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Application of multiwavelet to the edge element method
Author(s) -
Pan George W.,
Wang Ke,
Gilbert Barry K.
Publication year - 2002
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/mop.10384
Subject(s) - orthonormal basis , basis function , interpolation (computer graphics) , basis (linear algebra) , smoothness , divergence (linguistics) , mathematics , speedup , algorithm , convergence (economics) , function (biology) , mathematical analysis , computer science , geometry , parallel computing , physics , telecommunications , linguistics , philosophy , frame (networking) , quantum mechanics , evolutionary biology , economics , biology , economic growth
A new approach of using multiwavelets in the edge element method for electromagnetic‐wave problems is presented. In this approach, the multiscalets are employed as the basis functions. Because of the smoothness, completeness, compact support, and interpolation property of the multiscalets in terms of the basis function and its derivatives, fast convergence in approximating a function is achieved. The new basis functions are ∈ C 1 ; that is, the first derivatives of the bases are continuous on the connecting nodes. Thus the divergence‐free condition is satisfied at the end points. The multiscalets, along with their derivatives, are orthonormal in the discrete sampling nodes. Therefore no coupled system of equations in terms of the function and its derivative is involved, resulting in a simple and efficient algorithm. Numerical results demonstrate high efficiency and accuracy of the new method. For a partially loaded waveguide problem, a factor of 16 in memory reduction and 435 in CPU speedup over the linear edge element method has been achieved. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 34: 96–100, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10384