### Abstract

The wavelet concept has been introduced in the applied mathematics literature as a new mathematical subject for performing localized `Time-frequency' characterization. It is a versatile tool with `very rich mathematical content and great potential for applications'. Because of this localized property both in the original and in the transform domain it is expected that its application particularly to solution of partial differential equations would be quite interesting. Utilization of a wavelet type basis has the advantage that the condition number of the system matrix does not increase rapidly with an increase in the number of unknowns unlike the original version of the finite element methods. In this paper the wavelet concepts have been developed and explained with application to 1D-differential equations. It will be shown how this can be incorporated in a Galerkin's method (or equivalently, e.g. Finite Element Method) for efficient solution of 2D problems. Numerical examples will be been presented for efficient solution of waveguide problems utilizing this approach.

Original language | English (US) |
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Title of host publication | IEEE Antennas and Propagation Society, AP-S International Symposium (Digest) |

Publisher | IEEE Computer Society |

Pages | 7 |

Number of pages | 1 |

Volume | 1 |

State | Published - 1994 |

Event | Proceedings of the IEEE Antennas and Propagation International Symposium. Part 3 (of 3) - Seattle, WA, USA Duration: Jun 19 1994 → Jun 24 1994 |

### Other

Other | Proceedings of the IEEE Antennas and Propagation International Symposium. Part 3 (of 3) |
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City | Seattle, WA, USA |

Period | 6/19/94 → 6/24/94 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*IEEE Antennas and Propagation Society, AP-S International Symposium (Digest)*(Vol. 1, pp. 7). IEEE Computer Society.

**Utilization of wavelet concepts in finite elements for efficient solution of Maxwell's equation.** / Sarkar, Tapan Kumar; Garcia-Castillo, Luis Emilio; Salazar-Palma, Magdalena.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*IEEE Antennas and Propagation Society, AP-S International Symposium (Digest).*vol. 1, IEEE Computer Society, pp. 7, Proceedings of the IEEE Antennas and Propagation International Symposium. Part 3 (of 3), Seattle, WA, USA, 6/19/94.

}

TY - CHAP

T1 - Utilization of wavelet concepts in finite elements for efficient solution of Maxwell's equation

AU - Sarkar, Tapan Kumar

AU - Garcia-Castillo, Luis Emilio

AU - Salazar-Palma, Magdalena

PY - 1994

Y1 - 1994

N2 - The wavelet concept has been introduced in the applied mathematics literature as a new mathematical subject for performing localized `Time-frequency' characterization. It is a versatile tool with `very rich mathematical content and great potential for applications'. Because of this localized property both in the original and in the transform domain it is expected that its application particularly to solution of partial differential equations would be quite interesting. Utilization of a wavelet type basis has the advantage that the condition number of the system matrix does not increase rapidly with an increase in the number of unknowns unlike the original version of the finite element methods. In this paper the wavelet concepts have been developed and explained with application to 1D-differential equations. It will be shown how this can be incorporated in a Galerkin's method (or equivalently, e.g. Finite Element Method) for efficient solution of 2D problems. Numerical examples will be been presented for efficient solution of waveguide problems utilizing this approach.

AB - The wavelet concept has been introduced in the applied mathematics literature as a new mathematical subject for performing localized `Time-frequency' characterization. It is a versatile tool with `very rich mathematical content and great potential for applications'. Because of this localized property both in the original and in the transform domain it is expected that its application particularly to solution of partial differential equations would be quite interesting. Utilization of a wavelet type basis has the advantage that the condition number of the system matrix does not increase rapidly with an increase in the number of unknowns unlike the original version of the finite element methods. In this paper the wavelet concepts have been developed and explained with application to 1D-differential equations. It will be shown how this can be incorporated in a Galerkin's method (or equivalently, e.g. Finite Element Method) for efficient solution of 2D problems. Numerical examples will be been presented for efficient solution of waveguide problems utilizing this approach.

UR - http://www.scopus.com/inward/record.url?scp=0346044488&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346044488&partnerID=8YFLogxK

M3 - Chapter

VL - 1

SP - 7

BT - IEEE Antennas and Propagation Society, AP-S International Symposium (Digest)

PB - IEEE Computer Society

ER -