Dr. Yonglin Li, (ICMSEC, AMSS)

A CIP-FEM for High-Frequency Scattering Problem with the Truncated DtN Boundary Condition

Wednesday 14 October, 16:00-17:00 pm, N202

 A continuous interior penalty finite element method (CIP-FEM) is proposed to solve high-frequency Helmholtz scattering problem by an impenetrable obstacle in two dimensions. To formulate the problem on a bounded domain, a Dirichlet-toNeumann (DtN) boundary condition is proposed on the outer boundary by truncating the Fourier series of the original DtN mapping into finite terms. Assuming the truncation order $N≥kR$, where $k$ is the wave number and $R$ is the radius of the outer boundary, then the $H^j$ -stabilities, $j = 0,1,2$, are established for both original and dual problems, with explicit and sharp estimates of the upper bounds with respect to $k$. Moreover, we prove that, when $N≥λkR$ for some $λ>1$, the solution to the DtN-truncation problem converges exponentially to the original scattering problem as $N$ increases. Under the condition that $k^3h^2$ is sufficiently small, we prove that the preasymptotic error estimates for the linear CIP-FEM as well as the linear FEM are $C_1 kh+C_2 k^3h^2$. Numerical experiments are presented to validate the theoretical results. 

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