-
1
-
-
2342617546
-
An odyssey into local refinement and multilevel preconditioning III: implementation and numerical experiments
-
Aksoylu B., Bond S., Holst M.: An odyssey into local refinement and multilevel preconditioning III: implementation and numerical experiments. SIAM J. Sci. Comput. 25(2), 478-498 (2003).
-
(2003)
SIAM J. Sci. Comput.
, vol.25
, Issue.2
, pp. 478-498
-
-
Aksoylu, B.1
Bond, S.2
Holst, M.3
-
2
-
-
34547323661
-
Optimality of multilevel preconditioners for local mesh refinement in three dimensions
-
Aksoylu B., Holst M.: Optimality of multilevel preconditioners for local mesh refinement in three dimensions. SIAM J. Numer. Anal. 44(3), 1005-1025 (2006).
-
(2006)
SIAM J. Numer. Anal.
, vol.44
, Issue.3
, pp. 1005-1025
-
-
Aksoylu, B.1
Holst, M.2
-
3
-
-
0035075413
-
Locally adapted tetrahedral meshes using bisection
-
Arnold D. N., Mukherjee A., Pouly L.: Locally adapted tetrahedral meshes using bisection. SIAM J. Sci. Comput. 22(2), 431-448 (2000).
-
(2000)
SIAM J. Sci. Comput.
, vol.22
, Issue.2
, pp. 431-448
-
-
Arnold, D.N.1
Mukherjee, A.2
Pouly, L.3
-
4
-
-
0000845335
-
Local mesh refinement multilevel techniques
-
Bai D., Brandt A.: Local mesh refinement multilevel techniques. SIAM J. Sci. Stat. Comput. 8, 109-134 (1987).
-
(1987)
SIAM J. Sci. Stat. Comput.
, vol.8
, pp. 109-134
-
-
Bai, D.1
Brandt, A.2
-
6
-
-
0001377512
-
The hierarchical basis multigrid method
-
Bank R. E., Dupont T., Yserentant H.: The hierarchical basis multigrid method. Numer. Math. 52, 427-458 (1988).
-
(1988)
Numer. Math.
, vol.52
, pp. 427-458
-
-
Bank, R.E.1
Dupont, T.2
Yserentant, H.3
-
7
-
-
0002641609
-
Refinement algorithms and data structures for regular local mesh refinement
-
IMACS/North-Holland Publishing Company, Amsterdam
-
Bank, R. E., Sherman, A. H., Weiser, A.: Refinement algorithms and data structures for regular local mesh refinement. In: Scientific Computing, pp. 3-17. IMACS/North-Holland Publishing Company, Amsterdam (1983).
-
(1983)
Scientific Computing
, pp. 3-17
-
-
Bank, R.E.1
Sherman, A.H.2
Weiser, A.3
-
8
-
-
34250882899
-
Local mesh refinement in 2 and 3 dimensions
-
Bänsch E.: Local mesh refinement in 2 and 3 dimensions. Impact Comput. Sci. Eng. 3, 181-191 (1991).
-
(1991)
Impact Comput. Sci. Eng.
, vol.3
, pp. 181-191
-
-
Bänsch, E.1
-
9
-
-
0032762032
-
Efficient algorithms for Petersen's matching theorem
-
Biedl, T. C., Bose, P, Demaine, E. D., Lubiw, A.: Efficient algorithms for Petersen's matching theorem. In: Symposium on Discrete Algorithms, pp. 130-139 (1999).
-
(1999)
Symposium on Discrete Algorithms
, pp. 130-139
-
-
Biedl, T.C.1
Bose, P.2
Demaine, E.D.3
Lubiw, A.4
-
10
-
-
2442452617
-
Adaptive finite element methods with convergence rates
-
Binev P., Dahmen W., DeVore R.: Adaptive finite element methods with convergence rates. Numer. Math. 97(2), 219-268 (2004).
-
(2004)
Numer. Math.
, vol.97
, Issue.2
, pp. 219-268
-
-
Binev, P.1
Dahmen, W.2
Devore, R.3
-
12
-
-
0001791187
-
An adaptive multilevel approach to parabolic equations. III. 2D error estimation and multilevel preconditioning
-
Bornemann F. A.: An adaptive multilevel approach to parabolic equations. III. 2D error estimation and multilevel preconditioning. Impact Comput. Sci. Eng. 4(1), 1-45 (1992).
-
(1992)
Impact Comput. Sci. Eng.
, vol.4
, Issue.1
, pp. 1-45
-
-
Bornemann, F.A.1
-
13
-
-
21144473187
-
A basic norm equivalence for the theory of multilevel methods
-
Bornemann F. A., Yserentant H.: A basic norm equivalence for the theory of multilevel methods. Numer. Math. 64, 455-476 (1993).
-
(1993)
Numer. Math.
, vol.64
, pp. 455-476
-
-
Bornemann, F.A.1
Yserentant, H.2
-
14
-
-
84968468806
-
New estimates for multigrid algorithms including the V-cycle
-
Bramble J. H., Pasciak J. E.: New estimates for multigrid algorithms including the V-cycle. Math. Comput. 60, 447-471 (1993).
-
(1993)
Math. Comput.
, vol.60
, pp. 447-471
-
-
Bramble, J.H.1
Pasciak, J.E.2
-
15
-
-
84966234195
-
Parallel multilevel preconditioners
-
Bramble J. H., Pasciak J. E., Xu J.: Parallel multilevel preconditioners. Math. Comput. 55(191), 1-22 (1990).
-
(1990)
Math. Comput.
, vol.55
, Issue.191
, pp. 1-22
-
-
Bramble, J.H.1
Pasciak, J.E.2
Xu, J.3
-
16
-
-
67649463901
-
The analysis of multigrid methods
-
North-Holland, Amsterdam
-
Bramble, J. H., Zhang, X.: The analysis of multigrid methods. In: Handbook of Numerical Analysis, vol. VII, pp. 173-415. North-Holland, Amsterdam (2000).
-
(2000)
Handbook of Numerical Analysis
, vol.VII
, pp. 173-415
-
-
Bramble, J.H.1
Zhang, X.2
-
17
-
-
84966233568
-
Multi-level adaptive solutions to boundary-value problems
-
Brandt A.: Multi-level adaptive solutions to boundary-value problems. Math. Comput. 31, 333-390 (1977).
-
(1977)
Math. Comput.
, vol.31
, pp. 333-390
-
-
Brandt, A.1
-
18
-
-
54249162100
-
Quasi-optimal convergence rate for an adaptive finite element method
-
Cascón J. M., Kreuzer C., Nochetto R. H., Siebert K. G.: Quasi-optimal convergence rate for an adaptive finite element method. SIAM J. Numer. Anal. 46(5), 2524-2550 (2008).
-
(2008)
SIAM J. Numer. Anal.
, vol.46
, Issue.5
, pp. 2524-2550
-
-
Cascón, J.M.1
Kreuzer, C.2
Nochetto, R.H.3
Siebert, K.G.4
-
21
-
-
84855214782
-
-
(submitted)
-
Chen, L., Holst, M., Xu, J., Zhu, Y.: Local multilevel preconditioners for elliptic equations with jump coefficients on bisection grids (2010, submitted).
-
(2010)
Local multilevel preconditioners for elliptic equations with jump coefficients on bisection grids
-
-
Chen, L.1
Holst, M.2
Xu, J.3
Zhu, Y.4
-
22
-
-
78650181994
-
A coarsening algorithm on adaptive grids by newest vertex bisection and its applications
-
Chen L., Zhang C.-S.: A coarsening algorithm on adaptive grids by newest vertex bisection and its applications. J. Comput. Math. 28(6), 767-789 (2010).
-
(2010)
J. Comput. Math.
, vol.28
, Issue.6
, pp. 767-789
-
-
Chen, L.1
Zhang, C.-S.2
-
23
-
-
78651581893
-
New estimates for the rate of convergence of the method of subspace corrections
-
Cho D., Xu J., Zikatanov L.: New estimates for the rate of convergence of the method of subspace corrections. Numer. Math. Theor. Meth. Appl. 1, 44-56 (2008).
-
(2008)
Numer. Math. Theor. Meth. Appl.
, vol.1
, pp. 44-56
-
-
Cho, D.1
Xu, J.2
Zikatanov, L.3
-
24
-
-
33845592412
-
Multilevel preconditioning
-
Dahmen W., Kunoth A.: Multilevel preconditioning. Numer. Math. 63, 315-344 (1992).
-
(1992)
Numer. Math.
, vol.63
, pp. 315-344
-
-
Dahmen, W.1
Kunoth, A.2
-
26
-
-
1542639888
-
A convergent adaptive algorithm for Poisson's equation
-
Dörfler W.: A convergent adaptive algorithm for Poisson's equation. SIAM J. Numer. Anal. 33, 1106-1124 (1996).
-
(1996)
SIAM J. Numer. Anal.
, vol.33
, pp. 1106-1124
-
-
Dörfler, W.1
-
27
-
-
0032314774
-
Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences
-
Also as Proceedings Large-Scale Scientific Computations of Engineering and Environmental Problems, 7 June-11 June, 1997, Varna, Bulgaria, Notes on Numerical Fluid Mechanics 62, Vieweg-Verlag, Braunschweig, M. Griebel, O. Iliev, S. Margenov and P. Vassilevski (eds.)
-
Griebel, M.: Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences. Computing 61(2), 151-179 (1998). Also as Proceedings Large-Scale Scientific Computations of Engineering and Environmental Problems, 7 June-11 June, 1997, Varna, Bulgaria, Notes on Numerical Fluid Mechanics 62, Vieweg-Verlag, Braunschweig, M. Griebel, O. Iliev, S. Margenov and P. Vassilevski (eds.).
-
(1998)
Computing
, vol.61
, Issue.2
, pp. 151-179
-
-
Griebel, M.1
-
28
-
-
0242503926
-
On additive Schwarz preconditioners for sparse grid discretization
-
Griebel M., Oswald P.: On additive Schwarz preconditioners for sparse grid discretization. Numer. Math. 66, 449-464 (1994).
-
(1994)
Numer. Math.
, vol.66
, pp. 449-464
-
-
Griebel, M.1
Oswald, P.2
-
29
-
-
21844511143
-
On the abstract theory of additive and multiplicative Schwarz methods
-
Griebel M., Oswald P.: On the abstract theory of additive and multiplicative Schwarz methods. Numer. Math. 70, 163-180 (1995).
-
(1995)
Numer. Math.
, vol.70
, pp. 163-180
-
-
Griebel, M.1
Oswald, P.2
-
30
-
-
0033890867
-
Parallel adaptive subspace correction schemes with applications to elasticity
-
Griebel M., Zumbusch G.: Parallel adaptive subspace correction schemes with applications to elasticity. Comput. Methods Appl. Mech. Eng. 184(2-4), 303-332 (2000).
-
(2000)
Comput. Methods Appl. Mech. Eng.
, vol.184
, Issue.2-4
, pp. 303-332
-
-
Griebel, M.1
Zumbusch, G.2
-
31
-
-
70249144702
-
Local Multigrid in H(curl)
-
Hiptmair R., Zheng W.: Local Multigrid in H(curl). J. Comput. Math. 27(5), 573-603 (2009).
-
(2009)
J. Comput. Math.
, vol.27
, Issue.5
, pp. 573-603
-
-
Hiptmair, R.1
Zheng, W.2
-
32
-
-
0000947789
-
A recursive approach to local mesh refinement in two and three dimensions
-
Kossaczký I.: A recursive approach to local mesh refinement in two and three dimensions. J. Comput. Math. 55, 275-288 (1994).
-
(1994)
J. Comput. Math.
, vol.55
, pp. 275-288
-
-
Kossaczký, I.1
-
33
-
-
0000430187
-
Local bisection refinement for n-simplicial grids generated by reflection
-
Maubach J.: Local bisection refinement for n-simplicial grids generated by reflection. SIAM J. Sci. Comput. 16(1), 210-227 (1995).
-
(1995)
SIAM J. Sci. Comput.
, vol.16
, Issue.1
, pp. 210-227
-
-
Maubach, J.1
-
34
-
-
0002514884
-
Fast adaptive composite grid (FAC) methods: Theory for the variational case
-
(Oberwolfach, 1983), Comput. Suppl., Springer, Vienna
-
McCormick, S.: Fast adaptive composite grid (FAC) methods: theory for the variational case. In: Defect Correction Methods (Oberwolfach, 1983), volume 5 of Comput. Suppl., pp. 115-121. Springer, Vienna (1984).
-
(1984)
Defect Correction Methods
, vol.5
, pp. 115-121
-
-
McCormick, S.1
-
35
-
-
84966244637
-
The fast adaptive composite grid (FAC) method for elliptic equations
-
McCormick S. F., Thomas J. W.: The fast adaptive composite grid (FAC) method for elliptic equations. Math. Comput. 46, 439-456 (1986).
-
(1986)
Math. Comput.
, vol.46
, pp. 439-456
-
-
McCormick, S.F.1
Thomas, J.W.2
-
36
-
-
33644998367
-
Convergence of adaptive finite element methods for general second order linear elliptic PDE
-
Mekchay K., Nochetto R. H.: Convergence of adaptive finite element methods for general second order linear elliptic PDE. SIAM J. Numer. Anal. 43(5), 1803-1827 (2005).
-
(2005)
SIAM J. Numer. Anal.
, vol.43
, Issue.5
, pp. 1803-1827
-
-
Mekchay, K.1
Nochetto, R.H.2
-
38
-
-
0024883616
-
A comparison of adaptive refinement techniques for elliptic problems
-
Mitchell W. F.: A comparison of adaptive refinement techniques for elliptic problems. ACM Trans. Math. Softw. 15(4), 326-347 (1989).
-
(1989)
ACM Trans. Math. Softw.
, vol.15
, Issue.4
, pp. 326-347
-
-
Mitchell, W.F.1
-
39
-
-
0001721512
-
Optimal multilevel iterative methods for adaptive grids
-
Mitchell W. F.: Optimal multilevel iterative methods for adaptive grids. SIAM J. Sci. Stat. Comput. 13, 146-167 (1992).
-
(1992)
SIAM J. Sci. Stat. Comput.
, vol.13
, pp. 146-167
-
-
Mitchell, W.F.1
-
40
-
-
0034447334
-
Data oscillation and convergence of adaptive FEM
-
Morin P., Nochetto R. H., Siebert K. G.: Data oscillation and convergence of adaptive FEM. SIAM J. Numer. Anal. 38(2), 466-488 (2000).
-
(2000)
SIAM J. Numer. Anal.
, vol.38
, Issue.2
, pp. 466-488
-
-
Morin, P.1
Nochetto, R.H.2
Siebert, K.G.3
-
41
-
-
0036959161
-
Convergence of adaptive finite element methods
-
Morin P., Nochetto R. H., Siebert K. G.: Convergence of adaptive finite element methods. SIAM Rev. 44(4), 631-658 (2002).
-
(2002)
SIAM Rev.
, vol.44
, Issue.4
, pp. 631-658
-
-
Morin, P.1
Nochetto, R.H.2
Siebert, K.G.3
-
42
-
-
84892792498
-
Theory of adaptive finite element methods: an introduction
-
R. A. DeVore and A. Kunoth (Eds.), Berlin: Springer
-
Nochetto R. H., Siebert K. G., Veeser A.: Theory of adaptive finite element methods: an introduction. In: DeVore, R. A., Kunoth, A. (eds) Multiscale, Nonlinear and Adaptive Approximation, Springer, Berlin (2009).
-
(2009)
Multiscale, Nonlinear and Adaptive Approximation
-
-
Nochetto, R.H.1
Siebert, K.G.2
Veeser, A.3
-
43
-
-
0042513456
-
Norm equivalencies and multilevel Schwarz preconditioning for variational problems
-
Fak. Math. Informatik, FSU Jena
-
Oswald, P.: Norm equivalencies and multilevel Schwarz preconditioning for variational problems. Forschungsergebnisse Math-1-92, Fak. Math. Informatik, FSU Jena (1992).
-
(1992)
Forschungsergebnisse Math-1-92
-
-
Oswald, P.1
-
44
-
-
0002427932
-
On discrete norm estimates related to multilevel preconditioners in the finite element method
-
Proc. Int. Conf. Varna 1991, Sofia. Bulg. Acad. Sci
-
Oswald, P.: On discrete norm estimates related to multilevel preconditioners in the finite element method. In: Constructive Theory of Functions, Proc. Int. Conf. Varna 1991, pp. 203-214, Sofia. Bulg. Acad. Sci. (1992).
-
(1992)
Constructive Theory of Functions
, pp. 203-214
-
-
Oswald, P.1
-
45
-
-
0004139365
-
Multilevel Finite Element Approximation, Theory and Applications
-
Stuttgart: Teubner Verlag
-
Oswald P.: Multilevel Finite Element Approximation, Theory and Applications. Teubner Skripten zur Numerik. Teubner Verlag, Stuttgart (1994).
-
(1994)
Teubner Skripten Zur Numerik
-
-
Oswald, P.1
-
46
-
-
0033907129
-
Local refinement of simplicial grids based on the skeleton
-
Plaza A., Carey G. F.: Local refinement of simplicial grids based on the skeleton. Appl. Numer. Math. 32(2), 195-218 (2000).
-
(2000)
Appl. Numer. Math.
, vol.32
, Issue.2
, pp. 195-218
-
-
Plaza, A.1
Carey, G.F.2
-
47
-
-
0021488801
-
Design and data structure for fully adaptive, multigrid finite element software
-
Rivara M. C.: Design and data structure for fully adaptive, multigrid finite element software. ACM Trans. Math. Soft. 10, 242-264 (1984).
-
(1984)
ACM Trans. Math. Soft.
, vol.10
, pp. 242-264
-
-
Rivara, M.C.1
-
48
-
-
0021452023
-
Mesh refinement processes based on the generalized bisection of simplices
-
Rivara M. C.: Mesh refinement processes based on the generalized bisection of simplices. SIAM J. Numer. Anal. 21, 604-613 (1984).
-
(1984)
SIAM J. Numer. Anal.
, vol.21
, pp. 604-613
-
-
Rivara, M.C.1
-
49
-
-
27144549033
-
Design of adaptive finite element software: the finite element toolbox ALBERTA
-
Springer, Berlin, The finite element toolbox ALBERTA, With 1 CD-ROM (Unix/Linux)
-
Schmidt, A., Siebert, K. G.: Design of adaptive finite element software: the finite element toolbox ALBERTA. In: Lecture Notes in Computational Science and Engineering, vol. 42. Springer, Berlin (2005). The finite element toolbox ALBERTA, With 1 CD-ROM (Unix/Linux).
-
(2005)
Lecture Notes in Computational Science and Engineering
, vol.42
-
-
Schmidt, A.1
Siebert, K.G.2
-
50
-
-
84966200902
-
Finite element interpolation of nonsmooth functions satisfying boundary conditions
-
Scott R., Zhang S.: Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comput. 54, 483-493 (1990).
-
(1990)
Math. Comput.
, vol.54
, pp. 483-493
-
-
Scott, R.1
Zhang, S.2
-
52
-
-
0032390114
-
Stable three-point wavelet bases on general meshes
-
Stevenson R.: Stable three-point wavelet bases on general meshes. Numer. Math. 80(1), 131-158 (1998).
-
(1998)
Numer. Math.
, vol.80
, Issue.1
, pp. 131-158
-
-
Stevenson, R.1
-
53
-
-
34250183086
-
Optimality of a standard adaptive finite element method
-
Stevenson R.: Optimality of a standard adaptive finite element method. Found. Comput. Math. 7(2), 245-269 (2007).
-
(2007)
Found. Comput. Math.
, vol.7
, Issue.2
, pp. 245-269
-
-
Stevenson, R.1
-
54
-
-
38849110048
-
The completion of locally refined simplicial partitions created by bisection
-
Stevenson R.: The completion of locally refined simplicial partitions created by bisection. Math. Comput. 77, 227-241 (2008).
-
(2008)
Math. Comput.
, vol.77
, pp. 227-241
-
-
Stevenson, R.1
-
55
-
-
0031374455
-
An algorithm for adaptive mesh refinement in n dimensions
-
Traxler C. T.: An algorithm for adaptive mesh refinement in n dimensions. Computing 59(2), 115-137 (1997).
-
(1997)
Computing
, vol.59
, Issue.2
, pp. 115-137
-
-
Traxler, C.T.1
-
56
-
-
0031516197
-
Stabilizing the hierarchical basis by approximate wavelets, I: theory
-
Vassilevski P. S., Wang J.: Stabilizing the hierarchical basis by approximate wavelets, I: theory. Numer. Linear Alg. Appl. 4(2), 103-126 (1997).
-
(1997)
Numer. Linear Alg. Appl.
, vol.4
, Issue.2
, pp. 103-126
-
-
Vassilevski, P.S.1
Wang, J.2
-
57
-
-
0032228615
-
Stabilizing the hierarchical basis by approximate wavelets II: implementation and numerical results
-
Vassilevski P. S., Wang J.: Stabilizing the hierarchical basis by approximate wavelets II: implementation and numerical results. SIAM J. Sci. Comput. 20(2), 490-514 (1998).
-
(1998)
SIAM J. Sci. Comput.
, vol.20
, Issue.2
, pp. 490-514
-
-
Vassilevski, P.S.1
Wang, J.2
-
59
-
-
0026995615
-
Some Schwarz methods for symmetric and nonsymmetric elliptic problems
-
In: Keyes, D. E., Chan, T. F., Meurant, G. A., Scroggs, J. S., Voigt, R. G. (eds.)
-
Widlund, O. B.: Some Schwarz methods for symmetric and nonsymmetric elliptic problems. In: Keyes, D. E., Chan, T. F., Meurant, G. A., Scroggs, J. S., Voigt, R. G. (eds.) Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, pp. 19-36. SIAM, Philadelphia (1992).
-
(1992)
Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia
, pp. 19-36
-
-
Widlund, O.B.1
-
60
-
-
33845438715
-
Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems
-
Wu H., Chen Z.: Uniform convergence of multigrid V-cycle on adaptively refined finite element meshes for second order elliptic problems. Sci. China: Ser. A Math. 49(1), 1-28 (2006).
-
(2006)
Sci. China: Ser. A Math.
, vol.49
, Issue.1
, pp. 1-28
-
-
Wu, H.1
Chen, Z.2
-
61
-
-
0000570696
-
Iterative methods by space decomposition and subspace correction
-
Xu J.: Iterative methods by space decomposition and subspace correction. SIAM Rev. 34, 581-613 (1992).
-
(1992)
SIAM Rev.
, vol.34
, pp. 581-613
-
-
Xu, J.1
-
62
-
-
0030398920
-
The auxiliary space method and optimal multigrid preconditioning techniques for unstructured meshes
-
Xu J.: The auxiliary space method and optimal multigrid preconditioning techniques for unstructured meshes. Computing 56, 215-235 (1996).
-
(1996)
Computing
, vol.56
, pp. 215-235
-
-
Xu, J.1
-
63
-
-
2942528114
-
An introduction to multigrid convergence theory
-
R. Chan, T. Chan, and G. Golub (Eds.), Berlin: Springer
-
Xu J.: An introduction to multigrid convergence theory. In: Chan, R., Chan, T., Golub, G. (eds) Iterative Methods in Scientific Computing, Springer, Berlin (1997).
-
(1997)
Iterative Methods in Scientific Computing
-
-
Xu, J.1
-
64
-
-
0036016141
-
The method of alternating projections and the method of subspace corrections in Hilbert space
-
Xu J., Zikatanov L.: The method of alternating projections and the method of subspace corrections in Hilbert space. J. Am. Math. Soc. 15, 573-597 (2002).
-
(2002)
J. Am. Math. Soc.
, vol.15
, pp. 573-597
-
-
Xu, J.1
Zikatanov, L.2
-
65
-
-
34250126304
-
On the multi-level splitting of finite element spaces
-
Yserentant H.: On the multi-level splitting of finite element spaces. Numer. Math. 49, 379-412 (1986).
-
(1986)
Numer. Math.
, vol.49
, pp. 379-412
-
-
Yserentant, H.1
-
66
-
-
0000760561
-
Two preconditioners based on the multi-level splitting of finite element spaces
-
Yserentant H.: Two preconditioners based on the multi-level splitting of finite element spaces. Numer. Math. 58, 163-184 (1990).
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(1990)
Numer. Math.
, vol.58
, pp. 163-184
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Yserentant, H.1
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