메뉴 건너뛰기




Volumn 24, Issue 5, 2003, Pages 1733-1753

Matrix decomposition algorithms for modified spline collocation for Helmholtz problems

Author keywords

Boundary conditions; Convergence rates; Fast Fourier transforms; Helmholtz equation; Spline collocation; Superconvergence; Tensor product

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; FOURIER TRANSFORMS; MATRIX ALGEBRA; PIECEWISE LINEAR TECHNIQUES; POLYNOMIALS;

EID: 0142009981     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S106482750139964X     Document Type: Article
Times cited : (15)

References (30)
  • 1
    • 0141901856 scopus 로고
    • Some collocation methods for differential equations
    • Ph.D. thesis, Rice University, Houston, TX
    • D. Archer, Some Collocation Methods for Differential Equations, Ph.D. thesis, Rice University, Houston, TX 1973.
    • (1973)
    • Archer, D.1
  • 2
    • 0005720269 scopus 로고
    • 4) cubic spline collocation method for quasilinear parabolic equations
    • 4) cubic spline collocation method for quasilinear parabolic equations, SIAM J. Numer. Anal., 14, (1977), pp. 620-637.
    • (1977) SIAM J. Numer. Anal. , vol.14 , pp. 620-637
    • Archer, D.1
  • 3
    • 38249002591 scopus 로고
    • Matrix decomposition methods for separable elliptic boundary value problems in two dimensions
    • B. Bialecki and G. Fairweather, Matrix decomposition methods for separable elliptic boundary value problems in two dimensions, J. Comput. Appl. Math., 46 (1993), pp. 369-386.
    • (1993) J. Comput. Appl. Math. , vol.46 , pp. 369-386
    • Bialecki, B.1    Fairweather, G.2
  • 4
    • 0035281751 scopus 로고    scopus 로고
    • Orthogonal spline collocation methods for partial differential equations
    • B. Bialecki, and G. Fairweather, Orthogonal spline collocation methods for partial differential equations, J. Comput. Appl. Math., 128 (2001), pp. 55-82.
    • (2001) J. Comput. Appl. Math. , vol.128 , pp. 55-82
    • Bialecki, B.1    Fairweather, G.2
  • 5
    • 0004314129 scopus 로고
    • The method of projections as applied to the numerical solution of two point boundary value problems using cubic splines
    • Ph.D. thesis, University of Michigan, Ann Arbor, MI
    • C. De Boor, The Method of Projections as Applied to the Numerical Solution of Two Point Boundary Value Problems Using Cubic Splines, Ph.D. thesis, University of Michigan, Ann Arbor, MI, 1966.
    • (1966)
    • De Boor, C.1
  • 6
    • 0005657134 scopus 로고
    • The basis spline method and associated techniques
    • C. Bottcher, M. R. Strayer, and J. B. McGrory, eds., World Scientific, Singapore
    • C. Bottcher and M.R. Strayer, The basis spline method and associated techniques, in Computational Atomic and Nuclear Physics, C. Bottcher, M. R. Strayer, and J. B. McGrory, eds., World Scientific, Singapore, 1990, pp. 217-240.
    • (1990) Computational Atomic and Nuclear Physics , pp. 217-240
    • Bottcher, C.1    Strayer, M.R.2
  • 7
    • 0005738854 scopus 로고
    • Spline methods for conservation equations
    • D. Lee, A. R. Robinson, and R. Vichnevetsky, eds., Elsevier Science, Amsterdam
    • C. Bottcher and M. R. Strayer, Spline methods for conservation equations, in Computational Acoustics, Vol. 2, D. Lee, A. R. Robinson, and R. Vichnevetsky, eds., Elsevier Science, Amsterdam, 1993, 317-338.
    • (1993) Computational Acoustics , vol.2 , pp. 317-338
    • Bottcher, C.1    Strayer, M.R.2
  • 8
    • 0002502010 scopus 로고
    • Error bounds for bicubic spline interpolation
    • R. E. Carlson and C. A. Hall, Error bounds for bicubic spline interpolation, J. Approx. Theory, 7 (1973), pp. 41-47.
    • (1973) J. Approx. Theory , vol.7 , pp. 41-47
    • Carlson, R.E.1    Hall, C.A.2
  • 9
    • 0025152558 scopus 로고
    • Schur complement preconditioned conjugate gradient methods for spline collocation equations
    • C. C. Christara, Schur complement preconditioned conjugate gradient methods for spline collocation equations, Computer Architecture News, 18 (1990), pp. 108-120.
    • (1990) Computer Architecture News , vol.18 , pp. 108-120
    • Christara, C.C.1
  • 10
    • 0002751519 scopus 로고
    • Quadratic spline collocation methods for elliptic partial differential equations
    • C. C. Christara, Quadratic spline collocation methods for elliptic partial differential equations, BIT, 34 (1994), pp. 33-61.
    • (1994) BIT , vol.34 , pp. 33-61
    • Christara, C.C.1
  • 11
    • 0030269961 scopus 로고    scopus 로고
    • Parallel solvers for spline collocation equations
    • C. C. Christara, Parallel solvers for spline collocation equations, Advances in Engineering Software, 27 (1996), pp. 71-89.
    • (1996) Advances in Engineering Software , vol.27 , pp. 71-89
    • Christara, C.C.1
  • 12
    • 0001070444 scopus 로고    scopus 로고
    • Multigrid and multilevel methods for quadratic spline collocation
    • C. C. Christara, and B. Smith, Multigrid and multilevel methods for quadratic spline collocation, BIT, 37 (1997), pp. 781-803.
    • (1997) BIT , vol.37 , pp. 781-803
    • Christara, C.C.1    Smith, B.2
  • 13
    • 0005653925 scopus 로고
    • Extrapolated collocation for two-point boundary value problems using cubic splines
    • J. W. Daniel and B. K. Swartz, Extrapolated collocation for two-point boundary value problems using cubic splines, J. Inst. Math. Appl., 16 (1975), pp. 161-174.
    • (1975) J. Inst. Math. Appl. , vol.16 , pp. 161-174
    • Daniel, J.W.1    Swartz, B.K.2
  • 14
    • 85160630624 scopus 로고    scopus 로고
    • Matrix decomposition algorithms for modified spline collocation for separable elliptic boundary value problems. I. Helmholtz problems
    • Technical report TR/01/2000, Department of Mathematics and Statistics, University of Cyprus, Nicosia, Cyprus, revised
    • G. Fairweather, A. Karageorghis, and B. Bialecki, Matrix Decomposition Algorithms for Modified Spline Collocation for Separable Elliptic Boundary Value Problems. I. Helmholtz Problems, Technical report TR/01/2000, Department of Mathematics and Statistics, University of Cyprus, Nicosia, Cyprus, revised, 2001.
    • (2001)
    • Fairweather, G.1    Karageorghis, A.2    Bialecki, B.3
  • 15
    • 0000927601 scopus 로고
    • The use of cubic splines in the solution of two-point boundary value problems
    • D. J. Fyfe, The use of cubic splines in the solution of two-point boundary value problems, Comput. J., 13, (1969), pp. 188-192.
    • (1969) Comput. J. , vol.13 , pp. 188-192
    • Fyfe, D.J.1
  • 16
    • 0001618094 scopus 로고
    • Iterative line cubic spline collocation methods for elliptic partial differential equations in several dimensions
    • A. Hadjidimos, E. N. Houstis, J. R. Rice, and E. A. Vavalis, Iterative line cubic spline collocation methods for elliptic partial differential equations in several dimensions, SIAM J. Sci. Statist. Comput., 14 (1993), pp. 715-734.
    • (1993) SIAM J. Sci. Statist. Comput. , vol.14 , pp. 715-734
    • Hadjidimos, A.1    Houstis, E.N.2    Rice, J.R.3    Vavalis, E.A.4
  • 17
    • 0033632291 scopus 로고    scopus 로고
    • Analysis of iterative line spline collocation methods for elliptic partial differential equations
    • A. Hadjidimos, E. N. Houstis, J. R. Rice, and E. Vavalis, Analysis of iterative line spline collocation methods for elliptic partial differential equations, SIAM J. Matrix Anal. Appl., 21 (1999), pp. 508-521.
    • (1999) SIAM J. Matrix Anal. Appl. , vol.21 , pp. 508-521
    • Hadjidimos, A.1    Houstis, E.N.2    Rice, J.R.3    Vavalis, E.4
  • 18
    • 0024000108 scopus 로고
    • Quadratic-spline collocation methods for two-point boundary value problems
    • E. N. Houstis, C. C. Christara, and J. R. Rice, Quadratic-spline collocation methods for two-point boundary value problems, Internat. J. Numer. Methods Engrg., 26 (1988), pp. 935-952.
    • (1988) Internat. J. Numer. Methods Engrg. , vol.26 , pp. 935-952
    • Houstis, E.N.1    Christara, C.C.2    Rice, J.R.3
  • 19
    • 0000661169 scopus 로고
    • Parallelization of a new class of cubic spline collocation methods
    • R. Vichnevetsky and R. S. Stepleman, eds., IMACS, New Brunswick, NJ
    • E. N. Houstis, J. R. Rice, and E. A. Vavalis, Parallelization of a new class of cubic spline collocation methods, in Advances in Computer Methods for Partial Differential Equations VI, R. Vichnevetsky and R. S. Stepleman, eds., IMACS, New Brunswick, NJ, 1987, pp. 167-174.
    • (1987) Advances in Computer Methods for Partial Differential Equations VI , pp. 167-174
    • Houstis, E.N.1    Rice, J.R.2    Vavalis, E.A.3
  • 20
    • 0000725539 scopus 로고
    • 4) cubic spline collocation methods for elliptic partial differential equations
    • 4) cubic spline collocation methods for elliptic partial differential equations, SIAM J. Numer. Anal., 25 (1988), pp. 54-74.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 54-74
    • Houstis, E.N.1    Vavalis, E.A.2    Rice, J.R.3
  • 21
    • 0005755720 scopus 로고
    • 6) quintic spline collocation method for fourth order two-point boundary value problems
    • 6) quintic spline collocation method for fourth order two-point boundary value problems, BIT 28 (1988) pp. 288-301.
    • (1988) BIT , vol.28 , pp. 288-301
    • Irodotou-Ellina, M.1    Houstis, E.N.2
  • 22
    • 0030268704 scopus 로고    scopus 로고
    • Basis spline collocation method for solving the Schrödinger equation in axillary symmetric systems
    • D. R. Kegley,Jr., V. E. Oberacker, M. R. Strayer, A. S. Umar, and J. C. Wells, Basis spline collocation method for solving the Schrödinger equation in axillary symmetric systems, J. Comput. Phys., 128 (1996), pp. 197-208.
    • (1996) J. Comput. Phys. , vol.128 , pp. 197-208
    • Kegley Jr., D.R.1    Oberacker, V.E.2    Strayer, M.R.3    Umar, A.S.4    Wells, J.C.5
  • 24
    • 0012096419 scopus 로고
    • Some continuant determinants arising in physics and chemistry
    • D. E. Rutherford, Some continuant determinants arising in physics and chemistry, Proc. Roy. Soc. Edinburgh Sect. A, 63 (1952), pp. 232-241.
    • (1952) Proc. Roy. Soc. Edinburgh Sect. A , vol.63 , pp. 232-241
    • Rutherford, D.E.1
  • 26
    • 0142005635 scopus 로고
    • NCAR, Boulder, CO
    • P. N. Swarztrauber, FFTPACK, NCAR, Boulder, CO, 1985, also available online fromnetlib@ornl.gov.
    • (1985) FFTPACK
    • Swarztrauber, P.N.1
  • 27
    • 0005720278 scopus 로고    scopus 로고
    • ADI methods for cubic spline collocation discretizations of elliptic PDEs
    • P. Tsompanopoulou and E. Vavalis, ADI methods for cubic spline collocation discretizations of elliptic PDEs, SIAM J. Sci. Comput., 19 (1998), pp. 341-363.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 341-363
    • Tsompanopoulou, P.1    Vavalis, E.2
  • 28
    • 0005722507 scopus 로고
    • Three-dimensional HF and TDHF calculations with the basis-spline collocation technique
    • Bottcher, M. R. Strayer, and J. B. McGrory, eds., World Scientific, Singapore
    • A. S. Umar, Three-dimensional HF and TDHF calculations with the basis-spline collocation technique, in Computational Atomic and Nuclear Physics, Bottcher, M. R. Strayer, and J. B. McGrory, eds., World Scientific, Singapore, 1990, 337-390.
    • (1990) Computational Atomic and Nuclear Physics , pp. 377-390
    • Umar, A.S.1
  • 29
    • 0001373083 scopus 로고
    • Basis-spline collocation method for the lattice solution of boundary value problems
    • A. S. Umar, J. Wu, M. R. Strayer, and C. Bottcher, Basis-spline collocation method for the lattice solution of boundary value problems, J. Comput. Phys., 93 (1991), pp. 426-448.
    • (1991) J. Comput. Phys. , vol.93 , pp. 426-448
    • Umar, A.S.1    Wu, J.2    Strayer, M.R.3    Bottcher, C.4
  • 30
    • 0003417587 scopus 로고
    • Computational frameworks for the fast fourier transform
    • SIAM, Philadelphia
    • C, Van Loan, Computational Frameworks for the Fast Fourier Transform, Frontiers Appl. Math. 10, SIAM, Philadelphia, 1992.
    • (1992) Frontiers Appl. Math. , vol.10
    • Van Loan, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.