Best N - term capacitance approximation on sparse grids

نویسندگان

  • Tony Chan
  • Takashi Kako
  • Hideo Kawarada
  • Olivier Pironneau
  • P. Oswald
چکیده

In [GOS99], adaptive sparse grid spaces spanned by a finite number of tensor-product L2-orthogonal Haar functions have been applied to capacitance calculations on a unit screen. In this note, we state asymptotically optimal approximation rates for this problem when choosing the best possible adaptive sparse grid space of a given dimension N . We also compare the results with other recent approaches to efficiently solve this problem and comment on some numerical tests. Details of the proofs and a discussion of the approximation-theoretical aspects have appeared in [Osw99]. For a flat square screen I ≡ [0, 1], we consider the single layer potential equation

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تاریخ انتشار 2001