Legendre Gauss Spectral Collocation for the Helmholtz Equation on a Rectangle
A spectral collocation method with collocation at the Legendre Gauss points is discussed for solving the Helmholtz equation −Δu+κ(x,y)u=f(x,y) on a rectangle with the solution u subject to inhomogeneous Robin boundary conditions. The convergence analysis of the method is given in the case of u satis...
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| Published in | Numerical algorithms Vol. 36; no. 3; pp. 203 - 227 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer Nature B.V
01.07.2004
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1017-1398 1572-9265 |
| DOI | 10.1023/B:NUMA.0000040056.52424.49 |
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| Abstract | A spectral collocation method with collocation at the Legendre Gauss points is discussed for solving the Helmholtz equation −Δu+κ(x,y)u=f(x,y) on a rectangle with the solution u subject to inhomogeneous Robin boundary conditions. The convergence analysis of the method is given in the case of u satisfying Dirichlet boundary conditions. A matrix decomposition algorithm is developed for the solution of the collocation problem in the case the coefficient κ(x,y) is a constant. This algorithm is then used in conjunction with the preconditioned conjugate gradient method for the solution of the spectral collocation problem with the variable coefficient κ(x,y). |
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| AbstractList | A spectral collocation method with collocation at the Legendre Gauss points is discussed for solving the Helmholtz equation −Δu+κ(x,y)u=f(x,y) on a rectangle with the solution u subject to inhomogeneous Robin boundary conditions. The convergence analysis of the method is given in the case of u satisfying Dirichlet boundary conditions. A matrix decomposition algorithm is developed for the solution of the collocation problem in the case the coefficient κ(x,y) is a constant. This algorithm is then used in conjunction with the preconditioned conjugate gradient method for the solution of the spectral collocation problem with the variable coefficient κ(x,y). |
| Author | Karageorghis, Andreas Bialecki, Bernard |
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| CitedBy_id | crossref_primary_10_1007_s11075_017_0325_x crossref_primary_10_1016_j_camwa_2011_12_050 crossref_primary_10_1016_j_jcp_2010_03_033 crossref_primary_10_1016_j_fraope_2025_100218 crossref_primary_10_1007_s10915_007_9136_x crossref_primary_10_1007_s40324_016_0079_8 crossref_primary_10_1007_s11075_008_9216_5 crossref_primary_10_1016_j_amc_2017_11_024 crossref_primary_10_3846_mma_2023_16408 crossref_primary_10_1137_040609793 crossref_primary_10_1007_s11075_010_9384_y crossref_primary_10_1016_j_amc_2014_06_057 crossref_primary_10_32604_cmc_2022_021899 |
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| References | F. Auteri (5379559_CR2) 1999; 149 5379559_CR4 S.V. Parter (5379559_CR9) 2001; 39 J. Shen (5379559_CR14) 1994; 15 S.V. Parter (5379559_CR10) 2001; 39 C. Canuto (5379559_CR6) 1988 A. Quarteroni (5379559_CR12) 1994 J. Douglas Jr. (5379559_CR8) 1974 M.O. Deville (5379559_CR7) 1990; 11 C. Bernardi (5379559_CR3) 1988; 8 F. Auteri (5379559_CR1) 2003; 185 S.V. Parter (5379559_CR11) 1995; 32 A. Quarteroni (5379559_CR13) 1992; 29 5379559_CR15 C. Canuto (5379559_CR5) 1986; 23 |
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| SubjectTerms | Algorithms Boundary conditions Collocation methods Conjugate gradient method Dirichlet problem Helmholtz equations |
| Title | Legendre Gauss Spectral Collocation for the Helmholtz Equation on a Rectangle |
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