지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
초록· 키워드
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The Helmholtz equation represents acoustic or electromagnetic scattering phenomena. The Method of Lines are known to have many advantages in simulation of forward and inverse scattering problems due to the usage of angle rays and Bessel functions. However, the method does not account for the jump phenomena on obstacle boundary and the approximation includes many high order Bessel functions. The high order Bessel functions have extreme blow-up or die-out features in resonance region obstacle boundary. Therefore, in particular, when we consider shape reconstruction problems, the method is suffered from severe instabilities due to the logical confliction and the severe singularities of high order Bessel functions. In this paper, two approximation formulas for the Helmholtz equation are introduced. The formulas are new and powerful. The derivation is based on Method of Lines, Huygen's principle, boundary jump relations, Addition Formula, and the orthogonality of the trigonometric functions. The formulas reduce the approximation dimension significantly so that only lower order Bessel functions are required. They overcome the severe instability near the obstacle boundary and reduce the computational time significantly. The convergence is exponential. The formulas adopt the scattering jump phenomena on the boundary, and separate the boundary information from the measured scattered fields. Thus, the sensitivities of the scattered fields caused by the boundary changes can be analyzed easily. Several numerical experiments are performed. The results show the superiority of the proposed formulas in accuracy, efficiency, and stability.
목차
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참고문헌 (16)
참고문헌 신청
H. Ammari / 2008 / An Introduction to Mathematics of Emerging Biomedical Imaging (Mathematiques et Application) / Springer
M. Belonosov / 2017 / An iterative solver for the 3D Helmholtz equation / J. Computational Physics 345:330~344
D. Colton / 2013 / Inverse Acoustic and Electromagnetic Scattering Theory / Springer
U. Guo / 2011 / An optimization method for acoustic inverse obstacle scattering problems with multiple incident waves / Inverse Problems in Science and Engineering 19:461~484
B. Guzina / 2010 / On multi-frequency obstacle reconstruction via linear sampling method / Inverse Problems 26:125005
M. Belonosov / 2017 / An iterative solver for the 3D Helmholtz equation / J. Computational Physics 345:330~344
D. Colton / 2013 / Inverse Acoustic and Electromagnetic Scattering Theory / Springer
U. Guo / 2011 / An optimization method for acoustic inverse obstacle scattering problems with multiple incident waves / Inverse Problems in Science and Engineering 19:461~484
B. Guzina / 2010 / On multi-frequency obstacle reconstruction via linear sampling method / Inverse Problems 26:125005
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