Modified nodal cubic spline collocation for three-dimensional variable coefficient second order partial differential equations
We formulate a fourth order modified nodal cubic spline collocation scheme for variable coefficient second order partial differential equations in the unit cube subject to nonzero Dirichlet boundary conditions. The approximate solution satisfies a perturbed partial differential equation at the inter...
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| Published in | Numerical algorithms Vol. 64; no. 2; pp. 349 - 383 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.10.2013
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1017-1398 1572-9265 |
| DOI | 10.1007/s11075-012-9669-4 |
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| Abstract | We formulate a fourth order modified nodal cubic spline collocation scheme for variable coefficient second order partial differential equations in the unit cube subject to nonzero Dirichlet boundary conditions. The approximate solution satisfies a perturbed partial differential equation at the interior nodes of a uniform
partition of the cube and the partial differential equation at the boundary nodes. In the special case of Poisson’s equation, the resulting linear system is solved by a matrix decomposition algorithm with fast Fourier transforms at a cost
. For the general variable coefficient diffusion-dominated case, the system is solved using the preconditioned biconjugate gradient stabilized method. |
|---|---|
| AbstractList | We formulate a fourth order modified nodal cubic spline collocation scheme for variable coefficient second order partial differential equations in the unit cube subject to nonzero Dirichlet boundary conditions. The approximate solution satisfies a perturbed partial differential equation at the interior nodes of a uniform
partition of the cube and the partial differential equation at the boundary nodes. In the special case of Poisson’s equation, the resulting linear system is solved by a matrix decomposition algorithm with fast Fourier transforms at a cost
. For the general variable coefficient diffusion-dominated case, the system is solved using the preconditioned biconjugate gradient stabilized method. We formulate a fourth order modified nodal cubic spline collocation scheme for variable coefficient second order partial differential equations in the unit cube subject to nonzero Dirichlet boundary conditions. The approximate solution satisfies a perturbed partial differential equation at the interior nodes of a uniform $N\times N\times N$ partition of the cube and the partial differential equation at the boundary nodes. In the special case of Poisson's equation, the resulting linear system is solved by a matrix decomposition algorithm with fast Fourier transforms at a cost $O(N reversible reaction \log N)$ . For the general variable coefficient diffusion-dominated case, the system is solved using the preconditioned biconjugate gradient stabilized method. We formulate a fourth order modified nodal cubic spline collocation scheme for variable coefficient second order partial differential equations in the unit cube subject to nonzero Dirichlet boundary conditions. The approximate solution satisfies a perturbed partial differential equation at the interior nodes of a uniform partition of the cube and the partial differential equation at the boundary nodes. In the special case of Poisson’s equation, the resulting linear system is solved by a matrix decomposition algorithm with fast Fourier transforms at a cost . For the general variable coefficient diffusion-dominated case, the system is solved using the preconditioned biconjugate gradient stabilized method. |
| Author | Karageorghis, Andreas Bialecki, Bernard |
| Author_xml | – sequence: 1 givenname: Bernard surname: Bialecki fullname: Bialecki, Bernard organization: Department of Applied Mathematics and Statistics, Colorado School of Mines – sequence: 2 givenname: Andreas surname: Karageorghis fullname: Karageorghis, Andreas email: andreask@ucy.ac.cy organization: Department of Mathematics and Statistics, University of Cyprus |
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| Cites_doi | 10.1016/S0377-0427(01)00504-0 10.1137/040609793 10.1007/s11075-010-9384-y 10.1016/S0096-3003(99)00085-5 10.1007/s10915-008-9246-0 10.1137/050622833 10.1145/29380.214342 10.1137/S1064827595281794 10.1137/S0895479896309827 10.1002/num.20704 10.1137/0913035 10.1145/29380.29863 10.1137/0914045 10.1137/S106482750139964X 10.1007/978-3-0348-9142-4 |
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| DOI | 10.1007/s11075-012-9669-4 |
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| Keywords | Nodal spline collocation Fast Fourier transforms 65N35 65N22 Matrix decomposition algorithm |
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| References | Boisvert (CR9) 1987; 13 Pozo, Remington, Joubert (CR14) 1994 Bialecki, Fairweather, Karageorghis (CR4) 2011; 56 Boisvert (CR8) 1987; 13 Berikelashvili, Gupta, Mirianashvili (CR1) 2007; 45 CR17 CR15 Bjontegaard, Maday, Ronquist (CR7) 2009; 39 Bialecki, Fairweather, Karageorghis (CR3) 2005; 27 Bialecki, Wang (CR5) 2012; 28 van der Vorst (CR18) 1992; 13 de Boor (CR6) 2001 Bialecki, Fairweather, Karageorghis (CR2) 2003; 24 Hadjidimos, Houstis, Rice, Vavalis (CR13) 1999; 21 Tsompanopoulou, Vavalis (CR16) 1998; 19 Ge, Zhang (CR10) 2002; 143 Gupta, Zhang (CR11) 2000; 113 Hadjidimos, Houstis, Rice, Vavalis (CR12) 1993; 14 B Bialecki (9669_CR5) 2012; 28 P Tsompanopoulou (9669_CR16) 1998; 19 T Bjontegaard (9669_CR7) 2009; 39 C de Boor (9669_CR6) 2001 A Hadjidimos (9669_CR12) 1993; 14 L Ge (9669_CR10) 2002; 143 A Hadjidimos (9669_CR13) 1999; 21 MM Gupta (9669_CR11) 2000; 113 G Berikelashvili (9669_CR1) 2007; 45 RF Boisvert (9669_CR9) 1987; 13 HA van der Vorst (9669_CR18) 1992; 13 RF Boisvert (9669_CR8) 1987; 13 R Pozo (9669_CR14) 1994 B Bialecki (9669_CR3) 2005; 27 9669_CR15 B Bialecki (9669_CR2) 2003; 24 B Bialecki (9669_CR4) 2011; 56 9669_CR17 |
| References_xml | – volume: 143 start-page: 9 year: 2002 end-page: 27 ident: CR10 article-title: Symbolic computation of high order compact difference schemes for three dimensional linear elliptic partial differential equations with variable coefficients publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(01)00504-0 – volume: 27 start-page: 575 year: 2005 end-page: 598 ident: CR3 article-title: Optimal superconvergent one step nodal cubic spline collocation methods publication-title: SIAM J. Sci. Comput. doi: 10.1137/040609793 – year: 2001 ident: CR6 publication-title: A Practical Guide to Splines, Revised Edition, Applied Mathematical Sciences, vol. 27 – volume: 56 start-page: 253 year: 2011 end-page: 295 ident: CR4 article-title: Matrix decomposition algorithms for elliptic boundary value problems: a survey publication-title: Numer. Algorithms doi: 10.1007/s11075-010-9384-y – volume: 113 start-page: 249 year: 2000 end-page: 274 ident: CR11 article-title: High accuracy multigrid solution of the 3D convection-diffusion equation publication-title: Appl. Math. Comput. doi: 10.1016/S0096-3003(99)00085-5 – volume: 39 start-page: 28 year: 2009 end-page: 48 ident: CR7 article-title: Fast tensor-product solvers: partially deformed three-dimensional domains publication-title: J. Sci. Comput. doi: 10.1007/s10915-008-9246-0 – ident: CR15 – volume: 45 start-page: 443 year: 2007 end-page: 455 ident: CR1 article-title: Convergence of fourth order compact difference scheme for three-dimensional convection-diffusion equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/050622833 – ident: CR17 – volume: 13 start-page: 235 year: 1987 end-page: 249 ident: CR9 article-title: Algorithm 651: algorithm HFFT–high-order fast-direct solution of the Helmholtz equation publication-title: ACM Trans. Math. Softw. doi: 10.1145/29380.214342 – volume: 19 start-page: 341 year: 1998 end-page: 363 ident: CR16 article-title: ADI methods for cubic spline collocation discretizations of elliptic PDEs publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827595281794 – volume: 21 start-page: 508 year: 1999 end-page: 521 ident: CR13 article-title: Analysis of iterative line spline collocation methods for elliptic partial differential equations publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479896309827 – volume: 28 start-page: 1817 year: 2012 end-page: 1839 ident: CR5 article-title: Modified nodal cubic spline collocation for elliptic equations publication-title: Numer. Methods Partial Differ. Equ. doi: 10.1002/num.20704 – volume: 13 start-page: 631 year: 1992 end-page: 644 ident: CR18 article-title: BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems publication-title: SIAM J. Sci. Stat. Comput. doi: 10.1137/0913035 – volume: 13 start-page: 221 year: 1987 end-page: 234 ident: CR8 article-title: A fourth-order-accurate Fourier method for the Helmholtz equation in three dimensions publication-title: ACM Trans. Math. Softw. doi: 10.1145/29380.29863 – volume: 14 start-page: 715 year: 1993 end-page: 734 ident: CR12 article-title: Iterative line cubic spline collocation methods for elliptic partial differential equations in several dimensions publication-title: SIAM J. Sci. Comput. doi: 10.1137/0914045 – start-page: 201 year: 1994 end-page: 208 ident: CR14 article-title: Fast three-dimensional elliptic solvers on distributed network cluster publication-title: Parallel Computing: Trends and Applications – volume: 24 start-page: 1733 year: 2003 end-page: 1753 ident: CR2 article-title: Matrix decomposition algorithm for modified spline collocation for Helmholtz problems publication-title: SIAM J. Sci. Comput. doi: 10.1137/S106482750139964X – volume: 39 start-page: 28 year: 2009 ident: 9669_CR7 publication-title: J. Sci. Comput. doi: 10.1007/s10915-008-9246-0 – volume-title: A Practical Guide to Splines, Revised Edition, Applied Mathematical Sciences, vol. 27 year: 2001 ident: 9669_CR6 – volume: 13 start-page: 221 year: 1987 ident: 9669_CR8 publication-title: ACM Trans. Math. Softw. doi: 10.1145/29380.29863 – volume: 19 start-page: 341 year: 1998 ident: 9669_CR16 publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827595281794 – volume: 13 start-page: 235 year: 1987 ident: 9669_CR9 publication-title: ACM Trans. Math. Softw. doi: 10.1145/29380.214342 – volume: 13 start-page: 631 year: 1992 ident: 9669_CR18 publication-title: SIAM J. Sci. Stat. Comput. doi: 10.1137/0913035 – start-page: 201 volume-title: Parallel Computing: Trends and Applications year: 1994 ident: 9669_CR14 – ident: 9669_CR15 doi: 10.1007/978-3-0348-9142-4 – volume: 45 start-page: 443 year: 2007 ident: 9669_CR1 publication-title: SIAM J. Numer. Anal. doi: 10.1137/050622833 – volume: 14 start-page: 715 year: 1993 ident: 9669_CR12 publication-title: SIAM J. Sci. Comput. doi: 10.1137/0914045 – ident: 9669_CR17 – volume: 24 start-page: 1733 year: 2003 ident: 9669_CR2 publication-title: SIAM J. Sci. Comput. doi: 10.1137/S106482750139964X – volume: 113 start-page: 249 year: 2000 ident: 9669_CR11 publication-title: Appl. Math. Comput. doi: 10.1016/S0096-3003(99)00085-5 – volume: 28 start-page: 1817 year: 2012 ident: 9669_CR5 publication-title: Numer. Methods Partial Differ. Equ. doi: 10.1002/num.20704 – volume: 143 start-page: 9 year: 2002 ident: 9669_CR10 publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(01)00504-0 – volume: 56 start-page: 253 year: 2011 ident: 9669_CR4 publication-title: Numer. Algorithms doi: 10.1007/s11075-010-9384-y – volume: 21 start-page: 508 year: 1999 ident: 9669_CR13 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479896309827 – volume: 27 start-page: 575 year: 2005 ident: 9669_CR3 publication-title: SIAM J. Sci. Comput. doi: 10.1137/040609793 |
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| SubjectTerms | Algebra Algorithms Boundary conditions Coefficients Collocation Computer Science Cubes Diffusion rate Dirichlet problem Fast Fourier transformations Mathematical analysis Mathematical models Nodes Numeric Computing Numerical Analysis Original Paper Partial differential equations Poisson equation Splines Theory of Computation |
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| Title | Modified nodal cubic spline collocation for three-dimensional variable coefficient second order partial differential equations |
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