Efficient Numerical Techniques for Solving Pocklington's Integral Equation Using Multiwavelets

References

• Mallat , S. 1989 . Multiresolution approximations and wavelet orthonormal bases of L 2(R) . Trans. Amer. Math. Soc. , 315 ( No. 1 ) : 69 – 87 .
   Google Scholar
• Mallat , S. 1989 . Multifrequency channel decompositions of images and wavelet models . IEEE Trans. Acoust. Speech Signal Process , 37 ( No. 12 ) : 2091 – 2110 .
   Google Scholar
• Daubechies , I. 1990 . The wavelet transform, time-frequency localization and signal analysis . IEEE Trans. Info. Theory , 36 : 961 – 1005 .
   Web of Science ®Google Scholar
• Dahmen , W. , Proessdorf , S. and Schneider , R. 1993 . Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast algorithms . Adv. Comput. Math. , 1 : 259 – 335 .
   Google Scholar
• Micchelli , C. A. , Xu , Y. and Zhao , Y. 1997 . Wavelet Galerkin methods for second-kind integral equations . J. Comput. Appl. Math. , 86 : 251 – 270 .
   Web of Science ®Google Scholar
• Chen , Z. , Micchelli , C. A. and Xu , Y. 1997 . The Petrov-Galerkin method for second kind integral equations II: multiwavelet schemes . Adv. Comput. Math. , 7 : 199 – 233 .
   Web of Science ®Google Scholar
• Beylkin , G. and Keiser , J. M. 1997 . On the adaptive numerical solution of non-linear partial differential equations in wavelet bases . J. Comput. Phys. , 132 : 233 – 259 .
   Web of Science ®Google Scholar
• Alpert , B. , Beylkin , G. , Coifman , R. R. and Rokhlin , V. 1993 . Waveletlike bases for the fast solution of second-kind integral equations . SIAM J. Sci. Statist. Comput. , 14 ( No. 1 ) : 159 – 184 .
   Google Scholar
• Daubechies , I. 1988 . Orthonormal bases of compactly supported wavelets . Comm. Pure & Appl. Math. , 41 : 909 – 996 .
   Web of Science ®Google Scholar
• Daubechies , I. 1992 . “ Ten lectures on wavelets ” . In CBMS-NSF Lecture Notes nr. 61 , SIAM .
   Google Scholar
• Cohen , A. , Daubechies , I. and Feauveau , J. 1992 . Biorthogonal bases of compactly supported wavelet . Comm. Pure Appl. Math. , 45 : 485 – 560 .
   Web of Science ®Google Scholar
• Herve , A. 1994 . Multi-resolution analysis of multiplicity d. Application to dyadic interpolation . Comput. Harmonic Anal. , 1 : 299 – 315 .
   Google Scholar
• Alpert , B. 1993 . A class of bases in L 2 for the sparse representation of integral operators . SIAM J. Math. Anal. , 24 ( No. 1 ) : 159 – 184 .
   Google Scholar
• Beylkin , G. , Coifman , R. and Rokhlin , V. 1991 . Fast wavelet transforms and numerical algorithms, I . Commun. Pure Appl. Math. , 44 : 141 – 183 .
   Web of Science ®Google Scholar
• Alpert , B. 1992 . “ Wavelets and Other Bases for Fast Numerical Linear Algebra ” . In Wavelets—A Tutorial in Theory and Applications , Edited by: Chiu , C. K. 181 – 216 . Boston : Academic Press .
   Google Scholar
• Strang , G. and Strela , V. 1995 . Short wavelets and matrix dilation equations . IEEE Trans. Sig. Proc. , SP-43 : 108 – 115 .
   Google Scholar
• Su , C. and Sarkar , T. K. 1997 . A multiscale moment method for solving fredholm integral equation of the first kind . Progress in Electromagnetics Research , PIER 17 : 237 – 264 .
   Google Scholar
• Alpert , B. , Beylkin , G. , Gines , D. and Vozovoi , L. 2002 . Adaptive solution of partial differential equations in multiwavelet bases . J. Comput. Phys. , 182 : 149 – 190 .
   Web of Science ®Google Scholar
• Averbucha , A. , Israelib , M. and Vozovoi , L. 1999 . Solution of time-dependent diffusion equations with variable coefficients using multiwavelets . J. Comput. Phys. , 150 : 394 – 424 .
   Google Scholar
• Pocklington , H. C. 1897 . “ Electrical oscillation in wires ” . In Proc. Cambridge Phil. Soc Vol. 9 , 324 – 332 . London , , England
   Google Scholar
• Elliot , R. S. 1981 . Antenna Theory and Design , Prentice-Hall .
   Google Scholar
• Rynne , B. P. 2000 . On the well-posedness of Pocklington's equation for a straight wire antenna and convergence of numerical solutions . Journal of Electromagnetic Waves and Applications , 14 : 1489 – 1503 .
   Web of Science ®Google Scholar
• Wilton , D. R. , Butler , C. M. and Breakall , J. K. 1967 . Efficient numerical techniques for solving Pocklington's equation and their relationships to other methods . IEEE Trans. Antennas Propagat. , AP-24 : 83 – 86 .
   Google Scholar
• Davies , P. J. , Duncan , D. B. and Funkenz , S. A. 2001 . Accurate and efficient algorithms for frequency domain scattering from a thin wire . J. Comput. Phys. , 168 ( No. 1 ) : 155 – 183 .
   Google Scholar
• Werner , D. H. , Werner , P. L. and Breakall , J. K. 1994 . Some computational aspects of Pocklington's electric field integral equation for thin wires . IEEE Trans. Antennas Propagat. , 42 ( No. 4 ) : 561 – 563 .
   Google Scholar
• Canuto , C. , Hussaini , M. Y. , Quarteroni , A. and Zang , T. A. 1987 . Spectral Methods in Fluid Dynamic , Springer-Verlag .
   Google Scholar
• Coult , N. 1999 . “ Introduction to discontinuous wavelets ” . In Discontinuous Galerkin Methods: Theory, Computation, and Applications, Lecture Notes in Computational Science and Engineering 11 , Springer-Verlag .
   Google Scholar
• Richmond , J. H. 1965 . Digital computer solutions of the rigorous equations for scatter problems . Proc. IEEE , Aug 53 : 796 – 804 .
   Google Scholar
• Goswami , J. C. , Chan , A. K. and Chui , C. K. 1995 . On solving first-kind integral equations using wavelets on a bounded interval . IEEE Trans. Antennas Propagat. , 43 ( No. 6 ) : 614 – 622 .
   Google Scholar