### Abstract

Multiwavelet based moment method (MMM) is employed to solve the integral equations of the 1st and 2nd kind in 3D cases. We implement the partial derivative sampling along two orthogonal directions in order to keep tracking the directional derivative along arbitrary directions. This will produce a nonsquare impedance matrix if the traditional Galerkin's procedure is applied. We may obtain a square impedance matrix by reducing the number of the observation points, but the solution will be very sensitive to the distribution of the observation points. The least-mean-square method (LMS) is demon-strated to be very effective in solving nonsquare matrix equations. We conduct the LMS in our 3D MMM, thus the advantages of the MMM in 2D cases are preserved with a minor increase of the computational cost of the LMS.

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

Pages | 1479-1482 |

Number of pages | 4 |

Volume | 2 |

State | Published - 2004 |

Event | IEEE Antennas and Propagation Society Symposium 2004 Digest held in Conjunction with: USNC/URSI National Radio Science Meeting - Monterey, CA, United States Duration: Jun 20 2004 → Jun 25 2004 |

### Other

Other | IEEE Antennas and Propagation Society Symposium 2004 Digest held in Conjunction with: USNC/URSI National Radio Science Meeting |
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Country | United States |

City | Monterey, CA |

Period | 6/20/04 → 6/25/04 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*IEEE Antennas and Propagation Society, AP-S International Symposium (Digest)*(Vol. 2, pp. 1479-1482)

**Multiwavelets in solving integral equations of the 1st and 2nd kind.** / Tong, Meisong; Pan, George.

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

*IEEE Antennas and Propagation Society, AP-S International Symposium (Digest).*vol. 2, pp. 1479-1482, IEEE Antennas and Propagation Society Symposium 2004 Digest held in Conjunction with: USNC/URSI National Radio Science Meeting, Monterey, CA, United States, 6/20/04.

}

TY - GEN

T1 - Multiwavelets in solving integral equations of the 1st and 2nd kind

AU - Tong, Meisong

AU - Pan, George

PY - 2004

Y1 - 2004

N2 - Multiwavelet based moment method (MMM) is employed to solve the integral equations of the 1st and 2nd kind in 3D cases. We implement the partial derivative sampling along two orthogonal directions in order to keep tracking the directional derivative along arbitrary directions. This will produce a nonsquare impedance matrix if the traditional Galerkin's procedure is applied. We may obtain a square impedance matrix by reducing the number of the observation points, but the solution will be very sensitive to the distribution of the observation points. The least-mean-square method (LMS) is demon-strated to be very effective in solving nonsquare matrix equations. We conduct the LMS in our 3D MMM, thus the advantages of the MMM in 2D cases are preserved with a minor increase of the computational cost of the LMS.

AB - Multiwavelet based moment method (MMM) is employed to solve the integral equations of the 1st and 2nd kind in 3D cases. We implement the partial derivative sampling along two orthogonal directions in order to keep tracking the directional derivative along arbitrary directions. This will produce a nonsquare impedance matrix if the traditional Galerkin's procedure is applied. We may obtain a square impedance matrix by reducing the number of the observation points, but the solution will be very sensitive to the distribution of the observation points. The least-mean-square method (LMS) is demon-strated to be very effective in solving nonsquare matrix equations. We conduct the LMS in our 3D MMM, thus the advantages of the MMM in 2D cases are preserved with a minor increase of the computational cost of the LMS.

UR - http://www.scopus.com/inward/record.url?scp=4544308226&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4544308226&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:4544308226

VL - 2

SP - 1479

EP - 1482

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

ER -