We deduce the finite-element acoustic wave equation in the frequency domain. In order to eliminate boundary reflection, the absorbing boundary conditions of Clayton-Engquist paraxial wave equation are introduced to th...
详细信息
We deduce the finite-element acoustic wave equation in the frequency domain. In order to eliminate boundary reflection, the absorbing boundary conditions of Clayton-Engquist paraxial wave equation are introduced to the frequency domain. The finite-element stiffness matrix and mass matrix are compressed for storage. The solutions of forward modeling are obtained by using the generalized conjugate gradient algorithm. On these bases, we deduce the Jacobi matrix representing the relation between the wavefield data residuals δ Ů and the element material-property adjusted values δ λ at a certain frequency. Using the differences δ Ů between the surface 2D shot recorded data and theoretical modelling data, the adjusted values δ λ can be obtained iteratively. Because of the limitation of the computer's storage, larger number of unknowns is not permitted. The measure of compressing and assembling the element Jacobi matrix coefficients in the same medium is also proposed. By using this method, the unknowns' number of inversion is reduced. Combined with the conjugate gradient algorithm, only a few frequencies in valid-wave domain are needed in this inversion. Some numerical examples of the modeling and inversion are given. The effectivity of the method is proved using the results.
作者：
Sadkane, MiloudTouhami, AhmedUniv Brest
CNRS UMR 6205 Lab Math Bretagne Atlantique 6 Av Le Gorgeu F-29238 Brest 3 France Hassan I Univ
Fac Sci & Technol Dept Math & Comp Sci PB 577Route Casablanca Settat Morocco
The ChebFilterCG algorithm, proposed by Golub, Ruiz, and Touhami [SIAM J. Matrix Anal. Appl. 29 (2007), pp. 774-795] is an iterative method that combines Chebyshev filter and conjugategradient for solving symmetric p...
详细信息
The ChebFilterCG algorithm, proposed by Golub, Ruiz, and Touhami [SIAM J. Matrix Anal. Appl. 29 (2007), pp. 774-795] is an iterative method that combines Chebyshev filter and conjugategradient for solving symmetric positive definite linear systems with multiple right-hand sides. The Chebyshev filter is used to produce initial residuals rich in eigenvectors corresponding to the smallest eigenvalues, which are then used in the initial phase of the conjugategradient. This paper presents a convergence analysis of ChebFilterCG. In particular, it is shown theoretically and numerically that the algorithm yields an approximation of the invariant subspace associated with the smallest eigenvalues that can be recycled for solving several linear systems with the same matrix and different right-hand sides. A refined error bound when solving these systems is also given. The choice and influence of the Chebyshev filtering steps is discussed. Numerical experiments are described to illustrate that the Chebyshev filter does not degrade the distribution of the smallest eigenvalues and highlight the effect of rounding errors when large outlying eigenvalues are present. Finally, it is shown that the method may become more effective when an additional Chebyshev filtering step is used in the initialization phase of ChebFilterCG.
With the overwhelming success in the field of quantum computing, much attention has been paid to constructing a quantum neural network by combining a classical neural network with quantum computing. In this paper, we ...
详细信息
With the overwhelming success in the field of quantum computing, much attention has been paid to constructing a quantum neural network by combining a classical neural network with quantum computing. In this paper, we propose a novel quantum neural network model based on a quantum version of the sigmoid function, which skillfully combines the non-linear dissipation dynamics of neural computation with the linear unitary dynamics of quantum computation. Moreover, we also add connections from the input layer to the output layer to increase the non-linear expression ability of the network and the similarity to the human brain's information processing. The specific steps and relevant formulas of the conjugate gradient algorithm in the learning stage of the quantum network parameters are also given in this paper. Finally, the feasibility and properties of the model are demonstrated by MATLAB simulation with a encryption and decryption experiment.
Our work is devoted to a class of optimal control problems of parabolic partial differential equations. Because of the partial differential equations constraints, it is rather difficult to solve the optimization probl...
详细信息
Our work is devoted to a class of optimal control problems of parabolic partial differential equations. Because of the partial differential equations constraints, it is rather difficult to solve the optimization problem. The gradient of the cost function can be found by the adjoint problem approach. Based on the adjoint problem approach, the gradient of cost function is proved to be Lipschitz continuous. An improved conjugate method is applied to solve this optimization problem and this algorithm is proved to be convergent. This method is applied to set-point values in continuous cast secondary cooling zone. Based on the real data in a plant, the simulation experiments show that the method can ensure the steel billet quality. From these experiment results, it is concluded that the improved conjugate gradient algorithm is convergent and the method is effective in optimal control problem of partial differential equations.
The performance of adaptive beamforming techniques is limited by the nonhomogeneous clutter scenario. An augmented Krylov subspace method is proposed, which utilizes only a single snapshot of the data for adaptive pro...
详细信息
The performance of adaptive beamforming techniques is limited by the nonhomogeneous clutter scenario. An augmented Krylov subspace method is proposed, which utilizes only a single snapshot of the data for adaptive processing. The novel algorithm puts together a data preprocessor and adaptive Krylov subspace algorithm, where the data preprocessor suppresses discrete interference and the adaptive Krylov subspace algorithm suppresses homogeneous clutter. The novel method uses a single snapshot of the data received by the array antenna to generate a cancellation matrix that does not contain the signal of interest (SOI) component, thus, it mitigates the problem of highly nonstationary clutter environment and it helps to operate in real-time. The benefit of not requiring the training data comes at the cost of a reduced degree of freedom (DOF) of the system. Simulation illustrates the effectiveness in clutter suppression and adaptive beamforming. The numeric results show good agreement with the proposed theorem.
暂无评论