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Volume 25, Issue 3
Stable Solution of Time Domain Integral Equation Methods Using Quadratic B-Spline Temporal Basis Functions

M. Y. Xia, G. H. Zhang, G. L. Dai & C. H. Chan

J. Comp. Math., 25 (2007), pp. 374-384.

Published online: 2007-06

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  • Abstract

This paper is concerned with stable solutions of time domain integral equation (TDIE) methods for transient scattering problems with 3D conducting objects. We use the quadratic B-spline function as temporal basis functions, which permits both the induced currents and induced charges to be properly approximated in terms of completeness. Because the B-spline function has the least support width among all polynomial basis functions of the same order, the resulting system matrices seem to be the sparsest. The TDIE formulations using induced electric polarizations as unknown function are adopted and justified. Numerical results demonstrate that the proposed approach is accurate and efficient, and no late-time instability is observed.

  • Keywords

TDIE methods, B-spline temporal basis functions, Transient scattering problems.

  • AMS Subject Headings

65N12, 65R20, 74S15.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-25-374, author = {M. Y. Xia, G. H. Zhang, G. L. Dai and C. H. Chan}, title = {Stable Solution of Time Domain Integral Equation Methods Using Quadratic B-Spline Temporal Basis Functions}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {3}, pages = {374--384}, abstract = {

This paper is concerned with stable solutions of time domain integral equation (TDIE) methods for transient scattering problems with 3D conducting objects. We use the quadratic B-spline function as temporal basis functions, which permits both the induced currents and induced charges to be properly approximated in terms of completeness. Because the B-spline function has the least support width among all polynomial basis functions of the same order, the resulting system matrices seem to be the sparsest. The TDIE formulations using induced electric polarizations as unknown function are adopted and justified. Numerical results demonstrate that the proposed approach is accurate and efficient, and no late-time instability is observed.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8698.html} }
TY - JOUR T1 - Stable Solution of Time Domain Integral Equation Methods Using Quadratic B-Spline Temporal Basis Functions AU - M. Y. Xia, G. H. Zhang, G. L. Dai & C. H. Chan JO - Journal of Computational Mathematics VL - 3 SP - 374 EP - 384 PY - 2007 DA - 2007/06 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8698.html KW - TDIE methods, B-spline temporal basis functions, Transient scattering problems. AB -

This paper is concerned with stable solutions of time domain integral equation (TDIE) methods for transient scattering problems with 3D conducting objects. We use the quadratic B-spline function as temporal basis functions, which permits both the induced currents and induced charges to be properly approximated in terms of completeness. Because the B-spline function has the least support width among all polynomial basis functions of the same order, the resulting system matrices seem to be the sparsest. The TDIE formulations using induced electric polarizations as unknown function are adopted and justified. Numerical results demonstrate that the proposed approach is accurate and efficient, and no late-time instability is observed.

M. Y. Xia, G. H. Zhang, G. L. Dai and C. H. Chan. (2007). Stable Solution of Time Domain Integral Equation Methods Using Quadratic B-Spline Temporal Basis Functions. Journal of Computational Mathematics. 25 (3). 374-384. doi:
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