共查询到20条相似文献,搜索用时 31 毫秒
1.
Consider the electromagnetic scattering of a time-harmonic plane wave by
an open cavity which is embedded in a perfectly electrically conducting infinite ground
plane. This paper is concerned with the numerical solutions of the transverse electric
and magnetic polarizations of the open cavity scattering problems. In each polarization, the scattering problem is reduced equivalently into a boundary value problem of
the two-dimensional Helmholtz equation in a bounded domain by using the transparent boundary condition (TBC). An a posteriori estimate based adaptive finite element
method with the perfectly matched layer (PML) technique is developed to solve the
reduced problem. The estimate takes account ofboththe finite element approximation
error and the PML truncation error, where the latter is shown to decay exponentially
with respect to the PML medium parameter and the thickness of the PML layer. Numerical experiments are presented and compared with the adaptive finite element TBC
method for both polarizations to illustrate the competitive behavior of the proposed
method. 相似文献
2.
Xue Jiang Peijun Li & Weiying Zheng 《Communications In Computational Physics》2013,13(5):1227-1244
Consider the acoustic wave scattering by an impenetrable obstacle in two dimensions, where the wave propagation is governed by the Helmholtz equation. The scattering problem is modeled as a boundary value problem over a bounded domain. Based on the Dirichlet-to-Neumann (DtN) operator, a transparent boundary condition is introduced on an artificial circular boundary enclosing the obstacle. An adaptive finite element based on a posterior error estimate is presented to solve the boundary value problem with a nonlocal DtN boundary condition. Numerical experiments are included to compare with the perfectly matched layer (PML) method to illustrate the competitive behavior of the proposed adaptive method. 相似文献
3.
Hermann Brunner Hongwei Li & Xiaonan Wu 《Communications In Computational Physics》2013,14(3):574-598
The numerical solution of blow-up problems for nonlinear wave equations on unbounded spatial domains is considered. Applying the unified approach, which is based on the operator splitting method, we construct the efficient nonlinear local absorbing boundary conditions for the nonlinear wave equation, and reduce the nonlinear problem on the unbounded spatial domain to an initial-boundary-value problem on a bounded domain. Then the finite difference method is used to solve the reduced problem on the bounded computational domain. Finally, a broad range of numerical examples are given to demonstrate the effectiveness and accuracy of our method, and some interesting propagation and behaviors of the blow-up problems for nonlinear wave equations are observed. 相似文献
4.
Jiwei Zhang Zhizhong Sun Xiaonan Wu & Desheng Wang 《Communications In Computational Physics》2011,10(3):742-766
The paper is concerned with the numerical solution of Schrödinger equations
on an unbounded spatial domain. High-order absorbing boundary conditions
for one-dimensional domain are derived, and the stability of the reduced initial boundary
value problem in the computational interval is proved by energy estimate. Then a
second order finite difference scheme is proposed, and the convergence of the scheme
is established as well. Finally, numerical examples are reported to confirm our error
estimates of the numerical methods. 相似文献
5.
Split Local Artificial Boundary Conditions for the Two-Dimensional Sine-Gordon Equation on R2
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In this paper the numerical solution of the two-dimensional sine-Gordon
equation is studied. Split local artificial boundary conditions are obtained by the operator
splitting method. Then the original problem is reduced to an initial boundary
value problem on a bounded computational domain, which can be solved by the finite
difference method. Several numerical examples are provided to demonstrate the effectiveness
and accuracy of the proposed method, and some interesting propagation and
collision behaviors of the solitary wave solutions are observed. 相似文献
6.
We introduce the equivalent sources for the Helmholtz equation and establish their connections to the naturally induced sources for the sound-soft, sound-hard, and impedance obstacles for the inverse scattering problems of the Helmholtz equation. As two applications, we employ the naturally induced sources to improve the boundary integral equation formulations for the obstacle scattering problems, and develop a unified, straightforward approach to establishing boundary conditions governing the domain derivatives of scattered waves for the soft, hard, and impedance obstacles. 相似文献
7.
Acoustic Scattering Problems with Convolution Quadrature and the Method of Fundamental Solutions
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Labarca Ignacio & Hiptmair Ralf 《Communications In Computational Physics》2021,30(4):985-1008
Time-domain acoustic scattering problems in two dimensions are studied.
The numerical scheme relies on the use of the Convolution Quadrature (CQ) method
to reduce the time-domain problem to the solution of frequency-domain Helmholtz
equations with complex wavenumbers. These equations are solved with the method
of fundamental solutions (MFS), which approximates the solution by a linear combination of fundamental solutions defined at source points inside (outside) the scatterer for
exterior (interior) problems. Numerical results show that the coupling of both methods
works efficiently and accurately for multistep and multistage based CQ. 相似文献
8.
Analysis and Numerical Solution of Transient Electromagnetic Scattering from Overfilled Cavities
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A hybrid finite element (FEM) and Fourier transform method is implemented to analyze the time domain scattering of a plane wave incident on a 2-D overfilled cavity embedded in the infinite ground plane. The algorithm first removes the
time variable by Fourier transform, through which a frequency domain problem is obtained. An artificial boundary condition is then introduced on a hemisphere enclosing
the cavity that couples the fields from the infinite exterior domain to those inside. The
exterior problem is solved analytically via Fourier series solutions, while the interior
region is solved using finite element method. In the end, the image functions in frequency domain are numerically inverted into the time domain. The perfect link over
the artificial boundary between the FEM approximation in the interior and analytical
solution in the exterior indicates the reliability of the method. A convergence analysis
is also performed. 相似文献
9.
N. Anders Petersson & Bjö rn Sjö green 《Communications In Computational Physics》2009,6(3):483-508
We present an energy absorbing non-reflecting boundary condition of
Clayton-Engquist type for the elastic wave equation together with a discretization
which is stable for any ratio of compressional to shear wave speed. We prove stability
for a second-order accurate finite-difference discretization of the elastic wave equation
in three space dimensions together with a discretization of the proposed non-reflecting
boundary condition. The stability proof is based on a discrete energy estimate and is
valid for heterogeneous materials. The proof includes all six boundaries of the computational
domain where special discretizations are needed at the edges and corners.
The stability proof holds also when a free surface boundary condition is imposed on
some sides of the computational domain. 相似文献
10.
This paper investigates the reduction of backscatter radar cross section (RCS)
for a rectangular cavity embedded in the ground plane. The bottom of the cavity is
coated by a thin, multilayered radar absorbing material (RAM) with possibly different
permittivities. The objective is to minimize the backscatter RCS by the incidence
of a plane wave over a single or a set of incident angles. By formulating the scattering
problem as a Helmholtz equation with artificial boundary condition, the gradient
with respect to the material permittivities is determined efficiently by the adjoint state
method, which is integrated into a nonlinear optimization scheme. Numerical example
shows the RCS may be significantly reduced. 相似文献
11.
Lorella Fatone Maria Cristina Recchioni & Francesco Zirilli 《Communications In Computational Physics》2011,10(3):672-694
Acoustic scattering cross sections of smart furtive obstacles are studied and
discussed. A smart furtive obstacle is an obstacle that, when hit by an incoming field,
avoids detection through the use of a pressure current acting on its boundary. A highly
parallelizable algorithm for computing the acoustic scattering cross section of smart
obstacles is developed. As a case study, this algorithm is applied to the (acoustic)
scattering cross section of a "smart” (furtive) simplified version of the NASA space
shuttle when hit by incoming time-harmonic plane waves, the wavelengths of which
are small compared to the characteristic dimensions of the shuttle. The solution to this
numerically challenging scattering problem requires the solution of systems of linear
equations with many unknowns and equations. Due to the sparsity of these systems
of equations, they can be stored and solved using affordable computing resources. A
cross section analysis of the simplified NASA space shuttle highlights three findings:
i) the smart furtive obstacle reduces the magnitude of its cross section compared to the
cross section of a corresponding "passive” obstacle; ii) several wave propagation directions
fail to satisfactorily respond to the smart strategy of the obstacle; iii) satisfactory
furtive effects along all directions may only be obtained by using a pressure current of
considerable magnitude. Numerical experiments and virtual reality applications can
be found at the website: http://www.ceri.uniroma1.it/ceri/zirilli/w7. 相似文献
12.
Brian C. Fabien 《Optimal control applications & methods.》2014,35(2):204-230
This paper presents an algorithm for the indirect solution of optimal control problems that contain mixed state and control variable inequality constraints. The necessary conditions for optimality lead to an inequality constrained two‐point BVP with index‐1 differential‐algebraic equations (BVP‐DAEs). These BVP‐DAEs are solved using a multiple shooting method where the DAEs are approximated using a single‐step linearly implicit Runge–Kutta (Rosenbrock–Wanner) method. An interior‐point Newton method is used to solve the residual equations associated with the multiple shooting discretization. The elements of the residual equations, and the Jacobian of the residual equations, are constructed in parallel. The search direction for the interior‐point method is computed by solving a sparse bordered almost block diagonal (BABD) linear system. Here, a parallel‐structured orthogonal factorization algorithm is used to solve the BABD system. Examples are presented to illustrate the efficiency of the parallel algorithm. It is shown that an American National Standards Institute C implementation of the parallel algorithm achieves significant speedup with the increase in the number of processors used. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
13.
In this paper, first- and second-order necessary conditions for optimality are studied for a domain optimization problem. The optimization problem considered is the minimization of an objective function defined on the domain boundary through the solution of a boundary value problem. In order to derive the first and second variations of the objective function due to boundary variation, the first and second variations of the solution of the boundary value problem are calculated using a perturbation technique. An iterative shape optimization algorithm for potential flow problems in R2 with Dirichlet boundary conditions is presented. In the algorithm a boundary element method (BEM) is employed to solve the Laplace equation numerically. The validity and accuracy of the algorithm have been verified on a problem where the final solution is known. Finally, the problem of designing a 90° bend for two-dimensional potential flow is solved. 相似文献
14.
Necessary and sufficient conditions of optimality for an optimal control problem with non‐local boundary conditions and quadratic functional
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F. Criado‐Aldeanueva F. Criado N. Odisehlidze J. M. Sanchez 《Optimal control applications & methods.》2014,35(2):231-252
In this paper, the optimal control problem with a quadratic functional for Helmholtz equation with non‐local boundary conditions is considered. Necessary and sufficient conditions of optimality are obtained on the basis of which the existence and uniqueness of a solution to the optimal problem are proved. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
15.
N. Anders Petersson & Bj& ouml rn Sj& ouml green 《Communications In Computational Physics》2014,16(4):913-955
We develop a super-grid modeling technique for solving the elastic wave
equation in semi-bounded two- and three-dimensional spatial domains. In this method,
waves are slowed down and dissipated in sponge layers near the far-field boundaries.
Mathematically, this is equivalent to a coordinate mapping that transforms a very large
physical domain to a significantly smaller computational domain, where the elastic
wave equation is solved numerically on a regular grid. To damp out waves that become poorly resolved because of the coordinate mapping, a high order artificial dissipation operator is added in layers near the boundaries of the computational domain.
We prove by energy estimates that the super-grid modeling leads to a stable numerical
method with decreasing energy, which is valid for heterogeneous material properties
and a free surface boundary condition on one side of the domain. Our spatial discretization is based on a fourth order accurate finite difference method, which satisfies
the principle of summation by parts. We show that the discrete energy estimate holds
also when a centered finite difference stencil is combined with homogeneous Dirichlet conditions at several ghost points outside of the far-field boundaries. Therefore,
the coefficients in the finite difference stencils need only be boundary modified near
the free surface. This allows for improved computational efficiency and significant
simplifications of the implementation of the proposed method in multi-dimensional
domains. Numerical experiments in three space dimensions show that the modeling
error from truncating the domain can be made very small by choosing a sufficiently
wide super-grid damping layer. The numerical accuracy is first evaluated against analytical solutions of Lamb's problem, where fourth order accuracy is observed with
a sixth order artificial dissipation. We then use successive grid refinements to study
the numerical accuracy in the more complicated motion due to a point moment tensor
source in a regularized layered material. 相似文献
16.
This work proposes a generalized boundary integral method for variable coefficients
elliptic partial differential equations (PDEs), including both boundary value
and interface problems. The method is kernel-free in the sense that there is no need
to know analytical expressions for kernels of the boundary and volume integrals in
the solution of boundary integral equations. Evaluation of a boundary or volume integral
is replaced with interpolation of a Cartesian grid based solution, which satisfies
an equivalent discrete interface problem, while the interface problem is solved by a
fast solver in the Cartesian grid. The computational work involved with the generalized
boundary integral method is essentially linearly proportional to the number
of grid nodes in the domain. This paper gives implementation details for a second-order
version of the kernel-free boundary integral method in two space dimensions
and presents numerical experiments to demonstrate the efficiency and accuracy of
the method for both boundary value and interface problems. The interface problems
demonstrated include those with piecewise constant and large-ratio coefficients and
the heterogeneous interface problem, where the elliptic PDEs on two sides of the interface
are of different types. 相似文献
17.
Transition Operator Approach to Seismic Full-Waveform Inversion in Arbitrary Anisotropic Elastic Media
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Morten Jakobsen Ivan P&scaron enčí k Einar Iversen & Bjø rn Ursin 《Communications In Computational Physics》2020,28(1):297-327
We generalize the existing distorted Born iterative T-matrix (DBIT) method
to seismic full-waveform inversion (FWI) based on the scalar wave equation, so that it
can be used for seismic FWI in arbitrary anisotropic elastic media with variable mass
densities and elastic stiffness tensors. The elastodynamic wave equation for an arbitrary anisotropic heterogeneous medium is represented by an integral equation of
the Lippmann-Schwinger type, with a 9-dimensional wave state (displacement-strain)
vector. We solve this higher-dimensional Lippmann-Schwinger equation using a transition operator formalism used in quantum scattering theory. This allows for domain
decomposition and novel variational estimates. The tensorial nonlinear inverse scattering problem is solved iteratively by using an expression for the Fréchet derivatives
of the scattered wavefield with respect to elastic stiffness tensor fields in terms of modified Green's functions and wave state vectors that are updated after each iteration.
Since the generalized DBIT method is consistent with the Gauss-Newton method, it
incorporates approximate Hessian information that is essential for the reduction of
multi-parameter cross-talk effects. The DBIT method is implemented efficiently using
a variant of the Levenberg-Marquard method, with adaptive selection of the regularization parameter after each iteration. In a series of numerical experiments based
on synthetic waveform data for transversely isotropic media with vertical symmetry
axes, we obtained a very good match between the true and inverted models when
using the traditional Voigt parameterization. This suggests that the effects of cross-talk can be sufficiently reduced by the incorporation of Hessian information and the
use of suitable regularization methods. Since the generalized DBIT method for FWI
in anisotropic elastic media is naturally target-oriented, it may be particularly suitable
for applications to seismic reservoir characterization and monitoring. However, the
theory and method presented here is general. 相似文献
18.
A Two-Scale Asymptotic Analysis of a Time-Harmonic Scattering Problem with a Multi Layered Thin Periodic Domain
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Mounir Tlemcani 《Communications In Computational Physics》2009,6(4):758-776
The scope of this paper is to show how a two-scale asymptotic analysis,
based on a superposition principle, allows us to derive high order approximate boundary
conditions for a scattering problem of a time-harmonic wave by a thin and tangentially
periodic multi-layered domain. The periods are assumed of the same order of the
thickness. New terms like memory effect and variance-covariance ones are observed
contrarily to the laminar case. As a result, optimal error estimates are obtained. 相似文献
19.
A Distributed Control Approach for the Boundary Optimal Control of the Steady MHD Equations
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G. Bornia M. Gunzburger & S. Manservisi 《Communications In Computational Physics》2013,14(3):722-752
A new approach is presented for the boundary optimal control of the MHD equations in which the boundary control problem is transformed into an extended distributed control problem. This can be achieved by considering boundary controls in the form of lifting functions which extend from the boundary into the interior. The optimal solution is then sought by exploring all possible extended functions. This approach gives robustness to the boundary control algorithm which can be solved by standard distributed control techniques over the interior of the domain. 相似文献
20.
A Diagonal Sweeping Domain Decomposition Method with Source Transfer for the Helmholtz Equation
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Wei Leng & Lili Ju 《Communications In Computational Physics》2021,29(2):357-395
In this paper, we propose and test a novel diagonal sweeping domain
decomposition method (DDM) with source transfer for solving the high-frequency
Helmholtz equation in$\mathbb{R}^n$. In the method the computational domain is partitioned into
overlapping checkerboard subdomains for source transfer with the perfectly matched
layer (PML) technique, then a set of diagonal sweeps over the subdomains are specially
designed to solve the system efficiently. The method improves the additive overlapping DDM [43] and the L-sweeps method [50] by employing a more efficient subdomain solving order. We show that the method achieves the exact solution of the global
PML problem with $2^n$ sweeps in the constant medium case. Although the sweeping
usually implies sequential subdomain solves, the number of sequential steps required
for each sweep in the method is only proportional to the $n$-th root of the number of
subdomains when the domain decomposition is quasi-uniform with respect to all directions, thus it is very suitable for parallel computing of the Helmholtz problem with
multiple right-hand sides through the pipeline processing. Extensive numerical experiments in two and three dimensions are presented to demonstrate the effectiveness
and efficiency of the proposed method. 相似文献