An Explicit Marching-on-in-time Scheme for Solving the Kirchhoff Integral Equation

Rui Chen; Sadeed B Sayed; Hakan Bagci

doi:10.1109/APUSNCURSINRSM.2018.8608706

An Explicit Marching-on-in-time Scheme for Solving the Kirchhoff Integral Equation

Rui Chen, Sadeed B Sayed, Hakan Bagci

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

2 Scopus citations

Abstract

An explicit marching-on-in-time scheme for solving the Kirchhoff integral equation enforced on an acoustically rigid scatterer is proposed. The unknown velocity potential introduced on the surface of scatterer is expanded using unit pulse functions in space and Lagrange polynomial interpolation functions in time. The resulting system is cast in the form of an ordinary differential equation and then integrated numerically in time using a predictor-corrector scheme to obtain the unknown expansion coefficients. Numerical results demonstrate that the time step size required by the proposed explicit scheme to ensure an accurate and stable solution is as large as that used by its implicit counterpart.

Original language	English (US)
Title of host publication	2018 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	2409-2410
Number of pages	2
ISBN (Print)	9781538671023
DOIs	https://doi.org/10.1109/APUSNCURSINRSM.2018.8608706
State	Published - Jan 24 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01

Access to Document

10.1109/APUSNCURSINRSM.2018.8608706

https://repository.kaust.edu.sa/bitstream/10754/631727/1/Acoustic_aps2018_ver5_HB.pdf

Cite this

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title = "An Explicit Marching-on-in-time Scheme for Solving the Kirchhoff Integral Equation",

abstract = "An explicit marching-on-in-time scheme for solving the Kirchhoff integral equation enforced on an acoustically rigid scatterer is proposed. The unknown velocity potential introduced on the surface of scatterer is expanded using unit pulse functions in space and Lagrange polynomial interpolation functions in time. The resulting system is cast in the form of an ordinary differential equation and then integrated numerically in time using a predictor-corrector scheme to obtain the unknown expansion coefficients. Numerical results demonstrate that the time step size required by the proposed explicit scheme to ensure an accurate and stable solution is as large as that used by its implicit counterpart.",

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An Explicit Marching-on-in-time Scheme for Solving the Kirchhoff Integral Equation. / Chen, Rui; Sayed, Sadeed B ; Bagci, Hakan.
2018 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting. Institute of Electrical and Electronics Engineers (IEEE), 2019. p. 2409-2410.

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

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T1 - An Explicit Marching-on-in-time Scheme for Solving the Kirchhoff Integral Equation

AU - Chen, Rui

AU - Sayed, Sadeed B

AU - Bagci, Hakan

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2019/1/24

Y1 - 2019/1/24

N2 - An explicit marching-on-in-time scheme for solving the Kirchhoff integral equation enforced on an acoustically rigid scatterer is proposed. The unknown velocity potential introduced on the surface of scatterer is expanded using unit pulse functions in space and Lagrange polynomial interpolation functions in time. The resulting system is cast in the form of an ordinary differential equation and then integrated numerically in time using a predictor-corrector scheme to obtain the unknown expansion coefficients. Numerical results demonstrate that the time step size required by the proposed explicit scheme to ensure an accurate and stable solution is as large as that used by its implicit counterpart.

AB - An explicit marching-on-in-time scheme for solving the Kirchhoff integral equation enforced on an acoustically rigid scatterer is proposed. The unknown velocity potential introduced on the surface of scatterer is expanded using unit pulse functions in space and Lagrange polynomial interpolation functions in time. The resulting system is cast in the form of an ordinary differential equation and then integrated numerically in time using a predictor-corrector scheme to obtain the unknown expansion coefficients. Numerical results demonstrate that the time step size required by the proposed explicit scheme to ensure an accurate and stable solution is as large as that used by its implicit counterpart.

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BT - 2018 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -

An Explicit Marching-on-in-time Scheme for Solving the Kirchhoff Integral Equation

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