메뉴 건너뛰기




Volumn 218, Issue 19, 2012, Pages 9853-9865

A local radial basis function method for advection-diffusion-reaction equations on complexly shaped domains

Author keywords

Advection diffusion reaction equations; Chemotaxis; Diffusion reaction equations; Numerical partial differential equations; Radial basis functions; Turing equations

Indexed keywords

ADVECTION-DIFFUSION-REACTION EQUATIONS; CHEMOTAXIS; DIFFUSION-REACTION EQUATION; RADIAL BASIS FUNCTIONS; TURING EQUATIONS;

EID: 84860498525     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.03.062     Document Type: Article
Times cited : (183)

References (52)
  • 2
    • 0033038309 scopus 로고    scopus 로고
    • A two-dimensional numerical study of spatial pattern formation in interacting Turing systems
    • DOI 10.1006/bulm.1998.0093
    • R. Barrio, C. Varea, J. Aragon, and P. Maini A two-dimensional numerical study of spatial pattern formation in interacting Turing systems B. Math. Biol. 61 1999 483 505 (Pubitemid 29274617)
    • (1999) Bulletin of Mathematical Biology , vol.61 , Issue.3 , pp. 483-505
    • Barrio, R.A.1    Varea, C.2    Aragon, J.L.3    Maini, P.K.4
  • 3
    • 0026023209 scopus 로고
    • Complex patterns formed by motile cells of Escherichia coli
    • E.O. Budrene, and H.C. Berg Complex patterns formed by motile cells of Escherichia coli Nature 349 1991 630 633 (Pubitemid 21912121)
    • (1991) Nature , vol.349 , Issue.6310 , pp. 630-633
    • Budrene, E.O.1    Berg, H.C.2
  • 6
    • 73249116154 scopus 로고    scopus 로고
    • A finite-volume method for solving parabolic equations on logically cartesian curved surface meshes
    • D. Calhoun, and C. Helzel A finite-volume method for solving parabolic equations on logically cartesian curved surface meshes SIAM J. Sci. Comput. 31 6 2009 4066 4099
    • (2009) SIAM J. Sci. Comput. , vol.31 , Issue.6 , pp. 4066-4099
    • Calhoun, D.1    Helzel, C.2
  • 7
    • 56549128338 scopus 로고    scopus 로고
    • A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models
    • A. Chertock, and A. Kurganov A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models Numer. Math. 111 2008 169 205
    • (2008) Numer. Math. , vol.111 , pp. 169-205
    • Chertock, A.1    Kurganov, A.2
  • 8
    • 34547271985 scopus 로고    scopus 로고
    • An optimal adaptive time-stepping scheme for solving reaction-diffusion- chemotaxis systems
    • C. Chiu, and J.-L. Yu An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems Math. Biosci. Eng. 4 2 2007 187 203 (Pubitemid 47147347)
    • (2007) Mathematical Biosciences and Engineering , vol.4 , Issue.2 , pp. 187-203
    • Chiu, C.1    Yu, J.-L.2
  • 10
    • 33747373791 scopus 로고
    • Pattern formation in generalized Turing systems I: Steady-state patterns in systems with mixed boundary conditions
    • R. Dillon, P. Maini, and H. Othmer Pattern formation in generalized Turing systems I: Steady-state patterns in systems with mixed boundary conditions J. Math. Biol. 32 1994 345 393
    • (1994) J. Math. Biol. , vol.32 , pp. 345-393
    • Dillon, R.1    Maini, P.2    Othmer, H.3
  • 11
    • 67349163264 scopus 로고    scopus 로고
    • New interior penalty discontinuous Galerkin methods for the Keller-Segel chemotaxis model
    • Y. Epshteyn, and A. Kurganov New interior penalty discontinuous Galerkin methods for the Keller-Segel chemotaxis model SIAM J. Numer. Anal. 47 2008 386 408
    • (2008) SIAM J. Numer. Anal. , vol.47 , pp. 386-408
    • Epshteyn, Y.1    Kurganov, A.2
  • 13
    • 84860446897 scopus 로고    scopus 로고
    • Stable evaluation of Gaussian RBF interpolants
    • G.E. Fasshauer, and M. McCourt Stable evaluation of Gaussian RBF interpolants SIAM J. Sci. Comput. 34 2 2012 737 762
    • (2012) SIAM J. Sci. Comput. , vol.34 , Issue.2 , pp. 737-762
    • Fasshauer, G.E.1    McCourt, M.2
  • 15
    • 79957589881 scopus 로고    scopus 로고
    • Stable computations with Gaussian radial basis functions in 2-d
    • B. Fornberg, E. Larsson, and N. Flyer Stable computations with Gaussian radial basis functions in 2-d SIAM J. Sci. Comput. 33 2011 869 892
    • (2011) SIAM J. Sci. Comput. , vol.33 , pp. 869-892
    • Fornberg, B.1    Larsson, E.2    Flyer, N.3
  • 16
    • 79951859711 scopus 로고    scopus 로고
    • GPU-based fast gamma index calculation
    • X. Gu, X. Jia, and S. Jiang GPU-based fast gamma index calculation Phys. Med. Biol. 56 5 2011
    • (2011) Phys. Med. Biol. , vol.56 , Issue.5
    • Gu, X.1    Jia, X.2    Jiang, S.3
  • 17
    • 63049107118 scopus 로고    scopus 로고
    • A user's guide to PDE models for chemotaxis
    • T. Hillen, and K. Painter A user's guide to PDE models for chemotaxis J. Math. Biol. 58 2009 183 217
    • (2009) J. Math. Biol. , vol.58 , pp. 183-217
    • Hillen, T.1    Painter, K.2
  • 18
    • 79951644439 scopus 로고    scopus 로고
    • Solution of Burgers' equation using a local-RBF meshless method
    • B. Hosseini, and R. Hashemi Solution of Burgers' equation using a local-RBF meshless method Int. J. Comput. Meth. Eng. Sci. Mech. 12 1 2011 44 58
    • (2011) Int. J. Comput. Meth. Eng. Sci. Mech. , vol.12 , Issue.1 , pp. 44-58
    • Hosseini, B.1    Hashemi, R.2
  • 19
    • 0036680019 scopus 로고    scopus 로고
    • Accuracy and stability of splitting with Stabilizing Corrections
    • DOI 10.1016/S0168-9274(01)00152-0, PII S0168927401001520
    • W. Hundsdorfer Accuracy and stability of splitting with stabilizing corrections Appl. Numer. Math. 42 2002 213 233 (Pubitemid 34782553)
    • (2002) Applied Numerical Mathematics , vol.42 , Issue.1-3 , pp. 213-233
    • Hundsdorfer, W.1
  • 20
    • 0025229330 scopus 로고
    • Multiquadrics. A scattered data approximation scheme with applications to computational fluid-dynamics. I. Surface approximations and partial derivative estimates
    • E.J. Kansa Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics I: Surface approximations and partial derivative estimates Comput. Math. Appl. 19 8/9 1990 127 145 (Pubitemid 20668364)
    • (1990) Computers & mathematics with applications , vol.19 , Issue.8-9 , pp. 127-145
    • Kansa, E.J.1
  • 21
    • 0025210711 scopus 로고
    • Multiquadrics. A scattered data approximation scheme with applications to computational fluid-dynamics. II. Solutions to parabolic, hyperbolic and elliptic partial differential equations
    • E.J. Kansa Multiquadrics - a scattered data approximation scheme with applications to computational fluid dynamics II: Solutions to parabolic, hyperbolic, and elliptic partial differential equations Comput. Math. Appl. 19 8/9 1990 147 161 (Pubitemid 20668365)
    • (1990) Computers & mathematics with applications , vol.19 , Issue.8-9 , pp. 147-161
    • Kansa, E.J.1
  • 23
    • 79954530734 scopus 로고    scopus 로고
    • STOCHSIMGPU: Parallel stochastic simulation for the systems biology toolbox 2 for Matlab
    • G. Klingbeil, R. Erban, M. Giles, and P.K. Maini STOCHSIMGPU: parallel stochastic simulation for the systems biology toolbox 2 for Matlab Bioinformatics 27 8 2011 1170 1171
    • (2011) Bioinformatics , vol.27 , Issue.8 , pp. 1170-1171
    • Klingbeil, G.1    Erban, R.2    Giles, M.3    Maini, P.K.4
  • 24
    • 0002567674 scopus 로고
    • Bounds on multivariate interpolation and exponential error estimates for multiquadric interpolation
    • W.R. Madych, and S.A. Nelson Bounds on multivariate interpolation and exponential error estimates for multiquadric interpolation J. Approx. Theor. 70 1992 94 114
    • (1992) J. Approx. Theor. , vol.70 , pp. 94-114
    • Madych, W.R.1    Nelson, S.A.2
  • 25
    • 0141515669 scopus 로고    scopus 로고
    • A moving grid finite element method applied to a model biological pattern generator
    • DOI 10.1016/S0021-9991(03)00294-8
    • A. Madzvamuse, A. Wathen, and P. Maini A moving grid finite element method applied to a model biological pattern generator J. Comput. Phys. 190 2003 478 500 (Pubitemid 37141663)
    • (2003) Journal of Computational Physics , vol.190 , Issue.2 , pp. 478-500
    • Madzvamuse, A.1    Wathen, A.J.2    Maini, P.K.3
  • 27
    • 84860465576 scopus 로고    scopus 로고
    • Near-optimal data-independent point locations for radial basis function interpolation
    • S. De Marchi, R. Schaback, and H. Wendland Near-optimal data-independent point locations for radial basis function interpolation Adv. Comput. Math. 2004 1 14
    • (2004) Adv. Comput. Math. , pp. 1-14
    • De Marchi, S.1    Schaback, R.2    Wendland, H.3
  • 28
    • 34250122797 scopus 로고
    • Interpolation of scattered data: Distance matrices and conditionally positive definite functions
    • C. Micchelli Interpolation of scattered data: distance matrices and conditionally positive definite functions Constr. Approx. 2 1986 11 22
    • (1986) Constr. Approx. , vol.2 , pp. 11-22
    • Micchelli, C.1
  • 31
    • 3142698698 scopus 로고    scopus 로고
    • A simple mesh generator in Matlab
    • P. Persson, and G. Strang A simple mesh generator in Matlab SIAM Rev. 46 2002 329 345
    • (2002) SIAM Rev. , vol.46 , pp. 329-345
    • Persson, P.1    Strang, G.2
  • 32
    • 33745923525 scopus 로고    scopus 로고
    • Eigenvalue stability of radial basis function discretizations for time-dependent problems
    • DOI 10.1016/j.camwa.2006.04.007, PII S0898122106000770
    • R. Platte, and T. Driscoll Eigenvalue stability of radial basis functions discretizations for time-dependent problems Comput. Math. Appl. 51 2006 1251 1268 (Pubitemid 44041876)
    • (2006) Computers and Mathematics with Applications , vol.51 , Issue.8 SPEC. ISS. , pp. 1251-1268
    • Platte, R.B.1    Driscoll, T.A.2
  • 33
    • 79957584021 scopus 로고    scopus 로고
    • Multicore/multi-GPU accelerated simulations of multiphase compressible flows using wavelet adapted grids
    • D. Rossinelli, B. Hejazialhosseini, D.G. Spampinato, and P. Koumoutsakos Multicore/multi-GPU accelerated simulations of multiphase compressible flows using wavelet adapted grids SIAM J. Sci. Comput. 33 2 2011 512 540
    • (2011) SIAM J. Sci. Comput. , vol.33 , Issue.2 , pp. 512-540
    • Rossinelli, D.1    Hejazialhosseini, B.2    Spampinato, D.G.3    Koumoutsakos, P.4
  • 34
    • 84858024529 scopus 로고    scopus 로고
    • A RBF based local gridfree scheme for unsteady convection-diffusion problems
    • Y. Sanyasiraju, and G. Chandhini A RBF based local gridfree scheme for unsteady convection-diffusion problems CFD Lett. 1 2 2009 59 67
    • (2009) CFD Lett. , vol.1 , Issue.2 , pp. 59-67
    • Sanyasiraju, Y.1    Chandhini, G.2
  • 35
    • 40749138583 scopus 로고    scopus 로고
    • A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEs
    • S.A. Sarra A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEs Numer. Method. Partial Differ. Equat. 24 2 2008 670 686
    • (2008) Numer. Method. Partial Differ. Equat. , vol.24 , Issue.2 , pp. 670-686
    • Sarra, S.A.1
  • 36
    • 77957151972 scopus 로고    scopus 로고
    • Radial basis function approximation methods with extended precision floating point arithmetic
    • S.A. Sarra Radial basis function approximation methods with extended precision floating point arithmetic Eng. Anal. Bound. Elem. 35 1 2011 68 76
    • (2011) Eng. Anal. Bound. Elem. , vol.35 , Issue.1 , pp. 68-76
    • Sarra, S.A.1
  • 37
    • 84860450667 scopus 로고    scopus 로고
    • Multiquadric radial basis function approximation methods for the numerical solution of partial differential equations
    • S.A. Sarra, and E.J. Kansa Multiquadric radial basis function approximation methods for the numerical solution of partial differential equations Adv. Comput. Mech. 2 2009
    • (2009) Adv. Comput. Mech. , vol.2
    • Sarra, S.A.1    Kansa, E.J.2
  • 38
    • 65749310935 scopus 로고
    • Error estimates and condition numbers for radial basis function interpolation
    • R. Schaback Error estimates and condition numbers for radial basis function interpolation Adv. Comput. Math. 3 1995 251 264
    • (1995) Adv. Comput. Math. , vol.3 , pp. 251-264
    • Schaback, R.1
  • 40
    • 78650796062 scopus 로고    scopus 로고
    • Multiquadric finite difference (MQ-FD) method and its application
    • Y. Shan, C. Shu, and N. Qin Multiquadric finite difference (MQ-FD) method and its application Adv. Appl. Math. Mech. 5 1 2009 615 638
    • (2009) Adv. Appl. Math. Mech. , vol.5 , Issue.1 , pp. 615-638
    • Shan, Y.1    Shu, C.2    Qin, N.3
  • 41
    • 78651338789 scopus 로고    scopus 로고
    • Numerical solution of the Sturm-Liouville problem with local rbf-based differential quadrature collocation method
    • Q. Shen Numerical solution of the Sturm-Liouville problem with local rbf-based differential quadrature collocation method Int. J. Comput. Math. 88 2 2011 285 295
    • (2011) Int. J. Comput. Math. , vol.88 , Issue.2 , pp. 285-295
    • Shen, Q.1
  • 42
    • 0037436111 scopus 로고    scopus 로고
    • Local radial basis funcion-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations
    • DOI 10.1016/S0045-7825(02)00618-7, PII S0045782502006187
    • C. Shu, H. Ding, and K.S. Yeo Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations Comput. Method. Appl. Mech. Eng. 192 2003 941 954 (Pubitemid 36225326)
    • (2003) Computer Methods in Applied Mechanics and Engineering , vol.192 , Issue.7-8 , pp. 941-954
    • Shu, C.1    Ding, H.2    Yeo, K.S.3
  • 43
    • 57349159504 scopus 로고    scopus 로고
    • An efficient implementation of a numerical method for a chemotaxis system
    • M. Smiely An efficient implementation of a numerical method for a chemotaxis system Int. J. Comput. Math. 86 2009 219 235
    • (2009) Int. J. Comput. Math. , vol.86 , pp. 219-235
    • Smiely, M.1
  • 45
    • 29144506799 scopus 로고    scopus 로고
    • High-accuracy discretization methods for solid mechanics
    • A.I. Tolstykh, M.V. Lipavskii, and D.A. Shirobokov High-accuracy discretization methods for solid mechanics Arch. Mech. 55 2003 531 553 (Pubitemid 38046838)
    • (2003) Arch. Mech. , vol.55 , Issue.5-6 , pp. 531-553
    • Tolstykh, A.I.1    Lipavskii, M.V.2    Shirobokov, D.A.3
  • 46
    • 3042722159 scopus 로고    scopus 로고
    • On using radial basis functions in finite difference mode with applications to elasticity problems
    • A.I. Tolstykh, and D.A. Shirobokov On using radial basis functions in finite difference mode with applications to elasticity problems Comput. Mech. 33 2003 68 79
    • (2003) Comput. Mech. , vol.33 , pp. 68-79
    • Tolstykh, A.I.1    Shirobokov, D.A.2
  • 48
    • 0002011401 scopus 로고
    • The chemical basis of morphogenesis
    • A. Turing The chemical basis of morphogenesis Philos. Trans. R. Soc. B 237 1952 37 72
    • (1952) Philos. Trans. R. Soc. B , vol.237 , pp. 37-72
    • Turing, A.1
  • 49
    • 0033112265 scopus 로고    scopus 로고
    • Model and analysis of chemotactic bacterial patterns in a liquid medium
    • R. Tyson, S. Lubkin, and J. Murray Model and analysis of chemotactic bacterial patterns in a liquid medium J. Math. Biol. 38 1999 359 375
    • (1999) J. Math. Biol. , vol.38 , pp. 359-375
    • Tyson, R.1    Lubkin, S.2    Murray, J.3
  • 50
    • 0034331541 scopus 로고    scopus 로고
    • Fraction step methods applied to a chemotaxis model
    • R. Tyson, L. Stern, and R. LeVeque Fraction step methods applied to a chemotaxis model J. Math. Biol. 41 2000 455 475
    • (2000) J. Math. Biol. , vol.41 , pp. 455-475
    • Tyson, R.1    Stern, L.2    Leveque, R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.