### Abstract

The method of moments (MOM) has been used to solve antenna and scattering problems for several decades, due both to its flexibility in handling complex geometric structures and to its numerical accuracy. However, for electrically large problems, the MOM often becomes incapable of achieving solutions due to its requirements for vast amounts of local memory and processor cycles. To overcome this difficulty, orthonormal wavelets have been introduced, which create very sparse moment matrices that can be evaluated by iterative techniques. Nevertheless, the traditional orthonormal wavelets have demonstrated several limitations. The use of intervallic wavelets is presented; they form an orthonormal basis and preserve the same multi-resolution analysis as other unbounded wavelets. In contrast to periodic wavelets, endpoint values are not restricted if the unknown function is expanded in terms of intervallic wavelets. Very sparse impedance matrices have been obtained with this method. Zero elements of the matrices are identified directly, without using a truncation scheme with an artificially established threshold. The majority of matrix elements are evaluated directly, without performing numerical integration procedures such as Gaussian quadrature. The construction of intervallic wavelets is presented. Numerical examples of 2-D and 3-D scattering problems are discussed, and the relative error of this method is studied analytically.

Original language | English (US) |
---|---|

Title of host publication | IEE Proceedings: Microwaves, Antennas and Propagation |

Pages | 471-479 |

Number of pages | 9 |

Volume | 145 |

Edition | 6 |

State | Published - 1998 |

### Fingerprint

### Keywords

- Coifman wavelets
- Intervallic wavelets
- Scattering

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Computer Networks and Communications

### Cite this

*IEE Proceedings: Microwaves, Antennas and Propagation*(6 ed., Vol. 145, pp. 471-479)

**Use of Coifman intervallic wavelets in 2-D and 3-D scattering problems.** / Pan, George; Toupikov, M.; Du, J.; Gilbert, B. K.

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

*IEE Proceedings: Microwaves, Antennas and Propagation.*6 edn, vol. 145, pp. 471-479.

}

TY - CHAP

T1 - Use of Coifman intervallic wavelets in 2-D and 3-D scattering problems

AU - Pan, George

AU - Toupikov, M.

AU - Du, J.

AU - Gilbert, B. K.

PY - 1998

Y1 - 1998

N2 - The method of moments (MOM) has been used to solve antenna and scattering problems for several decades, due both to its flexibility in handling complex geometric structures and to its numerical accuracy. However, for electrically large problems, the MOM often becomes incapable of achieving solutions due to its requirements for vast amounts of local memory and processor cycles. To overcome this difficulty, orthonormal wavelets have been introduced, which create very sparse moment matrices that can be evaluated by iterative techniques. Nevertheless, the traditional orthonormal wavelets have demonstrated several limitations. The use of intervallic wavelets is presented; they form an orthonormal basis and preserve the same multi-resolution analysis as other unbounded wavelets. In contrast to periodic wavelets, endpoint values are not restricted if the unknown function is expanded in terms of intervallic wavelets. Very sparse impedance matrices have been obtained with this method. Zero elements of the matrices are identified directly, without using a truncation scheme with an artificially established threshold. The majority of matrix elements are evaluated directly, without performing numerical integration procedures such as Gaussian quadrature. The construction of intervallic wavelets is presented. Numerical examples of 2-D and 3-D scattering problems are discussed, and the relative error of this method is studied analytically.

AB - The method of moments (MOM) has been used to solve antenna and scattering problems for several decades, due both to its flexibility in handling complex geometric structures and to its numerical accuracy. However, for electrically large problems, the MOM often becomes incapable of achieving solutions due to its requirements for vast amounts of local memory and processor cycles. To overcome this difficulty, orthonormal wavelets have been introduced, which create very sparse moment matrices that can be evaluated by iterative techniques. Nevertheless, the traditional orthonormal wavelets have demonstrated several limitations. The use of intervallic wavelets is presented; they form an orthonormal basis and preserve the same multi-resolution analysis as other unbounded wavelets. In contrast to periodic wavelets, endpoint values are not restricted if the unknown function is expanded in terms of intervallic wavelets. Very sparse impedance matrices have been obtained with this method. Zero elements of the matrices are identified directly, without using a truncation scheme with an artificially established threshold. The majority of matrix elements are evaluated directly, without performing numerical integration procedures such as Gaussian quadrature. The construction of intervallic wavelets is presented. Numerical examples of 2-D and 3-D scattering problems are discussed, and the relative error of this method is studied analytically.

KW - Coifman wavelets

KW - Intervallic wavelets

KW - Scattering

UR - http://www.scopus.com/inward/record.url?scp=0032262230&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032262230&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:0032262230

VL - 145

SP - 471

EP - 479

BT - IEE Proceedings: Microwaves, Antennas and Propagation

ER -