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.
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.
A high-order accurate pseudospectral frequency-domain (PSFD) method is used to analyze light scattering by plasmonic cylinders. Field coupling and enhancement within the gap of close spaced cylinders are examined. Die...
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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 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.
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
Large-scale scientific computations are often organized as a composition of many computational tasks linked through data flow. After the completion of a computationalscientific experiment, a scientist has to analyze ...
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Reconstruction of unknown medium characteristics such as shape, refractive index by measurements of scattered acoustic wave data has wide application in nondestructive detection for engineering and medical use, which ...
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Reconstruction of unknown medium characteristics such as shape, refractive index by measurements of scattered acoustic wave data has wide application in nondestructive detection for engineering and medical use, which is a typical nonlinear and severely ill-posed problem. Under the setting of a smooth background containing a small number of unknown small inhomogeneous inclusions, we propose in this paper an efficient algorithm to reconstruct these inhomogeneities from scattered wave measurement data incited by a single-frequency acoustic wave. The proposed algorithm includes a modified treatment of quadrature rule for the singular kernel in the fundamental solution of Helmholtz equation, which enables a more accurate evaluation of the simulated total field. Numerical experiments validate the effectiveness and robustness of this algorithm in reconstructing small inhomogeneous medium in two dimensions.
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.
We prove existence and uniqueness of the global solution to the Cauchy problem on a universe fireworks model with finite total mass at the initial state when the ratio of the mass surviving the explosion, the probabil...
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We prove existence and uniqueness of the global solution to the Cauchy problem on a universe fireworks model with finite total mass at the initial state when the ratio of the mass surviving the explosion, the probability of the explosion of fragments and the probability function of the velocity change of a surviving particle satisfy the corresponding physical conditions. Although the nonrelativistic Boltzmann-like equation modeling the universe fireworks is mathematically easy, this article leads rather theoretically to an understanding of how to construct contractive mappings in a Banach space for the proof of the existence and uniqueness of the solution by means of methods taken from the famous work by DiPerna ＆ Lions about the Boltzmann equation. We also show both the regularity and the time-asymptotic behavior of solution to the Cauchy problem.
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