The inverse problem considered in this paper is to determine the shape and the impedance of crack from a knowledge of the time-harmonic incident field and the corresponding far field pattern of the scattered waves in ...The inverse problem considered in this paper is to determine the shape and the impedance of crack from a knowledge of the time-harmonic incident field and the corresponding far field pattern of the scattered waves in two-dimension.The combined single-and double-layer potential is used to approach the scattered waves.As an important feature,this method does not require the solution of u and δu/δv at each iteration.An approximate method is presented and the convergence of this method is proven.Numerical examples are given to show that this method is both accurate and simple to use.展开更多
The inverse problem considered in this paper is to determine the shape and the impedance of an obstacle from a knowledge of the time-harmonic incident field and the phase and amplitude of the far field pattern of the ...The inverse problem considered in this paper is to determine the shape and the impedance of an obstacle from a knowledge of the time-harmonic incident field and the phase and amplitude of the far field pattern of the scattered wave in two-dimension. Single-layer potential is used to approach the scattered waves. An approximation method is presented and the convergence of the proposed method is established. Numerical examples are given to show that this method is both accurate and easy to use.展开更多
We prove that a ball with the impedance boundary condition is uniquely determined by the far-field pattern corresponding to an incident plane wave at one given wavenumber and one given incident direction. In the uniqu...We prove that a ball with the impedance boundary condition is uniquely determined by the far-field pattern corresponding to an incident plane wave at one given wavenumber and one given incident direction. In the uniqueness proof, the impedance parameter in the impedance boundary condition is unknown.展开更多
We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the f...We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the first part,we obtain the well-posedness of the direct scattering problem by the variational method.In the second part,we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity,and the shape of the external obstacle,however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.展开更多
We briefly introduce the applications of the inverse scattering method to some particular class of problems,which yield the exact solution or long time asymptotics in terms of the unique solution of a matrix Riemann-H...We briefly introduce the applications of the inverse scattering method to some particular class of problems,which yield the exact solution or long time asymptotics in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the complex plane.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11101323)the Special Research Programs of ShaanXi Education Office(Grant No.09JK771,11JK1070).
文摘The inverse problem considered in this paper is to determine the shape and the impedance of crack from a knowledge of the time-harmonic incident field and the corresponding far field pattern of the scattered waves in two-dimension.The combined single-and double-layer potential is used to approach the scattered waves.As an important feature,this method does not require the solution of u and δu/δv at each iteration.An approximate method is presented and the convergence of this method is proven.Numerical examples are given to show that this method is both accurate and simple to use.
文摘The inverse problem considered in this paper is to determine the shape and the impedance of an obstacle from a knowledge of the time-harmonic incident field and the phase and amplitude of the far field pattern of the scattered wave in two-dimension. Single-layer potential is used to approach the scattered waves. An approximation method is presented and the convergence of the proposed method is established. Numerical examples are given to show that this method is both accurate and easy to use.
基金Guangdong Natural Science Foundation(2016A030313074)of China
文摘We prove that a ball with the impedance boundary condition is uniquely determined by the far-field pattern corresponding to an incident plane wave at one given wavenumber and one given incident direction. In the uniqueness proof, the impedance parameter in the impedance boundary condition is unknown.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China(2019D01A05)supported by the NSFC(11571132)。
文摘We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the first part,we obtain the well-posedness of the direct scattering problem by the variational method.In the second part,we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity,and the shape of the external obstacle,however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.
文摘We briefly introduce the applications of the inverse scattering method to some particular class of problems,which yield the exact solution or long time asymptotics in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the complex plane.
