Matsumoto, An application of fast multipole method to isogeometric boundary element method for laplace equation in two dimensions, Eng. Anal. Bound. Elem. 36 (12) (2012) 1766-1775.T. Takahashi, T. Matsumoto, An application of fast multipole method to isogeometric boundary element method for ...
Laplace's equation is reduced to solving two coupled, one-dimensional integral equations. The resulting linear equations are well-conditioned. A program package for solving Laplace's equation has been developed. The package solves Laplace's equation in two dimensions or in three dimensions with ...
5.2 Laplace's Equation As a focus of the new ideas met so far that are to be used in this chapter, the main fundamentals are summarized, using Cartesian coordinates for convenience, as follows: (i) The equation of continuity in two dimensions (incompressible flow) ∂u∂x+∂v∂y=0...
Laplace equation in two dimensions The Laplace equation in two independent variables has the form Analytic functions The real and imaginary parts of a complex analytic function both satisfy the Laplace equation. That is, if z = x + iy,
24.3Laplace’sEquationintwodimensions PhysicalproblemsinwhichLaplace’sequationarises •2DSteady-StateHeatConduction, •StaticDeflectionofaMembrane, •ElectrostaticPotential. u t =α 2 (u xx +u yy )−→u(x,y,t)insideadomainD.(24.4) •Steady-StateSolutionsatisfies: ∆u=u xx +u ...
B. M. Levitan, Expansion with Respect to the Eigenfunctions of a Second-Order Differential Equation [in Russian], Moscow-Leningrad (1950). B. M. Levitan, “On the expansions with respect to the eigenfunctions of the Laplace operator,” Dokl. Akad. Nauk SSSR,90, No. 2, 133–135 (1953...
Although here we solve the Laplace equation in two dimensions, the method is applicable to a more general class of problems. 展开 DOI: 10.1016/0021-9991(90)90060-E 被引量: 69 年份: 1991 收藏 引用 批量引用 报错 分享 全部来源 免费下载 求助全文 全文购买 Elsevier (全网免费下载) Elsevier dx...
equation. Although the Laplace transform is named in honor of Pierre-Simon Laplace, who used the transform in his work on probability theory, the transform was discovered originally by Leonhard Euler, the prolific eighteenth-centurySwissmathematician. The Laplace transform appears in all branches of ...
A new version of the Fast Multipole Method for the Laplace equation in three dimensions We introduce a new version of the Fast Multipole Method for the evaluation of potential fields in three dimensions. It is based on a new diagonal form for ......
However, most of the results are in two dimensions. For the high dimensional case, both theoretical analysis and numerical computation are very difficult. In [9], the authors transfer high dimensional Cauchy problem for Laplace equation into moment problem, and then construct a series of polynomial...