References from U. Rüde: Mathematical and Computational Techniques for Multilevel Adaptive Methods

These references are re-published electronically with permission of SIAM.

1

I. ADLER, Zur Spezifikation und Implementierung von finiten Element Netzgeneratoren, Diplomarbeit, Institut für Informatik, TU München, May 1987.

2

O. AXELSSON AND V. BARKER, Finite element solutions of boundary value problems, Academic Press, New York, 1984.

3

I. BABUSKA AND A. AZIZ, On the angle condition in the finite element method, SIAM J. Numer. Anal., 13 (1976), pp. 214-226.

4

I. BABUSKA, A. MILLER, AND M. VOGELIUS, Adaptive methods and error estimation for elliptic problems in structural mechanics, in Adaptive Computational Methods for Partial Differential Equations, I. Babuska, J. Chandra, and J. Flaherty, eds., Society for Industrial and Applied Mathematics, Philadelphia, 1983.

5

I. BABUSKA, B. A. SZABO, AND I. KATZ, The p-version of the finite element method, SIAM J. Numer. Anal., 18 (1981), pp. 515-545.

6

D. BAI AND A. BRANDT, Local mesh refinement multilevel techniques, SIAM J. Sci. Statist. Comput., 8 (1987), pp. 109-134.

7

R. BANK AND M. BENBOURENANE, The hierarchical basis multigrid method for convection-diffusion equations, preprint, Department of Mathematics, University of California at San Diego, 1991.

8

R. BANK, T. DUPONT, AND H. YSERENTANT, The hierarchical basis multigrid method, Numer. Math., 52 (1988), pp. 427-458.

9

R. BANK AND A. WEISER, Some a-posteriori estimators for elliptic partial differential equations, Math. Comp., 44 (1985), pp. 283-301.

10

R. E. BANK, PLTMG: A Software Package for Solving Elliptic Partial Differential Equations, Frontiers in Applied Mathematics, Vol. 7, Society for Industrial and Applied Mathematics, Philadelphia, 1990.

11

E. BäNSCH, Local mesh refinement in 2 and 3 dimensions, IMPACT of Computing in Science and Engineering, 3 (1991), pp. 181-191.

12

P. BASTIAN, Locally refined solution of unsymmetric and nonlinear problems, in Incomplete Decompositions: Proceedings of the Eigth GAMM-Seminar, Notes in Numerical Fluid Mechanics, Vol. 41, Vieweg-Verlag, Braunschweig, 1992, pp. 12-21.

13

F. BAUER AND H. WÖSSNER, Algorithmische Sprache und Programmentwicklung, 2. Auflage, Springer-Verlag, 1984. English translation: Algorithmic Language and Program Development.

14

F. BAUSE AND W. TöLLE, C++ für Programmierer, Vieweg-Verlag, Braunschweig, 1990.

15

O. BESOV, L. KUDRAYAVTSEV, P. LIZORKIN, AND S. NIKOL'SKI, Investigations in the theory of spaces of differentiable functions of several variables, Proceedings of the Steklov Institute of Mathematics, St. Petersburg, Russia, 1990.

16

H. BLUM, Asymptotic error expansion and defect correction in the finite element method, Habilitationsschrift, Universität Heidelberg, 1991.

17

H. BLUM, Q. LIN, AND R. RANNACHER, Asymptotic error expansions and Richardson extrapolation for linear finite elements, Numer. Math., 49 (1986), pp. 11-37.

18

H. BLUM AND R. RANNACHER, Extrapolation techniques for reducing the pollution effect of reentrant corners in the finite element method, Numer. Math., 52 (1988), pp. 539-564.

19

T. BONK AND U. RüDE, Performance analysis and optimization of numerically intensive programs, SFB Bericht 342/26/92 A, Institut für Informatik, TU München, November 1992.

20

F. BORNEMANN AND H. YSERENTANT, A basic norm equivalence for the theory of multilevel methods, Numer. Math., 64 (1993), pp. 455-476.

21

D. BRAESS, Finite Elemente, Springer-Verlag, Berlin, 1992.

22

D. BRAESS AND W. HACKBUSCH, A new convergence proof for the multigrid method including the V-cycle, SIAM J. Numer. Anal., 20 (1983), pp. 967-975.

23

J. BRAMBLE, J. PASCIAK, J. WANG, AND J. XU, Convergence estimates for multigrid algorithms without regularity assumptions, Report BNL-44512, Brookhaven National Laboratory, New York, August 1989.

24

J. BRAMBLE, J. PASCIAK, J. WANG, AND J. XU, Convergence estimates for product iterative methods with applications to domain decomposition and multigrid, Report BNL-44511, Brookhaven National Laboratory, New York, August 1989.

25

J. BRAMBLE, J. PASCIAK, AND J. XU, Parallel multilevel preconditioners, Math. Comp., 31 (1990), pp. 333-390.

26

J. H. BRAMBLE, J. E. PASCIAK, AND J. XU, The analysis of multigrid algorithms with nonnested spaces or noninherited quadratic forms, Math. Comp., 56 (1991), pp. 1-34.

27

A. BRANDT, Multi-level adaptive solutions to boundary value problems, Math. Comp., 31 (1977), pp. 333-390.

28

A. BRANDT, Multigrid techniques: 1984 guide with applications to fluid dynamics, GMD Studien, Vol. 85, 1984.

29

A. BRANDT, Algebraic multigrid theory: The symmetric case, Appl. Math. Comp., 19 (1986), pp. 23-65.

30

A. BRANDT, Rigorous local mode analysis of multigrid, in Preliminary Proceedings of the Fourth Copper Mountain Conference on Multigrid Methods, University of Colorado at Denver, April 9-14, 1989, S. McCormick, ed.

31

A. BRANDT AND D. OPHIR, Gridpack, in Proceedings IFIP Conference on PDE Software, Solderkoping, Sweden, 1983.

32

W. L. BRIGGS, A Multigrid Tutorial, Society for Industrial and Applied Mathematics, Philadelphia, 1987.

33

P. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, New York, London, 1978.

34

W. DAHMEN AND A. KUNOTH, Multilevel preconditioning, Numer. Math., 63 (1992), pp. 315-344.

35

P. DEUFLHARD, P. LEINEN, AND H. YSERENTANT, Concepts of an adaptive hierarchical finite element code, IMPACT of Computing in Science and Engineering, 1 (1989), pp. 3-35.

36

S. DEWHURST AND K. STARK, Programming in C++, Prentice Hall, Englewood Cliffs, NJ, 1989.

37

M. DRYJA AND O. WIDLUND, An additive variant of the Schwarz alternating method for the case of many subregions, Tech. Report 339 and Ultracomputer Note 131, Department of Computer Science, Courant Institute, 1987.

38

M. DRYJA AND O. WIDLUND, Multilevel additive methods for elliptic finite element problems, in Parallel Algorithms for Partial Differential Equations, Proceedings of the Sixth GAMM-Seminar, Kiel, January 19-21, 1990, W. Hackbusch, ed., Vieweg-Verlag, Braunschweig, 1991.

39

A. GEORGE AND W. LIU, Computer Solution of Large Sparse Positive Definite Systems, Prentice Hall, Englewood Cliffs, NJ, 1981.

40

M. GRIEBEL, Zur Lösung von Finite-Differenzen- und Finite-Element-Gleichungen mittels der Hierarchischen-Transformations-Mehrgitter-Methode, SFB Bericht 342/4/90 A, Institut für Informatik, TU München, February 1990.

41

M. GRIEBEL, Multilevel algorithms considered as iterative methods on indefinite systems, SFB Bericht 342/29/91 A, Institut für Informatik, TU München, October 1991; see also Preliminary Proceedings of the Second Copper Mountain Conference on Iterative Methods.

42

M. GRIEBEL, Grid- and point-oriented multilevel algorithms, SFB Bericht 342/14/92 A, Institut für Informatik, TU München, July 1992.

43

W. HACKBUSCH, Multigrid Methods and Applications, Springer-Verlag, Berlin, 1985.

44

W. HACKBUSCH, Theorie und Numerik elliptischer Differentialgleichungen, Teubner Studienbücher, Stuttgart, 1986.

45

P. HEMKER, H. VAN DER MAAREL, AND C. EVERAARS, BASIS: A data structure for adaptive multigrid computations, Report NM-R9014, Department of Numerical Mathematics, Centrum for Wiskunde en Informatica, Amsterdam, August 1990.

46

R. HEMPEL AND H. RITZDORF, The GMD communications library for grid-oriented problems, Arbeitspapiere der GMD 589, Gesellschaft für Mathematik und Datenverarbeitung, St. Augustin, 1991.

47

C. R. JÄNSCH, U. RÜDE, AND K. SCHNEPPER, Macro expansion, a tool for the systematic development of scientific software, Bericht I-8814, Institut für Informatik, TU München, November 1988.

48

H. JOHNEN AND K. SCHERER, On the equivalence of the K-functional and the moduli of continuity and some applications, Lecture Notes in Mathematics 571, Springer-Verlag, New York, 1977, pp. 119-140.

49

P. LEINEN, Ein schneller adaptiver Löser für elliptische Randwertprobleme auf Seriell- und Parallelrechnern, Dissertation, Universität Dortmund, 1990.

50

P. LEINEN AND H. YSERENTANT, Private communication, 1991.

51

M. LEMKE AND D. QUINLAN, P++, a C++ virtual shared grids based programming environment for architecture-independent development of structured grid applications, Arbeitspapiere der GMD 611, Gesellschaft für Mathematik und Datenverarbeitung, St. Augustin, Germany, February 1992.

52

R. LÖHNER AND K. MORGAN, Unstructured multigrid methods, in Multigrid Methods: Special Topics and Applications, Papers presented at the Second European Conference on Multigrid Methods, Cologne, October 1-4, 1985, U. Trottenberg and W. Hackbusch, eds., GMD Studien, Vol. 110, 1986.

53

D. LUENBERGER, Introduction to linear and nonlinear programming, Addison-Wesley, Reading, MA, 1973.

54

G. MARCHUK AND V. SHAIDUROV, Difference Methods and Their Extrapolations, Springer-Verlag, New York, 1983.

55

O. MCBRYAN, P. FREDERICKSON, J. LINDEN, A. SCHÜLLER, K. SOLCHENBACH, K. STüBEN, C.-A. THOLE, AND U. TROTTENBERG, Multigrid methods on parallel computers-a survey of recent developments, IMPACT of Computing in Science and Engineering, 3 (1991), pp. 1-75.

56

S. MCCORMICK, ED., Multigrid Methods, Frontiers in Applied Mathematics, Vol. 3, Society for Industrial and Applied Mathematics, Philadelphia, 1987.

57

S. MCCORMICK, Multilevel Adaptive Methods for Partial Differential Equations, Frontiers in Applied Mathematics, Vol. 6, Society for Industrial and Applied Mathematics, Philadelphia, 1989.

58

S. MCCORMICK, Multilevel Projection Methods for Partial Differential Equations, CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, 1992.

59

S. MCCORMICK AND U. RÜDE, On local refinement higher order methods for elliptic partial differential equations, Internat. J. High Speed Comput., 2 (1990), pp. 311-334; also available as TU-Bericht I-9034, Institut für Informatik, TU München, September 1990.

60

S. MCCORMICK AND J. RUGE, Multigrid methods for variational problems, SIAM J. Numer. Anal., 19 (1982), pp. 924-927.

61

S. MCCORMICK AND J. RUGE, Unigrid for multigrid simulation, Math. Comp., 41 (1983), pp. 43-62.

62

S. MCCORMICK AND J. THOMAS, The fast adaptive composite grid (FAC) method for elliptic equations, Math. Comp., 46 (1986), pp. 439-456.

63

V. MIKULINSKY, Multigrid Treatment of Boundary and Free-Boundary Conditions, Ph.D. thesis, The Weizmann Institute of Science, Rehovot, Israel, 1992.

64

W. MITCHELL, Adaptive refinement for arbitrary finite element spaces with hierarchical bases, J. Comp. Appl. Math., 36 (1991), pp. 65-78.

65

W. MITCHELL, Optimal multilevel iterative methods for adaptive grids, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 146-167; also in Proceedings of the First Copper Mountain Conference on Iterative Methods, April 1-5, 1990, T. Manteuffel, ed.

66

S. NIKOL'SKI, Approximation of Functions of Several Variables and Imbedding Theorems, Springer-Verlag, New York, 1975 (translated from Russian).

67

A. OSTROWSKI, Determinanten mit überwiegender Hauptdiagonale und die absolute Konvergenz von linearen Iterationsprozessen, Comment. Math. Helv., 30 (1956), pp. 175-210.

68

P. OSWALD, On H1-interpolating hierarchical spline bases, Tech. Report N/89/19, Friedrich Schiller Universität, Jena, July 1989.

69

P. OSWALD, On estimates for hierarchic basis representations of finite element functions, Tech. Report N/89/16, Friedrich Schiller Universität, Jena, June 1989.

70

P. OSWALD, On function spaces related to finite element approximation theory, Z. Anal. Anwendungen, 9 (1990), pp. 43-64.

71

P. OSWALD, On the degree of nonlinear spline approximation in Besov-Sobolev spaces, J. Approxim. Theory, 61 (1990), pp. 131-157.

72

P. OSWALD, On discrete norm estimates related to multilevel preconditioners in the finite element method, in Proceedings of International Conference on Constructive Theory of Functions, Varna 1991, Bulgarian Academy of Science, Sofia, K. Ivanov and B. Sendov, 1992, pp. 203-241.

73

P. OSWALD, Preconditioners for discretizations of the biharmonic equation by rectangular finite elements, Forschungsergebnisse Math/91/03, Friedrich Schiller Universität, Jena, November 1991.

74

P. OSWALD, Two remarks on multilevel preconditioners, Forschungsergebnisse Math/91/1, Friedrich Schiller Universität, Jena, 1991.

75

P. OSWALD, Norm equivalencies and multilevel Schwarz preconditioning for variational problems, Forschungsergebnisse Math/92/01, Friedrich Schiller Universität, Jena, January 1992.

76

P. OSWALD, Stable splittings of Sobolev spaces and fast solution of variational problems, Forschungsergebnisse Math/92/05, Friedrich Schiller Universität, Jena, May 1992.

77

L. PAVARINO, Some Schwarz algorithms for the p-version of the finite element method, Tech. Report 614, Department of Computer Science, Courant Institute, New York University, 1992.

78

A. QUARTERONI, Domain decomposition and parallel processing for the numerical solution of partial differential equations, Surv. Math. Ind., 1 (1991), pp. 75-118.

79

H. REGLER AND U. RüDE, Layout optimization with algebraic multigrid methods (AMG), in Proceedings of the Sixth Copper Mountain Conference on Multigrid Methods, Copper Mountain, April 4-9, 1993, Conference Publication, NASA, 1993.

80

M. RIVARA, Algorithms for refining triangular grids suitable for adaptive and multigrid techniques, Internat. J. Numer. Methods Engrg., 20 (1984), pp. 745-756.

81

M. RIVARA, Design and data structure of fully adaptive, multigrid, finite-element software, ACM Trans. Math. Software, 10 (1984), pp. 242-264.

82

R. ROITZSCH, Kaskade user's manual, Tech. Report TR 89-4, Konrad-Zuse-Zentrum für Informationstechnik, Berlin, August 1989.

83

U. RÜDE, Multiple tau-extrapolation for multigrid methods, Bericht I-8701, Institut für Informatik, TU München, January 1987.

84

U. RÜDE, On the accurate computation of singular solutions of Laplace's and Poisson's equation, in Multigrid Methods: Theory, Applications, Supercomputing: Proceedings of the Third Copper Mountain Conference on Multigrid Methods, April 5-10, 1987, S. McCormick, ed., Marcel Dekker, New York, 1988.

85

U. RÜDE, Extrapolation and related techniques for solving elliptic equations, Bericht I-9135, Institut für Informatik, TU München, September 1991.

86

U. RÜDE, Data structures for multilevel adaptive methods and iterative solvers, Bericht I-9217, Institut für Informatik, TU München, May 1992.

87

U. RÜDE, The hierarchical basis extrapolation method, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 307-318; also in Proceedings of the First Copper Mountain Conference on Iterative Methods, April 1-5, 1990, T. Manteuffel, ed.

88

U. RÜDE, On the multilevel adaptive iterative method, in Preliminary Proceedings of the Second Copper Mountain Conference on Iterative Methods, April 9-14, 1992, T. Manteuffel, ed.; SIAM J. Sci. Comput., 15 (1994), to appear.

89

U. RÜDE, Data abstraction techniques for multilevel algorithms, in Proceedings of the GAMM-Seminar on Multigrid Methods, in Gosen, Germany, Sept. 21-25, 1992; Report 5, Institut für Angewandte Analysis und Stochastik, Berlin, 1993. ISSN 0942-9077.

90

U. RÜDE, Extrapolation techniques for constructing higher order finite element methods, Bericht I-9304, Institut für Informatik, TU München, 1993; SIAM J. Numer. Anal., submitted.

91

U. RÜDE, Fully adaptive multigrid methods, SIAM J. Numer. Anal., 30 (1993), pp. 230-248.

92

U. RÜDE AND C. ZENGER, On the treatment of singularities in the finite element method, Bericht I-9220, Institut für Informatik, TU München, August 1992.

93

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94

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95

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96

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97

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98

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99

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100

M. STARK, Spezifikation und Implementierung einer Datenstruktur für dreidimensionale finite Elemente, Diplomarbeit, Institut für Informatik, TU München, May 1989.

101

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102

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103

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104

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105

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106

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107

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108

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109

J. XU, Iterative methods by space decomposition and subspace correction: A unifying approach, Report AM67, Department of Mathematics, Pennsylvania State University, State College, PA 1990.

110

J. XU, A new class of iterative methods for nonselfadjoint or indefinite problems, SIAM J. Numer. Anal., 29 (1992), pp. 303-319.

111

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112

H. YSERENTANT, Two preconditioners based on the multi-level splitting of finite element spaces, Numer. Math., 58 (1990), pp. 163-184.

113

H. YSERENTANT, Hierarchical bases, in Proceedings of the ICIAM 1991, Society for Industrial and Applied Mathematics, 1992.

114

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115

S. ZHANG, Multilevel iterative techniques, Report, Department of Mathematics, Pennsylvania State University, State College, PA, 1988.

116

X. ZHANG, Multilevel additive Schwarz methods, Tech. Report 582, Department of Computer Science, Courant Institute, New York University, 1991.