Summary
In this paper, we investigate the effectiveness of hierarchical matrix techniques when used as the linear solver in a certain domain decomposition algorithm. In particular, we provide a direct performance comparison between an algebraic multigrid solver and a hierarchical matrix solver which is based on nested dissection clustering within the software package PLTMG.
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Bank, R. E.: PLTMG: a software package for solving elliptic partial differential equations. Users’ Guide 9.0, Technical Report, University of California, San Diego (2004)
Bank R.E. (2006). Some variants of the Bank–Holst parallel adaptive meshing paradigm. Comput Vis Sci 9(3): 133–144
Bank R.E. and Holst M. (2000). A new paradigm for parallel adaptive meshing algorithms. SIAM J Sci Comput 22(4): 1411–1443 (electronic)
Bank R.E. and Holst M.J. (2003). A new paradigm for parallel adaptive meshing algorithms. SIAM Rev 45(2): 291–323
Bank R.E. and Lu S. (2004). A domain decomposition solver for a parallel adaptive meshing paradigm. SIAM J Sci Comput 26(1): 105–127 (electronic)
Bank R.E. and Smith R.K. (2002). An algebraic multilevel multigraph algorithm. SIAM J Sci Comput 25: 1572–1592
Bank, R. E., Vassilevski, P. S.: Convergence analysis of a domain decomposition paradigm. Numer Math (2006) (submitted)
Bebendorf M. and Hackbusch W. (2003). Numer Math 95(1): 1–28
Börm, S., Grasedyck, L., Hackbusch, W.: Hierarchical matrices. Lecture Note vol. 21, Max Planck Institute for Mathematics in the Sciences (2003)
Brainman I. and Toledo S. (2002). Nested-dissection orderings for sparse LU with partial pivoting (electronic). SIAM J Matrix Anal Appl 23(4): 998–1012
George, A.: Nested dissection of a regular finite element mesh. SIAM J Numer Anal 10, 345–363 (1973). Collection of articles dedicated to the memory of G. E. Forsythe
Grasedyck L. and Hackbusch W. (2003). Computing 70(4): 295–334
Hackbusch W. (1999). Computing 62(2): 89–108
Hackbusch, W., Khoromskij, B. N.: A sparse \({\mathcal{H}}\) -matrix arithmetic: general complexity estimates. J Comput Appl Math 125(1–2), 479–501 (2000). Numerical analysis 2000, vol. VI: Ordinary differential equations and integral equations
Hackbusch W. and Khoromskij B.N. (2000). Computing 64(1): 21–47
Holst, M.: Application of domain decomposition and partition of unity methods in physics and geometry. In: Domain decomposition methods in science and engineering, pp. 63–78 (electronic). National Autonomous University of Mexico, México (2003)
Le Borne, S., Grasedyck, L., Kriemann, R.: Parallel black box domain decomposition based \({\mathcal{H}}\) -LU preconditioning. Math Comp (2005) (submitted)
Le Borne, S., Grasedyck, L., Kriemann, R.: Domain-decomposition based \({\mathcal{H}}\) -LU preconditioners. In: 16th Int Conf on Domain Decomposition Methods. Lecture Notes in Computational Science and Engineering. Springer, New York (forthcoming)
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Ovall, J.S. Hierarchical matrix techniques for a domain decomposition algorithm. Computing 80, 287–297 (2007). https://doi.org/10.1007/s00607-007-0235-1
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DOI: https://doi.org/10.1007/s00607-007-0235-1