This paper presents an Euler and boundary-layer method capable of unsteady flow and aeroelastic simulations. An integral boundary-layer solver is coupled with an Euler solver in a “semi-inverse” manner. For the inviscid part, approximate wall boundaryconditions are implemented on non-moving mean chord positions, whereas the full nonlinear Euler equation is solved in the field for accurate resol...

We develop and investigate an integral equation connecting the first passage time distribution of a stochastic process in the presence of an absorbing boundary condition and the corresponding Green's function in the absence of the absorbing boundary. Analytical solutions to the integral equations are obtained for three diffusion processes in time-independent potentials which have been previousl...

A new single surface integral equation is derived for light scattering by circular dielectric cylinders. Without adopting the concept of equivalent electric or magnetic surface currents, our formulation is directly derived from coupled-surface integral equations by the property of commutative matrices of Green functions. Further development by such matrix equations leads to only one unknown fun...

This paper presents a posteriori error estimates for the hp{version of the boundary element method. We discuss two rst kind integral operator equations, namely Symm's integral equation and the integral equation with a hypersingular operator. The computable upper error bounds indicate an algorithm for the automatic hp{adaptive mesh{reenement. The eeciency of this method is shown by numerical exp...

This paper presents a posteriori error estimates for the hp{version of the boundary element method. We discuss two rst kind integral operator equations , namely Symm's integral equation and the integral equation with a hypersingular operator. The computable upper error bounds indicate an algorithm for the automatic hp{adaptive mesh{reenement. The eeciency of this method is shown by numerical ex...

In this paper, we first define the Teodorescu operator [Formula: see text] related to the Helmholtz equation and discuss its properties in quaternion analysis. Then we propose the Riemann boundary value problem related to the Helmholtz equation. Finally we give the integral representation of the boundary value problem by using the previously defined operator.