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Domain-decomposition Based -LU Preconditioners

  • Conference paper

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE,volume 55)


Hierarchical matrices (in short: ℌ -matrices) have first been introduced in 1998 [7] and since then have entered into a wide range of applications. They provide a format for the data-sparse representation of fully populated matrices.


  • Domain Decomposition
  • Cluster Tree
  • Domain Decomposition Method
  • Index Cluster
  • Interior Boundary

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  1. S. L. Borne, Hierarchical matrices for convection-dominated problems, in Proceedings of the 15th international conference on Domain Decomposition Methods, R. Kornhuber, R. H. W. Hoppe, J. Péeriaux, O. Pironneau, O. B. Widlund, and J. Xu, eds., vol. 40 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2004, pp. 631–638.

    Google Scholar 

  2. S. L. Borne and L. Grasedyck, H -matrix preconditioners in convectiondominated problems, SIAM J. Mat. Anal., 27 (2006), pp. 1172–1183.

    CrossRef  MATH  Google Scholar 

  3. I. Brainman and S. Toledo, Nested-dissection orderings for sparse LU with partial pivoting, SIAM J. Mat. Anal. Appl., 23 (2002), pp. 998–1012.

    CrossRef  MATH  Google Scholar 

  4. A. George, Nested dissection of a regular finite element mesh, SIAMJ. Numer. Anal., 10 (1973), pp. 345–363.

    CrossRef  MATH  Google Scholar 

  5. L. Grasedyck and W. Hackbusch, Construction and arithmetics of calH - matrices, Computing, 70 (2003), pp. 295–334.

    CrossRef  MATH  Google Scholar 

  6. L. Grasedyck, W. Hackbusch, and S. L. Borne, Adaptive geometrically balanced clustering of H - matrices, Computing, 73 (2004), pp. 1–23.

    CrossRef  MATH  Google Scholar 

  7. W. Hackbusch, A sparse matrix arithmetic based on H -matrices. Part I: Introduction to H -matrices, Computing, 62 (1999), pp. 89–108.

    CrossRef  MATH  Google Scholar 

  8. W. Hackbusch, Direct domain decomposition using the hierarchical matrix technique, in Fourteenth International Conference on Domain Decomposition Methods, I. Herrera, D. E. Keyes, O. B. Widlund, and R. Yates, eds.,, 2003, pp. 39–50.

    Google Scholar 

  9. W. Hackbusch and B. Khoromskij, A sparse H -matrix arithmetic. Part II: Application to multi-dimensional problems, Computing, 64 (2000), pp. 21–47.

    MATH  Google Scholar 

  10. W. Hackbusch, B. N. Khoromskij, and R. Kriemann, Hierarchical matrices based on a weak admissibility criterion, Computing, 73 (2004), pp. 207–243.

    CrossRef  MATH  Google Scholar 

  11. B. Hendrickson and E. Rothberg, Improving the run time and quality of nested dissection ordering, SIAM J. Sci. Comput., 20 (1998), pp. 468–489.

    CrossRef  Google Scholar 

  12. R. Kriemann, Parallel H -matrix arithmetics on shared memory systems, Computing, 74 (2005), pp. 273–297.

    CrossRef  MATH  Google Scholar 

  13. M. Lintner, The eigenvalue problem for the 2D laplacian in H -matrix arithmetic and application to the heat and wave equation, Computing, 72 (2004), pp. 293–323.

    CrossRef  MATH  Google Scholar 

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Le Borne, S., Grasedyck, L., Kriemann, R. (2007). Domain-decomposition Based -LU Preconditioners. In: Widlund, O.B., Keyes, D.E. (eds) Domain Decomposition Methods in Science and Engineering XVI. Lecture Notes in Computational Science and Engineering, vol 55. Springer, Berlin, Heidelberg.

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