An efficient algebraic multigrid preconditioner for a fast multipole boundary element method

Computing (Vienna/New York)

Volumn 82, Issue 2-3, 2008, Pages 139-155

  Of, G ^a  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Algebraic multigrid; Boundary element method; Fast multipole method

Indexed keywords

BOOLEAN ALGEBRA; ITERATIVE METHODS; MATRIX ALGEBRA; NUMERICAL ANALYSIS;

ALGEBRAIC MULTIGRID (AMG) METHOD; ALGEBRAIC MULTIGRID (AMG) PRECONDITIONER; BOUNDARY ELEMENTS; CLUSTER STRUCTURES; COARSE GRIDS; FAST MULTIPOLE; FAST MULTIPOLE METHOD (FMM); MULTI GRID; NEAR FIELDS; OPTIMAL COMPLEXITY; PRECONDITIONER; PRECONDITIONING TECHNIQUES; SINGLE LAYERS;

BOUNDARY ELEMENT METHOD;

EID: 47749143241     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00607-008-0002-y     Document Type: Article

References (32)

1. Bebendorf M (2005). Hierarchical LU decomposition-based preconditioners for BEM. Computing 74(3): 225-247
2. Bebendorf M and Rjasanow S (2003). Adaptive low-rank approximation of collocation matrices. Computing 70(1): 1-24
3. Bramble JH, Leyk Z and Pasciak JE (1994). The analysis of multigrid algorithms for pseudodifferential operators of order minus one. Math Comput 63(208): 461-478
4. Bramble JH, Pasciak JE and Xu J (1990). Parallel multilevel preconditioners. Math Comput 55(191): 1-22
5. Dahmen W, Prößdorf S and Schneider R (1993). Wavelet approximation methods for pseudodifferential equations. II. Matrix compression and fast solution. Adv Comput Math 1(3-4): 259-335
6. Funken SA and Stephan EP (1997). The BPX preconditioner for the single layer potential operator. Appl Anal 67(3-4): 327-340
7. Greengard L (1987). The rapid evaluation of potential fields in particle systems. The MIT Press, USA
8. Greengard L and Rokhlin V (1987). A fast algorithm for particle simulations. J Comput Phys 73: 325-348
9. Hackbusch W (1999). A sparse matrix arithmetic based on H-matrices. I. Introduction to H-matricesComputing 62(2): 89-108
10. Hackbusch W, Löhndorf M and Sauter SA (2006). Coarsening of boundary-element spaces. Computing 77(3): 253-273
11. Hackbusch W and Nowak ZP (1989). On the fast matrix multiplication in the boundary element method by panel clustering. Numer Math 54(4): 463-491
12. Heuer N, Stephan EP and Tran T (1998). Multilevel additive Schwarz method for the h-p version of the Galerkin boundary element method. Math Comput 67(222): 501-518
13. Khoromskij BN and Wendland WL (1993). Spectrally equivalent preconditioners for boundary equations in substructuring techniques. East West J Numer Math 1(1): 1-26
14. Langer U and Pusch D (2005). Data-sparse algebraic multigrid methods for large scale boundary element equations. Appl Numer Math 54(3-4): 406-424
15. Langer U, Pusch D (2007) Convergence analysis of geometrical multigrid methods for solving data-sparse boundary element equations. Comput Vis Sci (published online)
16. Langer U, Pusch D and Reitzinger S (2003). Efficient preconditioners for boundary element matrices based on grey-box algebraic multigrid methods. Int J Numer Methods Eng 58(13): 1937-1953
17. Maischak M, Stephan EP and Tran T (2000). Multiplicative Schwarz algorithms for the Galerkin boundary element method. SIAM J Numer Anal 38(4): 1243-1268
18. Nishimura N (2002). Fast multipole accelerated boundary integral equation methods. Appl Mech Rev 55(4): 299-324
19. Of G, Steinbach O and Wendland WL (2005). Applications of a fast multipole Galerkin boundary element method in linear elastostatics. Comput Vis Sci 8: 201-209
20. Of G, Steinbach O and Wendland WL (2006). The fast multipole method for the symmetric boundary integral formulation. IMA J Numer Anal 26: 272-296
21. Perez-Jorda JM and Yang W (1996). A concise redefinition of the solid spherical harmonics and its use in the fast multipole methods. J Chem Phys 104(20): 8003-8006
22. Stephan E (1992). Multigrid solvers and preconditioners for first kind integral equations. Numer Methods Partial Differ Equations 8(5): 443-450
23. Rjasanow S and Steinbach O (2007). The fast solution of boundary integral equations. Mathematical and analytical techniques with applications to engineering. Springer, New York
24. Samarskij AA, Nikolaev ES (1989) Numerical methods for grid equations. Direct methods, vol I. Iterative methods, vol II. Birkhäuser, Basel
25. Sauter S, Schwab C (2004) Randelementmethoden. Analyse, Numerik und Implementierung schneller Algorithmen. Teubner, Stuttgart
26. Schöberl J (1997). NETGEN: an advancing front 2D/3D-mesh generator based on abstract rules. Comput Vis Sci 1(1): 41-52
27. Steinbach O (2003). Artificial multilevel boundary element preconditioners. Proc Appl Math Mech 3: 539-542
28. Steinbach O (2008). Numerical approximation methods for elliptic boundary value problems. Finite and boundary elements. Springer, New York
29. Steinbach O and Wendland WL (1998). The construction of some efficient preconditioners in the boundary element method. Adv Comput Math 9(1-2): 191-216
30. Stephan EP (2000). Multilevel methods for the h-, p- and hp-versions of the boundary element method. J Comput Appl Math 125(1-2): 503-519
31. White CA and Head-Gordon M (1994). Derivation and efficient implementation of the fast multipole method. J Chem Phys 101(8): 6593-6605
32. Yoshida K, Nishimura N and Kobayashi S (2001). Application of fast multipole Galerkin boundary integral equation method to elastostatic crack problems in 3D. Int J Numer Methods Eng 50(3): 525-547