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Study on Solving Singularity in Helmholtz Surface Integral Function

Chengyuan Liu

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Abstract

For solving singularities in Helmholtz surface integral function,integral solution for scattered field of submerged target with the plane wave incidence was derived from Helmholtz surface integral equation,and then the formula of integral solution was given through numerical calculation by Boundary Element Method(BEM).Method of equivalent facet approximation was employed to solve the first order and the second order singularities.The calculated results of scattered echo from the rigid spheroid indicate that singularities in Helmholtz surface integral equation are solved with the proposed method and that numerical solution can be provided with high accuracy at a wider-frequency brand for scattered echo characteristics of submerged objects.

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What this paper is about

For solving singularities in Helmholtz surface integral function,integral solution for scattered field of submerged target with the plane wave incidence was derived from Helmholtz surface integral equation,and then the formula of integral solution was given through numerical calculation by Boundary Element Method(BEM).Method of equivalent facet approximation was employed to solve the first order and the second order singularities.The calculated results of scattered echo from the rigid spheroid indicate that singularities in Helmholtz surface integral equation are solved with the proposed method and that numerical solution can be provided with high accuracy at a wider-frequency brand for scattered echo characteristics of submerged objects.

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Available abstract

For solving singularities in Helmholtz surface integral function,integral solution for scattered field of submerged target with the plane wave incidence was derived from Helmholtz surface integral equation,and then the formula of integral solution was given through numerical calculation by Boundary Element Method(BEM).Method of equivalent facet approximation was employed to solve the first order and the second order singularities.The calculated results of scattered echo from the rigid spheroid indicate that singularities in Helmholtz surface integral equation are solved with the proposed method and that numerical solution can be provided with high accuracy at a wider-frequency brand for scattered echo characteristics of submerged objects.

Key concepts: Helmholtz equation, Boundary element method, Electric-field integral equation, Integral equation, Gravitational singularity, Helmholtz free energy, Singularity, Mathematics

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