Local nonreflecting boundary condition for time-dependent multiple scattering (original) (raw)

Nonreflecting boundary condition for time-dependent multiple scattering

Journal of Computational Physics, 2007

An exact nonreflecting boundary condition (NBC) is derived for the numerical solution of time-dependent multiple scattering problems in three space dimensions, where the scatterer consists of several disjoint components. Because each sub-scatterer can be enclosed by a separate artificial boundary, the computational effort is greatly reduced and becomes independent of the relative distances between the different sub-domains. In fact, the computational work due to the NBC only requires a fraction of the computational work inside X, due to any standard finite difference or finite element method, independently of the mesh size or the desired overall accuracy. Therefore, the overall numerical scheme retains the rate of convergence of the interior scheme without increasing the complexity of the total computational work. Moreover, the extra storage required depends only on the geometry and not on the final time. Numerical examples show that the NBC for multiple scattering is as accurate as the NBC for a single convex artificial boundary [M.J. Grote, J.B. Keller, Nonreflecting boundary conditions for time-dependent scattering, J. Comput. Phys. 127(1) (1996), 52-65], while being more efficient due to the reduced size of the computational domain.

Nonreflecting Boundary Conditions for Time-Dependent Scattering

Journal of Computational Physics, 1996

We describe a new, efficient approach to the imposition of exact nonreflecting boundary conditions for the scalar wave equation. We compare the performance of our approach with that of existing methods by coupling the boundary conditions to finite-difference schemes. Numerical experiments demonstrate a significant gain in accuracy at no additional cost.

Local and Nonlocal Nonreflecting Boundary Conditions for Electromagnetic Scattering

Springer eBooks, 2008

An exact nonre ecting boundary condition was derived previously for use with the time dependent Maxwell equations in three space dimensions 1. Here it is shown how to combine that boundary condition with the variational formulation for use with the nite element method. The fundamental theory underlying the derivation of the exact boundarycondition is reviewed. Numerical examples with the nite-di erence timedomain method are presented which demonstrate the high accuracy and con rm the expected rate of convergence of the numerical method.

Dirichlet-to-Neumann boundary conditions for multiple scattering problems

Journal of Computational Physics, 2004

A Dirichlet-to-Neumann (DtN) condition is derived for the numerical solution of time-harmonic multiple scattering problems, where the scatterer consists of several disjoint components. It is obtained by combining contributions from multiple purely outgoing wave fields. The DtN condition yields an exact nonreflecting boundary condition for the situation, where the computational domain and its exterior artificial boundary consist of several disjoint components. Because each sub-scatterer can be enclosed by a separate artificial boundary, the computational effort is greatly reduced and becomes independent of the relative distances between the different sub-domains.

On local nonreflecting boundary conditions for time dependent wave propagation

Chinese Annals of Mathematics, Series B, 2009

The simulation of wave phenomena in unbounded domains generally requires an artificial boundary to truncate the unbounded exterior and limit the computation to a finite region. At the artificial boundary a boundary condition is then needed, which allows the propagating waves to exit the computational domain without spurious reflection. In 1977, Engquist and Majda proposed the first hierarchy of absorbing boundary conditions, which allows a systematic reduction of spurious reflection without moving the artificial boundary farther away from the scatterer. Their pioneering work, which initiated an entire research area, is reviewed here from a modern perspective. Recent developments such as high-order local conditions and their extension to multiple scattering are also presented. Finally, the accuracy of high-order local conditions is demonstrated through numerical experiments.

Nonreflecting boundary conditions for time dependent wave propagation

2000

of the ordinary differential equation which occurs in the boundary condition. An exact nonreflecting boundary condition was derived previously for use with the time dependent wave equation in three Finally, we shall solve a sequence of scattering problems space dimensions. Here it is shown how to combine that boundary by using an explicit finite difference method and our condition with finite difference methods and finite element methboundary condition. We shall also solve the same problems ods. Uniqueness of the solution is proved, stability issues are disby using two of the standard artificial boundary conditions. cussed, and improvements are proposed for numerical computa-Comparison of these solutions with the ''exact'' solution, tion. Numerical examples are presented which demonstrate the improvement in accuracy over standard methods. ᮊ 1996 Academic obtained by computing in a very large domain so that Press, Inc. spurious reflections are postponed, shows that our boundary condition is much more accurate than the standard ones. Our boundary condition also has the advantage that

Non-reflecting boundary conditions for electromagnetic scattering

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 2000

The DtN nonreflecting boundary condition for multiple scattering problems in the half-plane

Computer Methods in Applied Mechanics and Engineering, 2012

The multiple-Dirichlet-to-Neumann (multiple-DtN) non-reflecting boundary condition is adapted to acoustic scattering from obstacles embedded in the half-plane. The multiple-DtN map is coupled with the method of images as an alternative model for multiple acoustic scattering in the presence of acoustically soft and hard plane boundaries. As opposed to the current practice of enclosing all obstacles with a large semicircular artificial boundary that contains portion of the plane boundary, the proposed technique uses small artificial circular boundaries that only enclose the immediate vicinity of each obstacle in the half-plane. The adapted multiple-DtN condition is simultaneously imposed in each of the artificial circular boundaries. As a result the computational effort is significantly reduced. A computationally advantageous boundary value problem is numerically solved with a finite difference method supported on boundary-fitted grids. Approximate solutions to problems involving two scatterers of arbitrary geometry are presented. The proposed numerical method is validated by comparing the approximate and exact far-field patterns for the scattering from a single and from two circular obstacles in the half-plane.

Local solutions to high frequency 2D scattering problems

2008

We consider the solution of high-frequency scattering problems in two dimensions, modelled by an integral equation on the boundary of the scattering object. We devise a numerical method to obtain solutions on only parts of the boundary with little computational effort. The method incorporates asymptotic properties of the solution and can therefore attain particularly good results for high frequencies. Potential uses of such partial solutions for non-convex objects and multiple scattering configurations are presented and a brief error analysis is included. We show that in the simplest implementation of the method the integral equation reduces to an ordinary differential equation.

Local nonreflecting boundary condition for time-dependent multiple scattering (original) (raw)

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