Space-frequency adaptive approximation for quantum hydrodynamic models

References

• Ancona , M. G. and Iafrate , G. J. 1989 . Quantum correction to the equation of state of an electron gas in a semiconductor . Phys. Rev. B , 39 : 9536 – 9540 .
   Web of Science ®Google Scholar
• Bertoluzza , S. 1996 . Adaptive wavelet collocation method for the solution of Burgers equation . Transport Theory and Stat. Phys. , 25 : 339 – 352 .
   Google Scholar
• Bertoluzza , S. 1997 . “ An adaptive wavelet collocation method based on interpo-latinwavelets ” . In Multiscale Wavelet Methods for Partial Differential Equations volume 6 of Wavelets Analysis and its Applications , 109 – 135 . Academic Press .
   Google Scholar
• Bertoluzza , S. and Pietra , P. 1996 . “ Adaptive wavelet collocation for nonlinear BVP's. In Proc. of ICAOS '96 ” . In Lecture Notes in Control and Information Sciences , London : Springer Verlag .
   Google Scholar
• Bertoluzza , S. , Ravel , J. C. and Maday , Y. 1994 . A dynamically adaptive wavelet method for solving partial differential equations . Comput. Methods Appl. Mech. Engrg. ,
   Web of Science ®Google Scholar
• Cohen , A. , Dahmen , W. and De Vore , R. 1998 . “ Adaptive wavelet methods for elliptic operator equations — convergence rates ” . Aachen : IGPM-RWTK . Technical report
   Google Scholar
• Cohen , A. , Daubechies , I. and Feauveau , J. 1992 . Biorthogonal bases of compactly supported wavelets . Comm. Pure Appl. Math. , 45 : 485 – 560 .
   Web of Science ®Google Scholar
• Cohen , A. , Daubechies , I. and Vial , P. 1993 . Wavelets on the interval and fast wavelet transforms . ACHA , 1 : 54 – 81 .
   Google Scholar
• Coifman , R. R. , Meyer , Y. , Quake , S. R. and Wickerhauser , M. V. 1993 . Progress in Wavelt Analysis and Applications, chapter Signal Processing and Compression with Wavelt Packets , Editions , 77 – 93 . Paris : Frontikres .
   Google Scholar
• Coifman , R. R. and Wickerhauser , M. V. 1992 . Entropy based algorithms for best basis selection . IEEE Trans. Inform. Theory ,
   Web of Science ®Google Scholar
• Dahmen , W. 1998 . “ Nonlinear functionals of wavelet expansion — adaptive reconstruction and fast evaluation ” . Aachen : IGPM — RWTH . Technical Report 160
   Google Scholar
• Frölich , J. and Schneider , K. 1994 . An adaptive wavelet Galerkin algorithm for one and two dimensional flame computation . Eur. J. Mech. B/Fluids , 13 : 439 – 471 .
   Web of Science ®Google Scholar
• Gardner , C. L. 1994 . The quantum hydrodynamic model for semiconductor devices . SIAM J. Appl. Math. , 54 : 409 – 427 .
   Web of Science ®Google Scholar
• Gardner , C. L. and Ringhofer , C. 1998 . Smooth quantum hydrodynamic model simulation of the resonant tunneling diode . VLSI Design , 143 : 146 – 8 .
   Google Scholar
• Gasser , I. and Markowich , P. A. 1997 . Quantum hydrodynamics, Wigner transforms and the classical limit . Asymptotic Analysis , 14 : 97 – 116 .
   Web of Science ®Google Scholar
• Grenier , E. 1995 . Limite semi—classique de l'equation de Schrödinger non lineaire en temps petit . C. R. Acad. Sci. Paris Sr. I Math. , 320 : 691 – 694 .
   Google Scholar
• Grubin , H. L. and Kreskovsky , J. P. 1989 . Quantum Moment Balance Equations and Resonant Tunneling Structures . Solid-State Electronics , 1071 : 1075 – 32 .
   Google Scholar
• Gyi , M. T. and Jüngel , A. 1998 . A quantum regularization of the one-dimensional hydrodynamic model for semiconductors . submitted ,
   Google Scholar
• Harten , A. 1994 . Multiresolution algorithms for the numerical solution of hyperbolic conservation laws . Jour. Comp. Phys. , 115 : 319 – 338 .
   Web of Science ®Google Scholar
• Joly , P. , Maday , Y. and Perrier , V. 1997 . “ A dynamical adaptive concept based on wavelet packet best bases: Application to convection diffusion partial differential equations ” . In Multiscale Wavelet Methods for Partial Differential Equations , 199 – 235 . Academic Press .
   Google Scholar
• Maday , Y. , Perrier , V. and Ravel , J. C. 1991 . Adaptivité dynamique sur bases d'ondelettes pour l'approximation d'équations aux derivées partielles . C. R. Acad. Sci Paris , 312 : 405 – 410 . Série I
   Google Scholar
• Meyer , Y. 1990 . Ondelettes et Opérateurs Hermann
   Google Scholar
• Pietra , P. and Pohl , C. 1999 . Weak limits of the quantum hydrodynamic model . VLSI Design , to appear
   Web of Science ®Google Scholar
• Wickerhauser , M. V. , Farge , M. and Goirand , E. 1997 . “ Theoretical dimension and the complexity of simulated turbulence ” . In Multiscale Wavelet Methods for Partial Differential Equations, volume 6 of Wavelets Analysis and its Applications , 473 – 492 . Academic Press .
   Google Scholar