A. Barinka, T. Barsch, Ph. Charton, A. Cohen, S. Dahlke, W. Dahmen, K. Urban, Adaptive wavelet schemes for elliptic problems | Implementation and numerical experiments, SIAM J. Sci. Comp., 23 (2001), 910-939. Home/Search Document Details and Download
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Adaptive Wavelet Methods For Linear{quadratic - Elliptic Control Problems Self-citation (Dahmen) (Correct)
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A. Barinka, T. Barsch, Ph. Charton, A. Cohen, S. Dahlke, W. Dahmen, K. Urban, Adaptive wavelet schemes for elliptic problems | Implementation and numerical experiments, SIAM J. Sci. Comp., 23 (2001), 910-939.
Adaptive Methods for PDE's Wavelets or Mesh Refinement? - Cohen Self-citation (Cohen) (Correct)
....goes for the indices of the matrix A which are used in the matrix vector algorithm (24) at each step of the algorithm. This dynamical adaptation, which requires appropriate data structure, result in major overheads in the computational cost which are observed in practice : the numerical results in [4] reveal that while the wavelet adaptive algorithms indeed exhibits the optimal rate of convergence and slightly outperforms adaptive nite element algorithms from this perspective, the latter remains signi cantly more ecient from the point of view of computational time. The curse of anisotropy : ....
Barinka, A., T. Barsch, P. Charton, A. Cohen, S. Dahlke, W. Dahmen, K. Urban (1999), Adaptive wavelet schemes for elliptic problems { Implementation and numerical experiments, IGPM Report # 173 RWTH Aachen, to appear in SISC.
Adaptive Wavelet Methods for Saddle Point Problems -.. - Dahlke, Dahmen, Urban (2001) (4 citations) Self-citation (Dahlke Dahmen Urban) (Correct)
....right from the beginning into an equivalent problem which is well posed in the Euclidean metric. All essential computational steps refer then to approximation in 2 and therefore bear a great potential of being portable to other problem classes. In fact, many of the basic routines developed in [2, 8] in the context of elliptic problems can be used here as well. The second important point is that the wavelet representation allows us to think of performing, up to a controlled perturbation, an iteration on the full in nite dimensional This work has been supported in part by the Deutsche ....
....dimensions suciently high order wavelet bases would give rise to adaptive schemes with arbitrarily high convergence rates. Finally in Section 6 we present some numerical experiments essentially guided by the above mentioned theoretical considerations. Here we make use of the software developed in [2] as well as in [25] The results con rm that the adaptive scheme performs essentially independently of the pairing of trial functions for velocities and pressure. For instance, the rate of best N term approximation is met within a factor two when both velocities and pressure are approximated by ....
[Article contains additional citation context not shown here]
A. Barinka, T. Barsch, P. Charton, A. Cohen, S. Dahlke, W. Dahmen, and K. Urban, Adaptive wavelet schemes for elliptic problems { Implementation and numerical experiments, IGPM-Report # 173, RWTH Aachen, 1999, to appear in: SIAM J. Scient. Comput. 28
Adaptive Wavelet Methods For Saddle Point Problems -.. - Dahlke, Dahmen, Urban (2001) (4 citations) Self-citation (Dahlke Dahmen Urban) (Correct)
....right from the beginning into an equivalent problem which is well posed in the Euclidean metric. All essential computational steps refer then to approximation in 2 and therefore bear a great potential of being portable to other problem classes. In fact, many of the basic routines developed in [2, 6] in the context of elliptic problems can be used here as well. The second important point is that the wavelet representation allows us to think of performing, up to a controlled perturbation, an iteration on the full in nite dimensional This work has been supported in part by the Deutsche ....
....dimensions suciently high order wavelet bases would give rise to adaptive schemes with arbitrarily high convergents rates. Finally in Section 6 we present some numerical experiments essentially guided by the above mentioned theoretical considerations. Here we make use of the software developed in [2] as well as in [22] The results con rm that the adaptive scheme performs essentially independently of the pairing of trial functions for velocities and pressure. For instance, the rate of best N term approximation is met within a factor two when both velocities and pressure are approximated by ....
[Article contains additional citation context not shown here]
A. Barinka, T. Barsch, P. Charton, A. Cohen, S. Dahlke, W. Dahmen, and K. Urban, Adaptive wavelet schemes for elliptic problems { Implementation and numerical experiments, IGPM-Report # 173, RWTH Aachen, 1999, to appear in: SIAM J. Scientic Comput.
Wavelet Methods for PDEs - Some Recent Developments - Dahmen (1999) (2 citations) Self-citation (Dahmen) (Correct)
....can be viewed as a mapping from the set of keys to the set of admissible values. The data structures map and multimap from the Standard Template Library [105] matches the requirements. A rst prototype implementation of an adaptive wavelet solver based on these STL libraries is developed in [7]. There one can nd a detailed discussion of rst numerical tests for one and two dimensional Poisson type problems. The performance of the scheme con rms for these examples the claimed optimality with a surprisingly tight relation between best N term approximation and adapted Galerkin solutions. ....
A. Barinka, T. Barsch, P. Charton, A. Cohen, S. Dahlke, W. Dahmen, K. Urban, Adaptive wavelet schemes for elliptic problems { Implementation and numerical experiments, IGPM Report # 173, June 1999, RWTH Aachen.
Adaptive Wavelet Methods II - Beyond the Elliptic Case - Cohen, Dahmen, DeVore (2000) (4 citations) Self-citation (Cohen Dahmen) (Correct)
....like [CTU1, CM, DS1] provide wavelets with arbitrarily high regularity only inside macro patches. It should be mentioned though that the bound s in (6.2.10) is not best possible. For constant coecient partial di erential operators and spline wavelets of order m, s = m 3=2 can be veri ed [BBCCDDU]. The above ndings may now be summarized as follows. Remark 6.2.3 (i) If there exists an s 0 such that each block A i;l of L from (6.2.2) belongs to C s then also L 2 C s as well as L 2 C s . ii) In each of the examples from Section 3.2 the operators L i;l are either of type ....
A. Barinka, T. Barsch, P. Charton, A. Cohen, S. Dahlke, W. Dahmen, K. Urban, Adaptive wavelet schemes for elliptic problems { Implementation and numerical experiments, IGPM Report # 173, June 1999, RWTH Aachen. 35
Adaptive Convex Optimization in Banach Spaces: a Multilevel.. - Canuto (Correct)
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A. Barinka, T. Barsch, Ph. Charton, A. Cohen, S. Dahlke, W. Dahmen and K. Urban, Adaptive wavelet schemes for elliptic problems - implementation and numerical experiments, SIAM J. Sci. Comput., 23, (2001), 910-939.
On The Compressibility Of Operators In Wavelet Coordinates - Stevenson (2002) (Correct)
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A. Barinka, T. Barsch, P. Charton, A. Cohen, S. Dahlke, W. Dahmen, and K. Urban. Adaptive wavelet schemes for elliptic problems - Implementation and numerical experiments. SISC, 23(3):910--939, 2001.
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