In this paper we derive boundary integral identities for the bi-Laplacian eigenvalue problems under Dirichlet, Navier and simply-supported boundary conditions. By using these integral identities, we first obtain uniqueness criteria for the solutions of the bi-Laplacian eigenvalue problems, and then prove that each eigenvalue of the problem with simply-supported boundary conditions increases str...

nowadays, combination of gps heights with orthometric heights, derived from precise leveling, is broadly used to obtain point-wise solutions of the geoid, which is called “gps/leveling geoid”. the “gps/leveling geoid” is commonly used to constrain the gravimetric geoid solutions in a least squares surface fitting process. in this paper, unlike the usual application, the “gps/leveling geoid” is ...

Boundary integral equations are a classical tool for the analysis of boundary value problems for partial differential equations. The term “ boundary element method” (BEM) denotes any method for the approximate numerical solution of these boundary integral equations. The approximate solution of the boundary value problem obtained by BEM has the distinguishing feature that it is an exact solution...

The boundary element method (BEM) for linear elasticity in its curent usage is based on the boundary integral equation for displacements. The stress field in the interior of the body is computed by differentiating the displacement field at the source point in the BEM formulation, via the strain field. However, at the boundary, this method gives rise to a hypersingular integral relation which be...

We develop the shape derivative analysis of solutions to the problem of scattering of time-harmonic electromagnetic waves by a bounded penetrable obstacle. Since boundary integral equations are a classical tool to solve electromagnetic scattering problems, we study the shape differentiability properties of the standard electromagnetic boundary integral operators. To this end, we start with the ...

Integral representations are derived from a differential-type boundary value problem using a fundamental solution. A set of integral representations is equivalent to a set of differential equations. If the boundary conditions are substituted into the integral representations, the integral equations are obtained, and the unknown variables are determined by solving the integral equations. In othe...

In the direct boundary integral equation method, boundary-value problems are reduced to integral equations by an application of Green’s theorem to the unknown function and a fundamental solution (Green’s function). Discretization of the integral equation then leads to a boundary element method. This approach was pioneered by Jaswon and his students in the early 1960s. Jaswon’s work is reviewed ...

In this paper,wepresent a parallel higher-order boundary integralmethod to solve the linear Poisson–Boltzmann (PB) equation. In our method, a well-posed boundary integral formulation is used to ensure the fast convergence of Krylov subspace linear solver such as GMRES. The molecular surfaces are first discretized with flat triangles and then converted to curved triangleswith the assistance of n...

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...