In this work, we propose an hN adaptive algorithm for optimal control problems whose space discretization is based on the spectral element method. We focus on a special class of problems described by quadratic cost fu...
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we present a new flexible alignment method to align two or more similar images, especially biological images. By minimizing an energy functional measuring the difference of the initial image and target image, an L...
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we present a new flexible alignment method to align two or more similar images, especially biological images. By minimizing an energy functional measuring the difference of the initial image and target image, an L2 -gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in the temporal direction. Multi-resolution representations are used for achieving efficient multi-scale alignment The experimental results on 2D images show that the proposed method is efficient, effective, robust and capable of capturing the variation of the initial and target images, from large to small scale.
作者：
L. YuanL. ZhangaLSEC
Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China bSchool of Science
China University of Mining and Technology (Beijing) Beijing 100083 China
We apply a Runge‐Kutta discontinuous Galerkin (RKDG) method to numerical solution of the reactive Euler equations. In order to keep conservation naturally, Taylor basis functions are utilized. We construct a new Tayl...
We apply a Runge‐Kutta discontinuous Galerkin (RKDG) method to numerical solution of the reactive Euler equations. In order to keep conservation naturally, Taylor basis functions are utilized. We construct a new Taylor basis function which has smaller numerical error than previous Taylor basis function when the TVD limiter is used. The program is written with MPI for parallel computation. Numerical results of two‐dimensional unstable detonation waves demonstrate that the resulting RKDG method performs well in resolving detonation wave structures. Load imbalance due to different stiffness in different subzones is discussed.
In this paper,a two-scale finite element approach is proposed and analyzed for approximationsof Green's function in *** approach is based on a two-scale finite elementspace defined,respectively,on the whole domain...
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In this paper,a two-scale finite element approach is proposed and analyzed for approximationsof Green's function in *** approach is based on a two-scale finite elementspace defined,respectively,on the whole domain with size H and on some subdomain containing singularpoints with size h (h << H).It is shown that this two-scale discretization approach is very *** particular,the two-scale discretization approach is applied to solve Poisson-Boltzmann equationssuccessfully.
作者：
Kong LinghuaHong JialinZhang JingjingSchool of Mathematics and Information Science
Jiangxi Normal UniversityNanchang Jiangxi 330022 China Institute of Computational Mathematics and Scientific/Engineering Computing AMSS CAS P.O.Box 2719 Beijing 100190 China School of Mathematics and Information Science Henan Polytechnic University Jiaozuo Henan 454000 China
We prove that the error estimates of a large class of nonconforming finite elements are dominated by their approximation errors, which means that the well-known Cea’s lemma is still valid for these nonconforming fini...
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We prove that the error estimates of a large class of nonconforming finite elements are dominated by their approximation errors, which means that the well-known Cea’s lemma is still valid for these nonconforming finite element methods. Furthermore, we derive the error estimates in both energy and L2 norms under the regularity assumption u ∈ H1+s(Ω) with any s > 0. The extensions to other related problems are possible.
The two-sided rank-one (TR1) update method was introduced by Griewank and Walther (2002) for solving nonlinear equations. It generates dense approximations of the Jacobian and thus is not applicable to large-scale spa...
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The two-sided rank-one (TR1) update method was introduced by Griewank and Walther (2002) for solving nonlinear equations. It generates dense approximations of the Jacobian and thus is not applicable to large-scale sparse problems. To overcome this difficulty, we propose sparse extensions of the TR1 update and give some convergence analysis. The numerical experiments show that some of our extensions are superior to the TR1 update method. Some convergence analysis is also presented.
The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplecticFourier spectral (MSFS) methods will be employed to solve the fourth-orderSchrodinger equations with trapped term. Using the idea of split-step numer...
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The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplecticFourier spectral (MSFS) methods will be employed to solve the fourth-orderSchrodinger equations with trapped term. Using the idea of split-step numericalmethod and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventionalmulti-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.
When large sparse symmetric systems of linear equations are solved by the Cholesky factorization, nonzero elements can be generated at positions where the original matrix contains zero elements. This phenomenon is cal...
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When large sparse symmetric systems of linear equations are solved by the Cholesky factorization, nonzero elements can be generated at positions where the original matrix contains zero elements. This phenomenon is called fill-in and it is often crucial in large-scale problems. The symbolic Cholesky factorization solely takes into account the nonzero structure of a sparse matrix to determine the nonzero structure of its Cholesky factor. Sequences of elimination graphs are typically used to model this combinatorial problem. We propose an interactive educational module to visualize and explore the symbolic Cholesky factorization in terms of both elimination graphs and matrix representation. We describe the design and implementation of this interactive module that is intended to be used in a face-to-face learning environment.
In this paper, we present a new flexible alignment method to align two or more similar images. By minimizing an energy functional measuring the difference of the initial image and target image, a L2-gradient flow is d...
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