共查询到7条相似文献,搜索用时 0 毫秒
1.
A. Tadeu C. S. Chen J. Antόnio & Nuno Simõ es 《advances in applied mathematics and mechanics.》2011,3(5):572-585
Fourier transform is applied to remove the time-dependent variable in the
diffusion equation. Under non-harmonic initial conditions this gives rise to a
non-homogeneous Helmholtz equation, which is solved by the method of
fundamental solutions and the method of particular solutions. The particular
solution of Helmholtz equation is available as shown in [4, 15].
The approximate solution in frequency domain is then inverted
numerically using the inverse Fourier transform algorithm. Complex frequencies
are used in order to avoid aliasing phenomena and to allow the computation of
the static response. Two numerical examples are given to illustrate the
effectiveness of the proposed approach for solving 2-D diffusion equations. 相似文献
2.
The Method of Fundamental Solutions for Solving Convection-Diffusion Equations with Variable Coefficients 下载免费PDF全文
A meshless method based on the method of fundamental solutions (MFS)
is proposed to solve the time-dependent partial differential equations with variable
coefficients. The proposed method combines the time discretization and the one-stage
MFS for spatial discretization. In contrast to the traditional two-stage process,
the one-stage MFS approach is capable of solving a broad spectrum of partial differential
equations. The numerical implementation is simple since both closed-form
approximate particular solution and fundamental solution are easier to find than the
traditional approach. The numerical results show that the one-stage approach is
robust and stable. 相似文献
3.
A Practical Algorithm for Determining the Optimal Pseudo-Boundary in the Method of Fundamental Solutions 下载免费PDF全文
A. Karageorghis 《advances in applied mathematics and mechanics.》2009,1(4):510-528
One of the main difficulties in the application of the method of
fundamental solutions (MFS) is the determination of the position of
the pseudo-boundary on which are placed the singularities in terms
of which the approximation is expressed. In this work, we propose a
simple practical algorithm for determining an estimate of the
pseudo-boundary which yields the most accurate MFS approximation
when the method is applied to certain boundary value problems.
Several numerical examples are provided. 相似文献
4.
J. R. Berger & Andreas Karageorghis 《advances in applied mathematics and mechanics.》2013,5(4):423-441
In this paper, we introduce two Galerkin formulations of the Method of Fundamental Solutions (MFS).
In contrast to the collocation formulation of the MFS, the proposed Galerkin formulations involve the evaluation
of integrals over the boundary of the domain under consideration. On the other hand, these formulations lead
to some desirable properties of the stiffness matrix such as symmetry in certain cases. Several numerical examples are considered
by these methods and their various features compared. 相似文献
5.
将局部基本解方法应用于静电场问题的模拟与分析。局部基本解方法是利用控制方程的基本解,基于局部理论和移动最小二乘原理提出的一种无网格算法。相比于有限元和有限差分等传统网格类方法,该方法仅需离散节点,避免了复杂的网格剖分难题。作为一种半解析数值技术,物理问题的基本解被作为插值基函数建立数值离散模型,从而保证了算法的较高精度。此外,与具有全局离散格式的无网格方法相比,局部基本解法更适用于高维复杂几何和大尺度模拟。二维和三维数值试验表明,该方法具有实施方便灵活,计算精度高和计算速度快等优势。为静电场仿真研究开辟新的途径,拓展了局部基本解方法的应用领域。 相似文献
6.
A procedure is described for matching a given stationary axisymmetric perfect fluid solution to a not necessarily asymptotically flat vacuum exterior. Using data on the zero pressure surface, the procedure yields the Ernst potential of the matching vacuum metric on the symmetry axis. From this the full metric can be constructed by established procedures. 相似文献