| Title:
|
Spectral methods for singular perturbation problems (English) |
| Author:
|
Heinrichs, Wilhelm |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
1994 |
| Pages:
|
161-188 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study spectral discretizations for singular perturbation problems. A special technique of stabilization for the spectral method is proposed. Boundary layer problems are accurately solved by a domain decomposition method. An effective iterative method for the solution of spectral systems is proposed. Suitable components for a multigrid method are presented. (English) |
| Keyword:
|
spectral methods |
| Keyword:
|
singular perturbation |
| Keyword:
|
stabilization |
| Keyword:
|
domain decomposition |
| Keyword:
|
iterative solver |
| Keyword:
|
multigrid method |
| MSC:
|
35B25 |
| MSC:
|
35J25 |
| MSC:
|
65F10 |
| MSC:
|
65N12 |
| MSC:
|
65N35 |
| MSC:
|
65N55 |
| idZBL:
|
Zbl 0812.65100 |
| idMR:
|
MR1273631 |
| DOI:
|
10.21136/AM.1994.134251 |
| . |
| Date available:
|
2009-09-22T17:43:38Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134251 |
| . |
| Reference:
|
[1] C. Canuto: Spectral methods and maximum principle, to appear in Math. Comp... MR 0930226 |
| Reference:
|
[2] C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang: Spectral methods in fluid dynamics.Springer-Verlag, New York-Berlin-Heidelberg, 1988. MR 0917480 |
| Reference:
|
[3] J. Doerfer: Mehrgitterverfahren bei singulaeren Stoerungen.Master Thesis, Duesseldorf, 1986. |
| Reference:
|
[4] J. Doerfer and K. Witsch: Stable second order discretization of singular perturbation problems using a hybrid technique.(to appear). |
| Reference:
|
[5] D. Funaro: Computing with spectral matrices.(to appear). |
| Reference:
|
[6] D. Funaro, A. Quarteroni and P. Zanolli: An iterative procedure with interface relaxation for domain decomposition methods.SIAM J. Num. Anal. 25 (1988). MR 0972451, 10.1137/0725069 |
| Reference:
|
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| Reference:
|
[8] W. Heinrichs: Line relaxation for spectral multigrid methods.J. Comp. Phys. 77 (1988), 166–182. Zbl 0649.65055, MR 0954308, 10.1016/0021-9991(88)90161-1 |
| Reference:
|
[9] W. Heinrichs: Multigrid methods for combined finite difference and Fourier problems.J. Comp. Phys. 78 (1988), 424–436. Zbl 0657.65118, MR 0965660, 10.1016/0021-9991(88)90058-7 |
| Reference:
|
[10] T. Meis, U. Markowitz: Numerische Behandlung partieller Differentialgleichungen.Springer-Verlag, Berlin-Heidelberg-New York, 1978. MR 0513829 |
| Reference:
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[11] S.A. Orszag: Spectral methods in complex geometries.J. Comp. Phys. 37 (1980), 70–92. MR 0584322, 10.1016/0021-9991(80)90005-4 |
| Reference:
|
[12] H. Yserentant: Die Mehrstellenformeln für den Laplaceoperator.Num. Math. 34 (1980), 171–187. MR 0566680, 10.1007/BF01396058 |
| Reference:
|
[13] T.A. Zang, Y.S. Wong and M.Y. Hussaini: Spectral multigrid methods for elliptic equations I.J. Comp. Phys. 48 (1982), 485–501. MR 0755459, 10.1016/0021-9991(82)90063-8 |
| Reference:
|
[14] T.A. Zang, Y.S. Wong and M.Y. Hussaini: Spectral multigrid methods for elliptic equations II.J. Comp. Phys. 54 (1984), 489–507. MR 0755456, 10.1016/0021-9991(84)90129-3 |
| . |
