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二维三温耦合差分方程组的解法 总被引:3,自引:0,他引:3
针对二维三温耦合热传导差分议程组的特点,给出并比较了块G-S算法与ICCG算法,数值结果表明,ICCG算法的收敛速度比块G-S算法的收敛速度可以快数千倍,并且,在二维激光黑腔靶耦合的数值计算中,如果能够实现向量化计算,使用ICCG方法将会大大提高数值模拟的计算效率。 相似文献
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We describe a method for introducing variations into predefined motion sequences using a chaotic symbol-sequence reordering technique. A progression of symbols representing the body positions in a dance piece, martial arts form, or other motion sequence is mapped onto a chaotic trajectory, establishing a symbolic dynamics that links the movement sequence and the attractor structure. A variation on the original piece is created by generating a trajectory with slightly different initial conditions, inverting the mapping, and using special corpus-based graph-theoretic interpolation schemes to smooth any abrupt transitions. Sensitive dependence guarantees that the variation is different from the original; the attractor structure and the symbolic dynamics guarantee that the two resemble one another in both aesthetic and mathematical senses. (c) 1998 American Institute of Physics. 相似文献
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Long Yuan & Qiya Hu 《advances in applied mathematics and mechanics.》2013,5(6):791-808
An interesting discretization method for Helmholtz equations was
introduced in B. Després [1]. This method is based on the
ultra weak variational formulation (UWVF) and the wave shape
functions, which are exact solutions of the governing Helmholtz
equation. In this paper we are concerned with fast solver for the
system generated by the method in [1]. We propose a new
preconditioner for such system, which can be viewed as a combination
between a coarse solver and the block diagonal preconditioner
introduced in [13]. In our numerical experiments, this
preconditioner is applied to solve both two-dimensional and
three-dimensional Helmholtz equations, and the numerical results
illustrate that the new preconditioner is much more efficient than
the original block diagonal preconditioner. 相似文献
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The mixed boundary value problem of the Laplace equation is considered. The method of fundamental solutions (MFS) approximates the exact solution to the Laplace equation by a linear combination of independent fundamental solutions with different source points. The accuracy of the numerical solution depends on the distribution of source points. In this paper, a weighted greedy QR decomposition (GQRD) is proposed to choose significant source points by introducing a weighting parameter. An index called an average degree of approximation is defined to show the efficiency of the proposed method. From numerical experiments, it is concluded that the numerical solution tends to be more accurate when the average degree of approximation is larger, and that the proposed method can yield more accurate solutions with a less number of source points than the conventional GQRD. 相似文献
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Numerical solution of Helmholtz equation of barotropic atmosphere using wavelets 总被引:1,自引:0,他引:1
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The numerical solution of the Helmholtz equation for barotropic atmosphere is estimated by use of the wavelet-Galerkin method. The solution involves the decomposition of a circulant matrix consisting up of 2-term connection coefficients of wavelet scaling functions. Three matrix decompositions, i.e. fast Fourier transformation (FFT), Jacobian and QR decomposition methods, are tested numerically. The Jacobian method has the smallest matrix-reconstruction error with the best orthogonality while the FFT method causes the biggest errors. Numerical result reveals that the numerical solution of the equation is very sensitive to the decomposition methods, and the QR and Jacobian decomposition methods, whose errors are of the order of 10^{-3}, much smaller than that with the FFT method, are more suitable to the numerical solution of the equation. With the two methods the solutions are also proved to have much higher accuracy than the iteration solution with the finite difference approximation. In addition, the wavelet numerical method is very useful for the solution of a climate model in low resolution. The solution accuracy of the equation may significantly increase with the order of Daubechies wavelet. 相似文献
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A new finite element method for the efficient discretization of elliptic homogenization problems is proposed. These problems, characterized by data varying over a wide range of scales cannot be easily solved by classical numerical methods that need mesh resolution down to the finest scales and multiscale methods capable of capturing the large scale components of the solution on macroscopic meshes are needed. Recently, the finite element heterogeneous multiscale method (FE-HMM) has been proposed for such problems, based on a macroscopic solver with effective data recovered from the solution of micro problems on sampling domains at quadrature points of a macroscopic mesh. Departing from the approach used in the FE-HMM, we show that interpolation techniques based on the reduced basis methodology (an offline-online strategy) allow one to design an efficient numerical method relying only on a small number of accurately computed micro solutions. This new method, called the reduced basis finite element heterogeneous multiscale method (RB-FE-HMM) is significantly more efficient than the FE-HMM for high order macroscopic discretizations and for three-dimensional problems, when the repeated computation of micro problems over the whole computational domain is expensive. A priori error estimates of the RB-FE-HMM are derived. Numerical computations for two and three dimensional problems illustrate the applicability and efficiency of the numerical method. 相似文献
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Sunyoung Bu Jingfang Huang Treavor H. Boyer Cass T. Miller 《Journal of computational physics》2010,229(13):4996-5010
The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC–FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications. 相似文献
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In this paper, we directly extend the
applications of the Adomian decomposition method to investigate the complex KdV equation. By choosing different forms of wave functions as the
initial values, three new types of realistic numerical solutions: numerical
positon, negaton solution, and particularly the numerical analytical
complexiton solution are obtained, which can rapidly converge to the exact
ones obtained by Lou et al. Numerical simulation figures are used
to illustrate the efficiency and accuracy of the proposed method. 相似文献
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Keizo Fujimoto 《Journal of computational physics》2011,230(23):8508-8526
A new electromagnetic particle-in-cell (EMPIC) model with adaptive mesh refinement (AMR) has been developed to achieve high-performance parallel computation in distributed memory system. For minimizing the amount and frequency of inter-processor communications, the present study uses the staggering grid scheme with the charge conservation method, which consists only of the local operations. However, the scheme provides no numerical damping for electromagnetic waves regardless of the wavenumber, which results in significant noise in the refinement region that eventually covers over physical signals. In order to suppress the electromagnetic noise, the present study introduces a smoothing method which gives numerical damping preferentially for short wavelength modes. The test simulations show that only a weak smoothing results in drastic reduction in the noise, so that the implementation of the AMR is possible in the staggering grid scheme. The computational load balance among the processors is maintained by a new method termed the adaptive block technique for the domain decomposition parallelization. The adaptive block technique controls the subdomain (block) structure dynamically associated with the system evolution, such that all the blocks have almost the same number of particles. The performance of the present code is evaluated for the simulations of the current sheet evolution. The test simulations demonstrate that the usage of the adaptive block technique as well as the staggering grid scheme enhances significantly the parallel efficiency of the AMR-EMPIC model. 相似文献
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We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss–Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss–Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources. 相似文献
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L.L. Doskolovich N.L. Kazanskiy S.I. Kharitonov G.V. Uspleniev 《Optics and Lasers in Engineering》1991,15(5):311-322
A new method is investigated for synthesis of computer-generated optical elements: focusators that are able to focus the radial-symmetrical laser beam into complex focal contours, in particular into alphanumeric symbols. The method is based on decomposition of the focal contour into segments of straight lines and semi-circles, following corresponding spacing out of the focusator on elementary segments (concentric rings or sectors) and solution of the inverse task of focusing from focusator segments into corresponding elements of the focal contour. The results of numerical computing of the field from synthesized focusators into the letters are presented. The theoretical efficiency of the focusators discussed is no less than 85%. The amplitude masks and the results of operational studies of synthesized focusators are presented. 相似文献
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采用2维三温非平衡辐射流体力学程序LARED-H数值模拟辐射驱动内爆过程。针对2维三温能量方程九点差分格式离散后的线性方程组,采用了高效的Krysolv子空间迭代解法,改进了代数解法器。将1维间接驱动内爆总体程序CFJ与LARED-H程序的计算结果进行比对,验证了LARED-H程序数值模拟1维内爆问题的正确性。并数值模拟了不同腔长辐射温度源驱动下的2维靶球运动,数值结果显示:随着腔长的增加,高压缩内爆燃料区分别被压缩成香肠形、球形和铁饼形,数值模拟结果与神光Ⅱ的实验结果定性上相同。 相似文献
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Mehmet Senol 《理论物理通讯》2020,72(5):55003-31
In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely BurgersKadomtsev-Petviashvili equation(Burgers-K-P) that arises in shallow water waves.Furthermore, using the residual power series method(RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations. 相似文献
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In this paper, numerical solutions of a reaction-diffusion chemotactic model of fractional orders for bacterial growth will
be present. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. We
compare the experimental result obtained with those obtained by simulation of the chemotactic model without fractional derivatives.
The results show that the solution continuously depends on the time-fractional derivative. The resulting solutions spread
faster than the classical solutions and may exhibit asymmetry, depending on the fractional derivative used. We present results
of numerical simulations to illustrate the method, and investigate properties of numerical solutions. The Adomian’s decomposition
method (ADM) is used to find the approximate solution of fractional ‘reaction-diffusion chemotactic model. Numerical results
show that the approach is easy to implement and accurate when applied to partial differential equations of fractional order. 相似文献