共查询到20条相似文献,搜索用时 31 毫秒
1.
《Journal of computational physics》2008,227(2):1046-1074
This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green’s functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green’s functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GMRES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong. 相似文献
2.
This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green’s functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green’s functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GMRES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong. 相似文献
3.
We present a novel compression algorithm for 2D scientific data
and images based on exponentially-convergent adaptive higher-order
finite element methods (FEM). So far, FEM has been used mainly for
the solution of partial differential equations (PDE), but we show
that it can be applied to data and image compression easily. The
adaptive compression algorithm is trivial compared to adaptive FEM
algorithms for PDE since the error estimation step is not present.
The method attains extremely high compression rates and is able to
compress a data set or an image with any prescribed error tolerance.
Compressed data and images are stored in the standard FEM format,
which makes it possible to analyze them using standard PDE
visualization software. Numerical examples are shown. The method is
presented in such a way that it can be understood by readers who may
not be experts of the finite element method. 相似文献
4.
《Journal of computational physics》2006,211(1):1-8
A numerical scheme based on the method of fundamental solutions (MFS) is proposed for the solution of 2D and 3D Stokes equations. The fundamental solutions of the Stokes equations, Stokeslets, are adopted as the sources to obtain flow field solutions. The present method is validated through other numerical schemes for lid-driven flows in a square cavity and a cubic cavity. Test results obtained for a rectangular cavity with wave-shaped bottom indicate that the MFS is computationally efficient than the finite element method (FEM) in dealing with irregular shaped domain. The paper also discusses the effects of number of source points and their locations on the numerical accuracy. 相似文献
5.
Ibrahim Yasser Mohamed A. Mohamed Ahmed S. Samra Fahmi Khalifa 《Entropy (Basel, Switzerland)》2020,22(11)
Chaos-based encryption has shown an increasingly important and dominant role in modern multimedia cryptography compared with traditional algorithms. This work proposes novel chaotic-based multimedia encryption schemes utilizing 2D alteration models for high secure data transmission. A novel perturbation-based data encryption for both confusion and diffusion rounds is proposed. Our chaotification structure is hybrid, in which multiple maps are combined combines for media encryption. Blended chaotic maps are used to generate the control parameters for the permutation (shuffling) and diffusion (substitution) structures. The proposed schemes not only maintain great encryption quality reproduced by chaotic, but also possess other advantages, including key sensitivity and low residual clarity. Extensive security and differential analyses documented that the proposed schemes are efficient for secure multimedia transmission as well as the encrypted media possesses resistance to attacks. Additionally, statistical evaluations using well-known metrics for specific media types, show that proposed encryption schemes can acquire low residual intelligibility with excessive nice recovered statistics. Finally, the advantages of the proposed schemes have been highlighted by comparing it against different state-of-the-art algorithms from literature. The comparative performance results documented that our schemes are extra efficacious than their data-specific counterpart methods. 相似文献
6.
Yagawa G 《Proceedings of the Japan Academy. Series B, Physical and biological sciences》2011,87(4):115-134
The finite element method (FEM) has been commonly employed in a variety of fields as a computer simulation method to solve such problems as solid, fluid, electro-magnetic phenomena and so on. However, creation of a quality mesh for the problem domain is a prerequisite when using FEM, which becomes a major part of the cost of a simulation. It is natural that the concept of meshless method has evolved. The free mesh method (FMM) is among the typical meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, especially on parallel processors. FMM is an efficient node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm for the finite element calculations. In this paper, FMM and its variation are reviewed focusing on their fundamental conception, algorithms and accuracy. 相似文献
7.
8.
The Osher–Chakrabarthy family of linear flux-modification schemes is considered. Improved lower bounds on the compression factors are provided, which suggest the viability of using the unlimited version. The LLF flux formula is combined with these schemes in order to obtain efficient finite-difference algorithms. The resulting schemes are applied to a battery of numerical tests, going from advection and Burgers equations to Euler and MHD equations, including the double Mach reflection and the Orszag–Tang 2D vortex problem. Total-variation-bounded (TVB) behavior is evident in all cases, even with time-independent upper bounds. The proposed schemes, however, do not deal properly with compound shocks, arising from non-convex fluxes, as shown by Buckley–Leverett test simulations. 相似文献
9.
L. Zhang J.M. Zhao L.H. Liu S.Y. Wang 《Journal of Quantitative Spectroscopy & Radiative Transfer》2012,113(14):1826-1835
The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J. Coelho, J. Quant. Spectrosc. Radiat. Transf., vol. 93, pp. 89–101, 2005) is extended to solve the radiative heat transfer in two-dimensional absorbing-emitting-scattering graded index media, in which the spatial discretization is carried out using a FVM, while the angular discretization is by a FEM. The FEM angular discretization is demonstrated to be preferable in dealing with the redistribution terms in the GRTE. Two stiff matrix assembly schemes of the angular FEM discretization, namely, the traditional assembly approach and a new spherical assembly approach (assembly on the unit sphere of the solid angular space), are discussed. The spherical assembly scheme is demonstrated to give better results than the traditional assembly approach. The predicted heat flux distributions and temperature distributions in radiative equilibrium are determined by the proposed method and compared with the results available in other references. The proposed hybrid FVM/FEM method can predict the radiative heat transfer in absorbing-emitting-scattering graded index medium with good accuracy. 相似文献
10.
In this paper, the combination of homotopy deform method (HDM) and simplified reproducing kernel method (SRKM) is introduced for solving the boundary value problems (BVPs) of nonlinear differential equations. The solution methodology is based on Adomian decomposition and reproducing kernel method (RKM). By the HDM, the nonlinear equations can be converted into a series of linear BVPs. After that, the simplified reproducing kernel method, which not only facilitates the reproducing kernel but also avoids the time-consuming Schmidt orthogonalization process, is proposed to solve linear equations. Some numerical test problems including ordinary differential equations and partial differential equations are analysed to illustrate the procedure and confirm the performance of the proposed method. The results faithfully reveal that our algorithm is considerably accurate and effective as expected. 相似文献
11.
基于直方图变换的多光谱图像3D SPIHT压缩编码算法 总被引:2,自引:0,他引:2
提出了新的多光谱图像压缩方案,直方图变换的三维分层树的集划分(3D SPIHT)压缩编码算法。基于多光谱图像的成像特点,在去相关之前,提出一种可逆的直方图变换方法对多光谱各波段图像灰度值进行调整,来提高各波段间的相关性,然后再对变换后的图像利用K_L和二维小波变换去除谱间冗余和空间冗余。小波编码采用两种编码方案:3D_SPIHT以及对它进行改进后的三维位平面的SPIHT算法,并对两者进行了比较。实验表明,采用直方图变换的这两种方法都获得了良好的效果,比没变换前有更好的图像质量和压缩性能。 相似文献
12.
Sh. J. Huang 《International Journal of Infrared and Millimeter Waves》2007,28(11):1025-1031
The exponential time differencing (ETD) formultion is proposed for Debye medium using finite-difference time-domain (FDTD)
method. The schemes of the auxiliary differential equation (ADE) and ETD algorithms are presented. The algorithms are validated
by comparing the simulation results with analytical values. The ETD method costs the same memory as the ADE method, and the
numerical results indicate that the ETD technique is more accurate than the ADE method.
This work is supported by the foundation under Grant No. Zl 0502. 相似文献
13.
14.
《Journal of computational physics》2008,227(1):602-632
This paper reports the three-dimensional (3D) generalization of our previous 2D higher-order matched interface and boundary (MIB) method for solving elliptic equations with discontinuous coefficients and non-smooth interfaces. New MIB algorithms that make use of two sets of interface jump conditions are proposed to remove the critical acute angle constraint of our earlier MIB scheme for treating interfaces with sharp geometric singularities, such as sharp edges, sharp wedges and sharp tips. The resulting 3D MIB schemes are of second-order accuracy for arbitrarily complex interfaces with sharp geometric singularities, of fourth-order accuracy for complex interfaces with moderate geometric singularities, and of sixth-order accuracy for curved smooth interfaces. A systematical procedure is introduced to make the MIB matrix optimally symmetric and banded by appropriately choosing auxiliary grid points. Consequently, the new MIB linear algebraic equations can be solved with fewer number of iterations. The proposed MIB method makes use of Cartesian grids, standard finite difference schemes, lowest order interface jump conditions and fictitious values. The interface jump conditions are enforced at each intersecting point of the interface and mesh lines to overcome the staircase phenomena in finite difference approximation. While a pair of fictitious values are determined along a mesh at a time, an iterative procedure is proposed to determine all the required fictitious values for higher-order schemes by repeatedly using the lowest order jump conditions. A variety of MIB techniques are developed to overcome geometric constraints. The essential strategy of the MIB method is to locally reduce a 2D or a 3D interface problem into 1D-like ones. The proposed MIB method is extensively validated in terms of the order of accuracy, the speed of convergence, the number of iterations and CPU time. Numerical experiments are carried out to complex interfaces, including the molecular surfaces of a protein, a missile interface, and van der Waals surfaces of intersecting spheres. 相似文献
15.
In this Letter, approximate solutions of singular two-point boundary value problems (BVPs) are obtained by the modified homotopy analysis methods (MHAM). MHAM provides a convenient way of controlling the convergence region and rate of the series solution. The numerical tests show the capability of MHAM for singular BVPs. 相似文献
16.
为了研究方位电阻率成像仪的定量解释方法,开发了一套能模拟方位电阻率成像仪在三维非均匀地层模拟中响应的三维有限元程序,在简化的地层模型中,将该程序与解析方法和二维有限差分方法进行了对比,结果表明此程序的误差不超过3%,在此程序得到验证后,用该程序考查了方位电阻率成在一些典型三维非均匀地层模型中的响应,结果表明此程序能为方位电阻率成像仪的定量解释提供支持。 相似文献
17.
Abdul-Majid Wazwaz 《Foundations of Physics Letters》2000,13(5):493-498
In this paper we outline a reliable strategy to use Adomian decomposition method properly for solving nonlinear partial differential equations with boundary conditions. Our fundamental goal in this paper has two features: (i) it introduces an efficient way for using Adomian decomposition method for boundary value problems, and (ii) it also would present the framework in a general way so that it may be used in BVPs of the same type. A numerical example is included to dwell upon the importance of the analysis presented. 相似文献
18.
The edge-based smoothed finite element method (ES-FEM) and the face-based smoothed finite element method (FS-FEM) developed recently have shown great efficiency in solving solid mechanics problems with triangular and tetrahedral meshes. In this paper, a coupled ES-/FS-FEM model is extended to solve the structural-acoustic problems consisting of a plate structure interacting with the fluid medium. Three-node triangular elements and four-node tetrahedral elements are used to discretize the two-dimensional (2D) plate and three-dimensional (3D) fluid, respectively, as they can be generated easily and even automatically for complicated geometries. The field variable in each element is approximated using the linear shape functions, which is exactly the same as that in the standard FEM. The gradient field of the problem is obtained particularly using the gradient smoothing operation over the edge-based and face-based smoothing domains in 2D and 3D, respectively. The gradient smoothing technique can provide a proper softening effect to the model, effectively solve the problems caused by the well-known “overly-stiff” phenomenon existing in the standard FEM, and hence significantly improve the accuracy of the solution for the coupled systems. Intensive numerical studies have been conducted to verify the effectiveness of the coupled ES-/FS-FEM for structural-acoustic problems. 相似文献
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20.
S.W. KANG 《Journal of sound and vibration》2002,256(3):533-549
A new approach using the non-dimensional dynamic influence functions has been developed for free vibration analysis of arbitrarily shaped plates with a mixed boundary condition involving both simply supported edges and clamped ones. Since the proposed method is based on the collocation method using one-dimensional and wave-type functions, no integration procedure is needed on boundary edges of the plate of interest and numerical calculation schemes are relatively concise. In order to settle the incompleteness of the system matrix, which is due to the discarding of a complex natural boundary condition at simply supported edges, an additional simple equation is devised by means of using a geometric approximation on curved edges. Finally, verification examples show that a complete system matrix formed in this way successfully gives accurate eigenvalues compared with FEM (ANSYS) and other methods. 相似文献