A Plane Wave Discontinuous Galerkin Method with a Dirichlet-to- Neumann Boundary Condition for a Scattering Problem in Acoustics
نویسندگان
چکیده
We consider the numerical solution of an acoustic scattering problem by the Plane Wave Discontinuous Galerkin Method (PWDG) in the exterior of a bounded domain in R2. In order to apply the PWDG method, we introduce an artificial boundary to truncate the domain, and we impose a non-local Dirichlet-to-Neumann (DtN) boundary condition on the artificial curve. To define the method, we introduce new consistent numerical fluxes that incorporate the truncated series of the DtN map. Error estimates with respect to the truncation order of the DtN map, and with respect to mesh width are derived. Numerical results suggest that the accuracy of the PWDG method for the acoustic scattering problem can be significantly improved by using DtN boundary conditions.
منابع مشابه
A plane wave discontinuous Galerkin method with a Dirichlet-to-Neumann boundary condition for the scattering problem in acoustics
We consider the numerical solution of an acoustic scattering problem by the Plane Wave Discontinuous Galerkin Method (PWDG) in the exterior of a bounded domain in R2. In order to apply the PWDG method, we introduce an artificial boundary to truncate the domain, and we impose a non-local Dirichlet-to-Neumann (DtN) boundary conditions on the artificial curve. To define the method, we introduce ne...
متن کاملA Collocation Method with Modified Equilibrium on Line Method for Imposition of Neumann and Robin Boundary Conditions in Acoustics (TECHNICAL NOTE)
A collocation method with the modified equilibrium on line method (ELM) forimposition of Neumann and Robin boundary conditions is presented for solving the two-dimensionalacoustical problems. In the modified ELM, the governing equations are integrated over the lines onthe Neumann (Robin) boundary instead of the Neumann (Robin) boundary condition equations. Inother words, integration domains are...
متن کاملA Neumann series based method for photoacoustic tomography on irregular domains
Recently, a Neumann series based numerical method is developed for photoacoustic tomography in a paper by Qian, Stefanov, Uhlmann, and Zhao [An efficient neumann series-based algorithm for thermoacoustic and photoacoustic tomography with variable sound speed. SIAM J. Imag. Sci., 4:850–883, 2011]. It is an efficient and convergent numerical scheme that recovers the initial condition of an acoust...
متن کاملOn a Uniquely Solvable Integral Equation in a Mixed Dirichlet-neumann Problem of Acoustic Scattering
The mixed Dirichlet-Neumann problem for the Helmholtz equation in the exterior of several bodies (obstacles) is studied in 2 and 3 dimensions. The problem is investigated by a special modification of the boundary integral equation method. This modification can be called the "method of interior boundaries", because additional boundaries are introduced inside scattering bodies, where the Neumann ...
متن کاملImplementation of Sinc-Galerkin on Parabolic Inverse problem with unknown boundary condition
The determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. For solving these ill-posed inverse problems, Galerkin method based on Sinc basis functions for space and time will be used. To solve the system of linear equation, a noise is imposed and Tikhonove regularization is applied. By using a sensor located at a point in the domain of $x$, say $...
متن کامل