Fast matrix-vector multiplication in the sparse-grid Galerkin method

Journal of Scientific Computing

Volumn 47, Issue 3, 2011, Pages 328-346

  Zeiser, Andreas ^a  

^a NONE

Author keywords

Fast algorithms; Linear scaling; Multilevel methods; Sparse grid; Unidirectional principle

Indexed keywords

FAST ALGORITHMS; LINEAR SCALING; MULTILEVEL METHOD; SPARSE GRID; UNIDIRECTIONAL PRINCIPLE;

ALGORITHMS; GALERKIN METHODS; PARTIAL DIFFERENTIAL EQUATIONS;

MATRIX ALGEBRA;

EID: 79959534906     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-010-9438-2     Document Type: Article

References (13)

1. Balder, R., Zenger, C.: The solution of multidimensional real Helmholtz equations on sparse grids. SIAM J. Sci. Comput. 17(3), 631-646 (1996) (Pubitemid 126621171)
2. Bungartz, H.J.: Dünne Gitter und deren Anwendung bei der adaptiven Lösung der dreidimensionalen Poisson-Gleichung. Ph.D. thesis, TU München (1992)
3. Bungartz, H.J.: A multigrid algorithm for higher order finite elements on sparse grids. ETNA Electron. Trans. Numer. Anal. 6, 63-77 (1997)
4. Bungartz, H.J.: Finite elements of higher order on sparse grids. Habilitationsschrift, Fakultät für Informatik, TU München (1998)
5. Bungartz, H.J., Griebel, M.: Sparse grids. Acta Numer. 13, 147-269 (2004) (Pubitemid 38773594)
6. Chernov, A., Schwab, C.: Sparse p-version BEM for first kind boundary integral equations with random loading. Appl. Numer. Math. 59(11), 2698-2712 (2009). doi:10.1016/j.apnum.2008.12.023
7. Griebel, M., Oeltz, D.: A sparse grid space-time discretization scheme for parabolic problems. Computing 81(1), 1-34 (2007) (Pubitemid 351168840)
8. Harbrecht, H., Schneider, R., Schwab, C.: Multilevel frames for sparse tensor product spaces. Numer. Math. 110(2), 199-220 (2008)
9. Niedermeier, A.: Implementational aspects of prewavelet sparse grid methods. In: Lai, C.H., Bjoerstad, P., Cross, M., Widlund, O. (eds.) Eleventh International Conference of Domain Decomposition Methods (1999)
10. Schwab, C., Todor, R.A.: Sparse finite elements for elliptic problems with stochastic loading. Numer. Math. 95(4), 707-734 (2003) (Pubitemid 37364569)
11. Weidmann, J.: Linear Operators in Hilbert Spaces. Springer, New York (1980)
12. Yserentant, H.: On the multi-level splitting of finite element spaces. Numer. Math. 49, 379-412 (1986)
13. Zenger, C.: Sparse grids. In: Hachbusch, W. (ed.) Parallel Algorithms for Partial Differential Equations. Notes on Numerical Fluid Mechanics, vol. 31, pp. 241-251. Vieweg, Wiesbaden (1990)