一类可直接化为累次积分的曲面积分

本文给出柱面、旋转曲面的曲面积分直接化为定积分和曲线积分二次积分的方法,从而简化了此类曲面积分的计算。     

曲线曲面积分中利用对称性及曲线曲面方程化简

证明了曲线曲面积分中有关对称性的两个命题,并举例说明了命题结论在一些特殊类型曲线曲面积分计算中的应用.还探讨了在对坐标的曲线积分及曲面积分中利用曲线方程或曲面方程化简的问题.     

关于重积分与线面积分内容体系的探讨

本文将二重积分、三重积分、第一类曲线积分及第一类曲面积分统一为多元数量值函数的积分，并且用第一类曲线、曲面积分定义第二类曲线、曲面积分。     

正交变换在曲线,曲面积分计算中的应用

正交变换在曲线、曲面积分计算中的应用林元重（江西萍乡高等专科学校３３７０５５）对于三维空间的曲线积分与曲面积分，如果知道其积分曲线或积分曲面的参数形式，一般可按数学分析教材所介绍的公式计算．但是，对于某些曲线、曲面积分，要把积分曲线或曲面用适当的参数...     

旋转曲面面积的曲线积分表示

利用旋转曲面方程,以及曲面积分和曲线积分的计算方法,可将旋转曲面的面积通过第一型曲线积分表示出来并进行计算.     

关于重积分与线面积分内容体系的探讨

本文将二重积分、三重积分、第一类曲线积分及第一类曲面积分统一为多元数量值函数的积分，并且用第一类曲线、曲面积分定义第二类曲线、曲面积分．     

曲面积分的参数矢量表示式及其应用

曲面积分的参数矢量表示式及其应用郭洪芝，陈荣胜（天津大学）曲面积分的参数矢量表示式不仅在场论中有着比较广泛地应用，而且它对简化曲面积分的计算，特别是当曲面积分的积分域为圆柱面或球面时。掌握并运用参数矢量表示式去计算曲面积分，往往比通常所采用的基本计算...     

一类曲面积分的简单计算与推广

第一类曲面积分的积分表达式具有如下特点时:(1)积分曲面是可求曲面面积的曲面;(2)被积函数是单变量函数或可化为单变量函数的函数,利用积分元素法,能将其直接化为定积分计算,这种简单的算法还可以推广到计算具有类似特征的三重积分.     

基于结构特征的第二类曲面积分的计算

本文归纳总结了一类具有结构特征的第二类曲面积分的计算方法，旨在帮助学生深入理解曲面积分.     

对称性及其在曲面积分计算中的应用

讨论了曲面积分中的奇偶对称性和轮换对称性问题,并通过具体例子说明了对称性在曲面积分计算中的作用.     

基于球坐标计算第一型曲面积分注记

给出了利用球坐标求解第一型曲面积分的方法及在球坐标系下第一型曲面积分转化为二重积分的公式,实例表明这种方法是可行的.此研究丰富了第一型曲面积分的计算方法,也可为在高校《高等数学》课程教学中对学生能力的培养提供素材.     

曲线积分在曲面积分中的应用

提出用曲线积分解决投影为曲线的一类曲面积分的方法 ,证明了方法的可行性 .并通过实例表明该方法在解决问题时所带来的方便 .     

Convergence of the piecewise linear approximation and collocation method for a hypersingular integral equation on a closed surface

We study the numerical solution of a linear hypersingular integral equation arising when solving the Neumann boundary value problem for the Laplace equation by the boundary integral equation method with the solution represented in the form of a double layer potential. The integral in this equation is understood in the sense of Hadamard finite value. We construct quadrature formulas for the integral occurring in this equation based on a triangulation of the surface and an application of the linear approximation to the unknown function on each of the triangles approximating the surface. We prove the uniform convergence of the quadrature formulas at the interpolation nodes as the triangulation size tends to zero. A numerical solution scheme for this integral equation based on the suggested quadrature formulas and the collocation method is constructed. Under additional assumptions about the shape of the surface, we prove a uniform estimate for the error in the numerical solution at the interpolation nodes.     

一类曲面积分的解法

本文对定义在柱面上的一类函数给出了用定积分求曲面积分的方法 ,并证明了方法的可行性 .     

Convergence of a numerical scheme of the type of the vortex loop method on a closed surface with an approximation to the surface shape

We consider a linear integral equation with a hypersingular integral treated in the sense of the Hadamard finite value. This equation arises when solving the Neumann boundary value problem for the Laplace equation with the use of the representation of the solution in the form of a double layer potential. We study the case in which an exterior or interior boundary value problem is solved in a domain whose boundary is a smooth closed surface and the integral equation is written out on that surface. For the numerical solution of the integral equation, the surface is approximated by spatial polygons whose vertices lie on the surface. We construct a numerical scheme for solving the integral equation on the basis of such an approximation to the surface with the use of quadrature formulas of the type of the method of discrete singularities with regularization. We prove that the numerical solutions converge to the exact solution of the hypersingular integral equation uniformly on the grid.     

A boundary integral equation method for three-dimensional crack problems in elasticity

This paper presents a solution procedure for three-dimensional crack problems via first kind boundary integral equations on the crack surface. The Dirichlet (Neumann) problem is reduced to a system of integral equations for the jump of the traction (of the field) across the crack surface. The calculus of pseudodifferential operators is used to derive existence and regularity of the solutions of the integral equations. With the concept of the principal symbol and the Wiener-Hopf technique we derive the explicit behavior of the densities of the integral equations near the edge of the crack surface. Based on the detailed regularity results we show how to improve the boundary element Galerkin method for our integral equations. Quasi-optimal asymptotic estimates for the Galerkin error are given.     

Numerical methods for some inverse problems of heart electrophysiology

We consider numerical methods for solving inverse problems that arise in heart electrophysiology. The first inverse problem is the Cauchy problem for the Laplace equation. Its solution algorithm is based on the Tikhonov regularization method and the method of boundary integral equations. The second inverse problem is the problem of finding the discontinuity surface of the coefficient of conductivity of a medium on the basis of the potential and its normal derivative given on the exterior surface. For its numerical solution, we suggest a method based on the method of boundary integral equations and the assumption on a special representation of the unknown surface.     

求解平片裂纹问题的有限部积分与边界元法

本文利用位移的Somigliana公式和有限部积分的概念,导出了求解三维弹性力学中的任意形状平片裂纹问题的超奇异积分方程组,进而联合使用有限部积分法与边界元法对所得方程建立了数值法.为验证本文的方法,计算了若干数值例子的裂纹面的位移间断及裂纹前沿的应力强度因子,它们与理论值相比符合很好.     

Nyström discretization of parabolic boundary integral equations

A Nyström method for the discretization of thermal layer potentials is proposed and analyzed. The method is based on considering the potentials as generalized Abel integral operators in time, where the kernel is a time dependent surface integral operator. The time discretization is the trapezoidal rule with a corrected weight at the endpoint to compensate for singularities of the integrand. The spatial discretization is a standard quadrature rule for surface integrals of smooth functions. We will discuss stability and convergence results of this discretization scheme for second-kind boundary integral equations of the heat equation. The method is explicit, does not require the computation of influence coefficients, and can be combined easily with recently developed fast heat solvers.     

The well‐posedness of the electric field integral equation for transient scattering from a perfectly conducting body

We consider the scattering of a transient electromagnetic field incident on a body with a smooth, perfectly conducting surface. A standard numerical method for calculating the scattered field is to use a time dependent, surface integral equation (called the electric field integral equation) to calculate the surface currents and charges induced by the incident field—these currents and charges then yield the scattered fields by means of standard integral representations (vector and scalar potentials). In this paper we show that the time‐dependent electric field integral equation is well‐posed in a suitable function space setting. We also investigate the behaviour of the solutions at large time. Copyright © 1999 John Wiley & Sons, Ltd.