Greengard, G.B. McFadden, Laplace's equation and the Dirichlet-Neumann map in multiply connected domains, Journal of Computational Physics 105 (1993) 267-278.
    • (1993) Journal of Computational Physics , vol.105 , pp. 267-278
    • Greenbaum, A.1    Greengard, L.2    McFadden, G.B.3
  • 19
    • 0040086760 scopus 로고    scopus 로고
    • Rapid parallel evaluation of integrals in potential theory on general three-dimensional regions
    • A. Greenbaum, A. Mayo, Rapid parallel evaluation of integrals in potential theory on general three-dimensional regions, Journal of Computational Physics 145 (2) (1998) 731-742.
    • (1998) Journal of Computational Physics , vol.145 , Issue.2 , pp. 731-742
    • Greenbaum, A.1    Mayo, A.2
  • 20
  • 22
    • 85011484616 scopus 로고    scopus 로고
    • A new version of the fast multipole method for the Laplace equation in three dimensions
    • L. Greengard, V. Rokhlin, A new version of the fast multipole method for the Laplace equation in three dimensions, Acta Numerica (1997) 229-269.
    • (1997) Acta Numerica , pp. 229-269
    • Greengard, L.1    Rokhlin, V.2
  • 25
    • 0001827481 scopus 로고    scopus 로고
    • A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
    • H. Johansen, P. Colella, A Cartesian grid embedded boundary method for Poisson's equation on irregular domains, Journal of Computational Physics 147 (1998) 60-85.
    • (1998) Journal of Computational Physics , vol.147 , pp. 60-85
    • Johansen, H.1    Colella, P.2
  • 27
    • 0032182058 scopus 로고    scopus 로고
    • IES Efficient electrostatic and electromagnetic simulation
    • S. Kapur, D.E. Long, IES efficient electrostatic and electromagnetic simulation, IEEE Computational Science and Engineering 5 (4) (1998) 60-67.
    • (1998) IEEE Computational Science and Engineering , vol.5 , Issue.4 , pp. 60-67
    • Kapur, S.1    Long, D.E.2
  • 28
    • 0030706522 scopus 로고    scopus 로고
    • A fast method of moments solver for efficient parameter extraction of MCMs
    • S. Kapur, Jinsong Zhao, A fast method of moments solver for efficient parameter extraction of MCMs, in: Design Automation Conference, 1997, pp. 141-146.
    • (1997) Design Automation Conference , pp. 141-146
    • Kapur, S.1    Zhao, J.2
  • 30
    • 0004173267 scopus 로고    scopus 로고
    • Ph.D. Thesis, Courant Institute, New York University, New York, NY 10021
    • A. Klawonn, Preconditioners for Indefinite Systems, Ph.D. Thesis, Courant Institute, New York University, New York, NY 10021, 1996.
    • (1996) Preconditioners for Indefinite Systems
    • Klawonn, A.1
  • 31
    • 0028485385 scopus 로고
    • The immersed interface method for elliptic equations with discontinuous coefficients and singular sources
    • R.J. LeVeque, Zhilin Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM Journal on Numerical Analysis 31 (1994) 1019-1044.
    • (1994) SIAM Journal on Numerical Analysis , vol.31 , pp. 1019-1044
    • LeVeque, R.J.1    Li, Z.2
  • 32
    • 0031129202 scopus 로고    scopus 로고
    • Immersed interface methods for Stokes flow with elastic boundaries or surface tension
    • R.J. LeVeque, Zhilin Li, Immersed interface methods for Stokes flow with elastic boundaries or surface tension, SIAM Journal on Scientific Computing 18 (1997) 709-735.
    • (1997) SIAM Journal on Scientific Computing , vol.18 , pp. 709-735
    • LeVeque, R.J.1    Li, Z.2
  • 33
    • 85190301281 scopus 로고    scopus 로고
    • Generating well-shaped Delaunay meshes in 3D
    • Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms, ACM, Washington, DC
    • Xiang-Yang Li, Shang-Hua Teng, Generating well-shaped Delaunay meshes in 3D, in: Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms, ACM, Washington, DC, 2001.
    • (2001)
    • Li, X.-Y.1    Teng, S.-H.2
  • 34
    • 0000641836 scopus 로고    scopus 로고
    • A fast iterative algorithm for elliptic interface problems
    • Zhilin Li, A fast iterative algorithm for elliptic interface problems, SIAM Journal on Numerical Analysis 35 (1998) 23-254.
    • (1998) SIAM Journal on Numerical Analysis , vol.35 , pp. 23-254
    • Li, Z.1
  • 35
    • 0001439074 scopus 로고    scopus 로고
    • The immersed interface method for the Navier-Stokes equations with singular forces
    • Zhilin Li, Ming-Chih Lai, The immersed interface method for the Navier-Stokes equations with singular forces, Journal of Computational Physics 171 (2001) 822-842.
    • (2001) Journal of Computational Physics , vol.171 , pp. 822-842
    • Li, Z.1    Lai, M.-C.2
  • 37
    • 0021417514 scopus 로고
    • The fast solution of Poisson's and the biharmonic equations on irregular regions
    • A. Mayo, The fast solution of Poisson's and the biharmonic equations on irregular regions, SIAM Journal on Numerical Analysis 21 (2) (1984) 285-299.
    • (1984) SIAM Journal on Numerical Analysis , vol.21 , Issue.2 , pp. 285-299
    • Mayo, A.1
  • 38
    • 0040647493 scopus 로고    scopus 로고
    • An adaptation of the Fast Multipole Method for evaluating layer potentials in two dimensions
    • A. McKenney, An adaptation of the Fast Multipole Method for evaluating layer potentials in two dimensions, Computers and Mathematics with Applications 32 (1) (1996) 33-57.
    • (1996) Computers and Mathematics With Applications , vol.32 , Issue.1 , pp. 33-57
    • McKenney, A.1
  • 41
    • 45149143078 scopus 로고
    • A three-dimensional computational method for blood flow in the heart. I: Immersed elastic fibers in a viscous incompressible fluid
    • C.S. Peskin, D.M. McQueen, A three-dimensional computational method for blood flow in the heart. I: immersed elastic fibers in a viscous incompressible fluid, Journal of Computational Physics 81 (1989) 372-405.
    • (1989) Journal of Computational Physics , vol.81 , pp. 372-405
    • Peskin, C.S.1    McQueen, D.M.2
  • 42
    • 85190262395 scopus 로고
    • Improved volume conservation in the computation of flows with immersed elastic boundaries
    • C.S. Peskin, B.F. Prinz, Improved volume conservation in the computation of flows with immersed elastic boundaries, Journal of Computational Physics 105 (1993) 113-132.
    • (1993) Journal of Computational Physics , vol.105 , pp. 113-132
    • Peskin, C.S.1    Prinz, B.F.2
  • 43
    • 0344360928 scopus 로고    scopus 로고
    • Large scale simulation of suspensions with PVM
    • The SCxy Conference Series, ACM/IEEE, San Jose, CA
    • Nhan Phan-Thien, Ka Yan Lee, D. Tullock, Large scale simulation of suspensions with PVM, in: Proceedings of SC97, The SCxy Conference Series, ACM/IEEE, San Jose, CA, 1997.
    • (1997) Proceedings of SC97
    • Phan-Thien, N.1    Lee, K.Y.2    Tullock, D.3
  • 45
    • 0027790983 scopus 로고
    • The completed double layer integral equation method for two-dimensional stokes flow
    • H. Power, The completed double layer integral equation method for two-dimensional stokes flow, IMA Journal of Applied Mathematics 51 (1993) 123-145.
    • (1993) IMA Journal of Applied Mathematics , vol.51 , pp. 123-145
    • Power, H.1
  • 49
    • 84966208957 scopus 로고
    • On the numerical solution of Helmholtz's equation by the capacitance matrix method
    • W. Proskurowski, O.B. Widlund, On the numerical solution of Helmholtz's equation by the capacitance matrix method, Mathematics of Computation 30 (135) (1976) 433-468.
    • (1976) Mathematics of Computation , vol.30 , Issue.135 , pp. 433-468
    • Proskurowski, W.1    Widlund, O.B.2
  • 50
    • 0002359421 scopus 로고    scopus 로고
    • Algorithm 790: CSHEP2D: Cubic Shepard method for bivariate interpolation of scattered data
    • R.J. Renka, Algorithm 790: CSHEP2D: Cubic Shepard method for bivariate interpolation of scattered data, ACM Transactions on Mathematical Software 25 (1) (1999) 70-73.
    • (1999) ACM Transactions on Mathematical Software , vol.25 , Issue.1 , pp. 70-73
    • Renka, R.J.1
  • 51
    • 46549096170 scopus 로고
    • Rapid solution of integral equations of classical potential theory
    • V. Rokhlin, Rapid solution of integral equations of classical potential theory, Journal of Computational Physics 60 (1983) 187-207.
    • (1983) Journal of Computational Physics , vol.60 , pp. 187-207
    • Rokhlin, V.1
  • 52
    • 0345655516 scopus 로고
    • On the difficulty of triangulating three-dimensional nonconvex polyedra
    • J. Ruppert, R. Seidel, On the difficulty of triangulating three-dimensional nonconvex polyedra, Discrete and Computational Geometry 7 (3) (1992).
    • (1992) Discrete and Computational Geometry , vol.7 , Issue.3
    • Ruppert, J.1    Seidel, R.2
  • 53
    • 85180696458 scopus 로고    scopus 로고
    • Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations
    • Proceedings of the sixteenth annual symposium on computational geometry, ACM, Kowloon, Hong Kong
    • J.R. Shewchuk, Sweep algorithms for constructing higher-dimensional constrained Delaunay triangulations, in: Proceedings of the sixteenth annual symposium on Computational geometry, ACM, Kowloon, Hong Kong, 2000.
    • (2000)
    • Shewchuk, J.R.1
  • 54
    • 0000671160 scopus 로고
    • Locally-corrected multidimensional quadrature rules for singular functions
    • J. Strain, Locally-corrected multidimensional quadrature rules for singular functions, SIAM Journal on Scientific Computing 6 (4) (1995) 992-1017.
    • (1995) SIAM Journal on Scientific Computing , vol.6 , Issue.4 , pp. 992-1017
    • Strain, J.1
  • 56
    • 0009853243 scopus 로고    scopus 로고
    • The explicit-jump immersed interface method: Finite difference methods for PDEs with piecewise smooth solutions
    • A. Wiegmann, K.P. Bube, The explicit-jump immersed interface method: finite difference methods for PDEs with piecewise smooth solutions, SIAM Journal on Numerical Analysis 37 (3) (2000) 827-862.
    • (2000) SIAM Journal on Numerical Analysis , vol.37 , Issue.3 , pp. 827-862
    • Wiegmann, A.1    Bube, K.P.2
  • 57
    • 0034687899 scopus 로고    scopus 로고
    • An efficient algorithm for hydrodynamical interaction of many deformable drops
    • A.Z. Zinchenko, R.H. Davis, An efficient algorithm for hydrodynamical interaction of many deformable drops, Journal of Computational Physics 157 (1999) 539-587.
    • (1999) Journal of Computational Physics , vol.157 , pp. 539-587
    • Zinchenko, A.Z.1    Davis, R.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.