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  • The design of most adaptive wavelet methods for solving differential equations follows a general concept proposed by A. Cohen, W. Dahmen and R. DeVore in [5, 6]. The essential steps are: transformation of the variational formulation into the well-conditioned infinite-dimensional l2 problem, finding of the convergent iteration process for the l2 problem and finally derivation of its finite dimensional version which works with an inexact right hand side and approximate matrix-vector multiplication. In our contribution, we shortly review all these parts with emphasis on the approximate matrix-vector multiplication. Efficient approximation of matrix-vector multiplication is enabled by an off-diagonal decay of entries of the wavelet stiffness matrix and by decay of entries of load vector in wavelet coordinates. Besides an usual truncation in scale, we apply here also a truncation in space to compress wavelet stiffness matrices efficiently. At the end, we show some numerical experiments.
  • The design of most adaptive wavelet methods for solving differential equations follows a general concept proposed by A. Cohen, W. Dahmen and R. DeVore in [5, 6]. The essential steps are: transformation of the variational formulation into the well-conditioned infinite-dimensional l2 problem, finding of the convergent iteration process for the l2 problem and finally derivation of its finite dimensional version which works with an inexact right hand side and approximate matrix-vector multiplication. In our contribution, we shortly review all these parts with emphasis on the approximate matrix-vector multiplication. Efficient approximation of matrix-vector multiplication is enabled by an off-diagonal decay of entries of the wavelet stiffness matrix and by decay of entries of load vector in wavelet coordinates. Besides an usual truncation in scale, we apply here also a truncation in space to compress wavelet stiffness matrices efficiently. At the end, we show some numerical experiments. (en)
Title
  • On Wavelet Matrix Compression for Differential Equations
  • On Wavelet Matrix Compression for Differential Equations (en)
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  • On Wavelet Matrix Compression for Differential Equations
  • On Wavelet Matrix Compression for Differential Equations (en)
skos:notation
  • RIV/46747885:24510/11:#0000792!RIV13-GA0-24510___
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  • P(GP201/09/P641)
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  • 218331
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  • RIV/46747885:24510/11:#0000792
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  • matrix algebra; partial differential equations; mathematical operators; Poisson equation (en)
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  • [0F23F9748C13]
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  • Halkidiki, (Greece)
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  • Melville, New York
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  • NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011
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  • Finěk, Václav
  • Černá, Dana
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  • 302239800378
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  • 10.1063/1.3637931
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  • American Institute of Physics
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  • 978-0-7354-0956-9
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  • 24510
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