Asymptotic expansions of the Helmholtz equation solutions using approximations of the Dirichlet to Neumann operator

作者：Lazergui Souaad^*; Boubendir Yassine

来源：Journal of Mathematical Analysis and Applications, 2017, 456(2): 767-786.

DOI：10.1016/j.jmaa.2017.07.047

• Wave equation
• Dirichlet to Neumann operator
• Asymptotic analysis

This paper is concerned with the asymptotic expansions of the amplitude of the solution of the Helmholtz equation. The original expansions were obtained using a pseudo-differential decomposition of the Dirichlet to Neumann operator. This work uses first and second order approximations of this operator to derive new asymptotic expressions of the normal derivative of the total field. The resulting expansions can be used to appropriately choose the ansatz in the design of high-frequency numerical solvers, such as those based on integral equations, in order to produce more accurate approximation of the solutions around the shadow and the deep shadow regions than the ones based on the usual ansatz.

• 出版日期2017-12-15