| Title:
|
Complexity of an algorithm for solving saddle-point systems with singular blocks arising in wavelet-Galerkin discretizations (English) |
| Author:
|
Kučera, Radek |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
291-308 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with fast solving of large saddle-point systems arising in wavelet-Galerkin discretizations of separable elliptic PDEs. The periodized orthonormal compactly supported wavelets of the tensor product type together with the fictitious domain method are used. A special structure of matrices makes it possible to utilize the fast Fourier transform that determines the complexity of the algorithm. Numerical experiments confirm theoretical results. (English) |
| Keyword:
|
wavelet-Galerkin discretization |
| Keyword:
|
fictitious domain method |
| Keyword:
|
saddle-point system |
| Keyword:
|
conjugate gradient method |
| Keyword:
|
circulant matrix |
| Keyword:
|
fast Fourier transform |
| Keyword:
|
Kronecker product |
| MSC:
|
65F10 |
| MSC:
|
65N30 |
| MSC:
|
65T50 |
| MSC:
|
65T60 |
| idZBL:
|
Zbl 1099.65150 |
| idMR:
|
MR2133731 |
| DOI:
|
10.1007/s10492-005-0018-y |
| . |
| Date available:
|
2009-09-22T18:22:25Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134607 |
| . |
| Reference:
|
[1] F. Brezzi, M. Fortin: Mixed and Hybrid Finite Element Methods.Springer-Verlag, New York, 1991. MR 1115205 |
| Reference:
|
[2] P. G. Ciarlet: The Finite Element Method for Elliptic Problems.North-Holland, Amsterdam, 1978. Zbl 0383.65058, MR 0520174 |
| Reference:
|
[3] M. Fortin, R. Glowinski: Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems.North-Holland, Amsterdam, 1983. MR 0724072 |
| Reference:
|
[4] I. Daubechies: Ten Lectures on Wavelets.SIAM, Philadelphia, 1992. Zbl 0776.42018, MR 1162107 |
| Reference:
|
[5] R. Glowinski, T. Pan, and J. Periaux: A fictitious domain method for Dirichlet problem and applications.Comput. Methods Appl. Mech. Eng. 111 (1994), 283–303. MR 1259864, 10.1016/0045-7825(94)90135-X |
| Reference:
|
[6] R. Glowinski, T. Pan, R. O. Wells, X. Zhou: Wavelets methods in computational fluid dynamics.In: Proc. Algorithms Trends in Computational Dynamics (1993), M. Y. Hussaini, A. Kumar, and M. D. Salas (eds.), Springer-Verlag, New York, pp. 259–276. MR 1295640 |
| Reference:
|
[7] G. H. Golub, C. F. Van Loan: Matrix Computation.The Johns Hopkins University Press, Baltimore, 1996, 3rd ed. |
| Reference:
|
[8] N. I. M. Gould: On practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem.Math. Program. 32 (1985), 90–99. Zbl 0591.90068, MR 0787745, 10.1007/BF01585660 |
| Reference:
|
[9] R. Kučera: Wavelet solution of elliptic PDEs.In: Proc. Matematyka v Naukach Technicznych i Przyrodniczych (2000), S. Bialas (ed.), AGH Krakow, pp. 55–62. |
| Reference:
|
[10] W. Rudin: Real and Complex Analysis.McGraw-Hill, New York, 1987, 3rd ed. Zbl 0925.00005, MR 0924157 |
| . |
