This paper is concerned with the numerical simulation for shape optimization of the Stokes flow around a solid body. The shape gradient for the shape optimization problem in a viscous incompressible flow is evaluated by the velocity method. The flow is governed by the steady-state Stokes equations coupled with a thermal model. The structure of continuous shape gradient of the cost functional is derived by employing the differentiability of a minimax formulation involving a Lagrange functional with the function space parametrization technique. A gradient-type algorithm is applied to the shape optimization problem. Numerical examples show that our theory is useful for practical purpose, and the proposed algorithm is feasible and effective.

A new absorbing boundary method for diffusive-viscous wave equation(DVW) is proposed to deal with the artificial reflections from boundaries caused by a truncated computational domain in seismic wave numerical modeling.The main idea is to make the seismic waves exponentially attenuate with propagation distance by adding a proper absorbing layer around the boundary of computational domain.The solution of the wave equation in infinite homogenous space is obtained by using Fourier transform.Then,auxiliary equations are constructed by introducing decay functions such that the solution of auxiliary equations is the solution of the DVW equation in computational domain and decays exponentially at boundaries.The wave equation is finally solved by using finite-difference method in both homogeneous media and homogeneous layered media.Numerical results are given through comparison of the results from the proposed method and those of non-absorbing boundary condition,and show that boundary reflections are absorbed with the proposed method.The proposed method is also applicable to acoustic equation and Stokes equation.

Dispersion properties of Rayleigh-type surface waves can be used for imaging and characterizing the shallow subsurface. This paper models Rayleigh waves in complex viscoelastic media by using the time-domain finite difference method on the rotated staggered grid. We compared the dispersion properties of the viscoelastic Rayleigh wave with the elastic one. We proposed a method to model the Rayleigh wave based on the second-order displacement-stress viscoelastic wave equations and the unsplit convolutional perfectly matched layer absorbing boundary condition. The validity of our method is tested by two examples. Then, the wave fields are calculated in a laterally heterogeneous media and a media with cavity. We analyzed the dispersion properties of the Rayleigh waves. The dispersion curve varies considerably with quality factor Q in shallow subsurface; the higher modes of Rayleigh waves are generated and possess significant amounts of energy for strong attenuation.

This paper investigates the first Steklov eigenvalue problem by the method of shape optimization.This first Steklov eigenvalue problem is established in the domain which contains a smooth open subset with its functions vanishing in and the subset is optimized in order to get the first eigenvalue of the Steklov eigenvalue problem.The first order optimality conditions of the corresponding shape optimization problem are established by using the function space parametrization techniques,the continuous conjugated method and the velocity method to describe the perturbation of the domain.Then an appropriate gradient type algorithm is proposed.Finally numerical examples are applied to validate the theory and the efficiency of this proposed algorithm.

This paper is concerned with a shape optimal design problem for a convective heat transfer flow described by the steady-state Stokes equations coupled with a thermal model.The problem consists in minimizing a cost functional which depends on the solution with respect to the domain of the state equations.We calculate the expression of the exact differential for the cost functional by the adjoint state equations,and propose a gradient type algorithm to solve the shape optimal design problem.Numerical examples indicate that our method is efficient and feasible in practical implementations.

In this paper, we use the asymptotic numerical method (ANM) to solve continuation power flow (CPF) problems. ANM can be considered as a higher-order predictor without any corrections. The method has been applied with great success to the areas of fluids, elasticity and structural mechanics. Compared to the general predictor–corrector continuation methods used in power systems, ANM has the following advantages. Firstly, the computation time is smaller. With ANM, the nonlinear problems to be solved are transformed into a recursive sequence of linear systems with the same coefficient matrix, and only one sparse Jacobian matrix factorization is required at each continuation step. Secondly, the computational procedure is automatic. A simple criterion proposed by B. Cochelin et al. can be used to determine the step-length, which makes the continuation easy, and no special step-length control strategy is required. Thirdly, as the solution branch has been expressed into a closed analytical form, the Q-limit points on P–V curves due to reactive power limits violations and other breaking points with the control devices actions can be precisely located with ANM easily. Numerical examples in several power systems were presented to validate the method.

This article considers the time-dependent optimal control problem of tracking the velocity for the viscous incompressible flows which is governed by a Ladyzhenskaya equations with distributed control. The existence of the optimal solution is shown and the first-order optimality condition is established. The semidiscrete-in-time approximation of the optimal control problem is also given. The spatial discretization of the optimal control problem is accomplished by using a new stabilized finite element method which does not need a stabilization parameter or calculation of high order derivatives. Finally a gradient algorithm for the fully discrete optimal control problem is effectively proposed and implemented with some numerical examples. (C) 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 263-287, 2012

This article is concerned with the shape reconstruction for the inviscid fluid governed by the Euler equations. By formulating the domain derivative of the Euler equations and applying a regularized Gauss-Newton iterative algorithm, the numerical examples are given for recovering the shape. The results show that our theory is useful for practical purpose and the proposed algorithm is feasible. (c) 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 587-596, 2012

This paper is concerned with the shape reconstruction of a bounded domain with a viscous incompressible fluid driven by the Oseen equations. For the approximate solution of the ill-posed and nonlinear problem we propose a regularized Gauss–Newton method. A theoretical foundation for the method is given by establishing the differentiability of the boundary value problem with respect to the boundary in the sense of the domain derivative. The results of several numerical experiments show that our theory is useful for practical purpose, and the proposed algorithm is feasible.

This article is concerned about an optimization‐based domain decomposition method for numerical simulation of the incompressible Navier‐Stokes flows. Using the method, an classical domain decomposition problem is transformed into a constrained minimization problem for which the objective functional is chosen to measure the jump in the dependent variables across the common interfaces between subdomains. The Lagrange multiplier rule is used to transform the constrained optimization problem into an unconstrained one and that rule is applied to derive an optimality system from which optimal solutions may be obtained. The optimality system is also derived using “sensitivity” derivatives instead of the Lagrange multiplier rule. We consider a gradient‐type approach to the solution of domain decomposition problem. The results of some numerical experiments are presented to demonstrate the feasibility and applicability of the algorithm developed in this article. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011

In some seismic numerical applications we have to simulate wave propagation with sharp medium discontinuities. The rotated staggered grid (RSG) finite difference (FD) scheme and the arbitrary high-order derivatives discontinuous Galerkin (ADER-DG) finite element (FE) scheme can both be used for the problem of strong material heterogeneities. In this paper we study their behavior in a two-layer model with a varying ratio of the material parameters in the first layer to the second. We compared the results of the numerical schemes with the exact solution. The FD method and the FE method can both get small envelop misfits. The FE scheme has advantage over the FD method on phase misfits, but it needs a high CPU effort.

For a class of Generalized Cubic Bezier(GCB) curves with 3 shape parameters,the relationship between its basis function and quartic Bernstein basis function is deduced.The matrix form of the GCB curve is given.The geometric construction of GCB curve is obtained and the relationship between the GCB curve and classical quartic Bezier curves is established by degree elevation.It has been shown that the main advantage compared to the ordinary Bezier curves is that after inputting a set of control points and values of newly introduced 3 shape parameters,the desired curve can be flexibly chosen from a set of curves which differ either locally or globally by suitably modifying the values of the shape parameters,when the control polygon remains.Some examples illustrate the new curves are very valuable for the design of curves and surfaces.

The Hongjiannao is very important for the ecological environment and the climatic environment nearby. The surface area of the Hongjiannao is decreasing quickly in the last decade. We extract the surface areas of the Hongjiannao in different periods of the past decade from the remote sensing images. In order to predict variation trend of Hongjiannao's area, we fit the data with a line use least square technical. Finally, we analyze the reasons that cause the decreasing and show some severe influence to the ecological environment and the climatic environment nearby if the decreasing keep as this condition.

PreviousNext No AccessSEG Technical Program Expanded Abstracts 2011A new absorbing boundary condition for diffusive‐viscous wave equationAuthors: Haixia ZhaoJinghuai GaoYichen MaBin WengZhenjiang HaoHaixia ZhaoXi'an Jiaotong University.Search for more papers by this author, Jinghuai GaoXi'an Jiaotong University.Search for more papers by this author, Yichen MaXi'an Jiaotong University.Search for more papers by this author, Bin WengChina National Offshore Oil Corporation Research Center.Search for more papers by this author, and Zhenjiang HaoChina National Offshore Oil Corporation Research Center.Search for more papers by this authorhttps://doi.org/10.1190/1.3627823 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Abstract We derive a new governing equation of an absorbing boundary reflection for the diffusive‐viscous wave (DVW) equation which is used to describe seismic wave propagation in fluid‐saturated rocks, the basic idea is to make the seismic waves exponentially attenuate with propagation distance by adding an absorbing layer around the boundary of computational domain, thus achieves the effect of absorbing boundary reflection. Numerical modeling results are given, which show significant absorption and demonstrate the effectiveness of this governing equation.Permalink: https://doi.org/10.1190/1.3627823FiguresReferencesRelatedDetailsCited ByModeling the Propagation of Diffusive-Viscous Waves Using Flux-Corrected Transport–Finite-Difference MethodIEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 7, No. 3Modeling the propagation of diffusive-viscous waves using Flux Corrected Transport-Finite Difference Method SEG Technical Program Expanded Abstracts 2011ISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 2011 Pages: 4424 Publisher:Society of Exploration Geophysicists HistoryPublished: 08 Aug 2011 CITATION INFORMATION Haixia Zhao, Jinghuai Gao, Yichen Ma, Bin Weng, and Zhenjiang Hao, (2011), "A new absorbing boundary condition for diffusive‐viscous wave equation," SEG Technical Program Expanded Abstracts : 3022-3026. https://doi.org/10.1190/1.3627823 Plain-Language Summary PDF DownloadLoading ...

A new formulation for the representation and designing of curves is presented,which can be regarded as a novel generalization of cubic Bezier curves.Firstly,a class of polynomial basis functions with 3 adjustable shape parameters is present.It is a natural extension to classical Bernstein basis functions.The corresponding Bezier curves,the so-called generalized cubic Bezier(GCB)curves,are also constructed and their properties studied.It has been shown that the main advantage compared to the ordinary Bezier curves is that after inputting a set of control points and values of newly introduced 3 shape parameters,the desired curve can be flexibly chosen from a set of curves which differ either locally or globally by suitably modifying the values of the shape parameters,when the control polygon remains.The C2 GCB spline curve is constructed.The resulted curves are locally adjustable.Some examples illustrate the new curves are very valuable for the design of curves and surfaces.

This paper investigates shape optimization of a solid body located in Navier-Stokes flow in two dimensions. The minimization problem of total dissipated energy is established in the fluid domain. The discretization of Navier-Stokes equations is accomplished using a new stabilized finite element method which does not need a stabilization parameter or calculation of high order derivatives. We derive the structures of discrete Eulerian derivative of the cost functional by a discrete adjoint method with a function space parametrization technique. A gradient type optimization algorithm with a mesh adaptation technique and a mesh moving strategy is effectively formulated and implemented.

Principal component analysis (PCA) is a powerful technique for extracting structure from possibly high-dimensional data sets, while kernel PCA (KPCA) is the application of PCA in a kernel-defined feature space. For standard PCA and KPCA, if the size of dataset is large, it will need a very large memory to store kernel matrix and a lot of time to calculate eigenvalues and corresponding eigenvectors. The aim of this paper is to learn linear and nonlinear principal components by using a few partial data points and determine which data points can be used. To verify the performance of the proposed approaches, a series of experiments on artificial datasets and UCI benchmark datasets are accomplished. Simulation results demonstrate that the proposed approaches can compete with or outperform the standard PCA and KPCA in generalization ability but with much less memory and time consuming.

Fictitious domain method shows great advantages when handling problems with complex and constantly varying domains. In this article, we propose an algorithm which extends the fictitious domain method by introducing penalties. Test results with the numerical examples of backward facing step problem and the flow around steady and dynamic cylinder problem show that the algorithm we propose is highly efficient for solving incompressible fluid problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

The shape optimal design for fluid is very important in applications. For a fluid in a region described by a Navier-Stokes equation, our cost fuction is a functional of states of the fluid. Based on the adjoint method and a parametrization method, a formulae of the shape derivatives is established for the problem. Then a conjugate-graduate algorithm is proposed. The numerical examples show the effectiveness and stability of the algorithm.

For the cubic trigonometric polynomial curves with a shape parameter (TB curves, for short), the effects of the shape parameter on the TB curve are made clear, the shape features of the TB curve are analyzed. The necessary and sufficient conditions are derived for these curves having single or double inflection points, a loop or a cusp, or be locally or globally convex. The results are summarized in a shape diagram of TB curves, which is useful when using TB curves for curve and surface modeling. Furthermore the influences of shape parameter on the shape diagram and the ability for adjusting the shape of the curve are shown by graph examples, respectively.