We introduce Integral Curve Coordinates, which identify each point in a bounded domain with a parameter along an integral curve of the gradient of a function f on that domain; suitable functions have exactly one critical point, a maximum, in the domain, and the gradient of the function on the boundary points inward. Because every integral curve intersects the boundary exactly once, Integral Cur...

This paper presents a new uniquely solvable boundary integral equation for computing the conformal mapping, its derivative and its inverse from bounded multiply connected regions onto the five classical canonical slit regions. The integral equation is derived by reformulating the conformal mapping as an adjoint Riemann-Hilbert problem. From the adjoint Riemann-Hilbert problem, we derive a bound...

Elastic boundary eigensolution problems are converted into boundary integral equations by potential theory. The kernels of the boundary integral equations have both the logarithmic and Hilbert singularity simultaneously. We present the mechanical quadrature methods for solving eigensolutions of the boundary integral equations by dealing with two kinds of singularities at the same time. The meth...

With the conventional BEM, a significant analytical step is taken at the outset, and this involves only the simplest Green's functions. The result is a representation integral for desired fields in terms of boundary values of the fields. This result is obtained before elements and approximations of any kind are introduced. Unfortunately, when only the simplest Green's functions are used, about ...

Fractional differential equations arise in various fields of science and engineering such as rheology, fluid flows, electrical networks, viscoelasticity, chemical physics, biosciences, signal processing, systems control theory, electrochemistry, mechanics and diffusion processes. Fractional differential equations also serve as an excellent tool for the description of hereditary properties of va...

The paper provides boundary integral equations for solving the problem of viscous scattering of a pressure wave by a rigid body. By using this mathematical tool uniqueness and existence theorems are proved. Since the boundary conditions are written in terms of velocities, vector boundary integral equations are obtained for solving the problem. The paper introduces single-layer viscous potential...

In this paper several methods of dealing with Cauchy Principal Value integrals in advanced boundary element methods are discussed and compared. An attempt is made to present a comprehensive description of these methods in a unified, systematic manner. It is shown that the methods can be grouped into two basic approaches, the (more classical) indirect approach, such as the rigid-body motion tech...

Suppose L is a differential operator of order k. Moreover, let u be a function defined and k times continuously differentiable in the closure of a domain Ω of R. Provided the adjoint differential operator possesses a fundamental solution, we shall see that u can be recovered from Lu and the boundary values of u. Strictly speaking, we shall get an integral representation of u in form of the sum ...

This paper deals with a general framework for a posteriori error estimates in boundary element methods which is specified for three examples, namely Symm's integral equation, an integral equation with a hypersingular operator, and a boundary integral equation for a transmission problem. Based on these estimates, an analog of Eriksson and Johnson's adaptive finite element method is proposed for ...

in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...