Related papers: On the numerical solution of a boundary integral e…
This paper examines the Laplace equation with mixed boundary conditions, the Neumann and Steklov boundary conditions. This models a container with holes in it, like a pond filled with water but partly covered by immovable pieces on the…
In this paper we consider a Robin problem for the Klein-Gordon equation in a doubly connected domain. The solution domain considered is a bounded smooth doubly connected planar domain bounded by two simple disjoint closed curves. The…
We give explicit integral formulas for the solutions of planar conjugate conductivity equations in a circular domain of the right half-plane with conductivity $\sigma(x,y)=x^p$, $p\in\mathbb{Z}$. The representations are obtained via a…
In this paper, we present numerical methods to implement the probabilistic representation of third kind (Robin) boundary problem for the Laplace equations. The solution is based on a Feynman-Kac formula for the Robin problem which employs…
We deal with probabilistic numerical solutions for linear elliptic equations with Neumann boundary conditions in a Lipschitz domain, by using a probabilistic numerical scheme introduced by Milstein and Tretyakov based on new numerical layer…
We study boundary integral formulations for an interior/exterior initial boundary value problem arising from the thermo-elasto-dynamic equations in a homogeneous and isotropic domain. The time dependence is handled, based on Lubich's…
We present an integral equation-based method for the numerical solution of two-point boundary value systems. Special care is devoted to the mathematical formulation, namely the choice of the background Green's function that leads to a…
We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the…
Boundary integral equations are an efficient and accurate tool for the numerical solution of elliptic boundary value problems. The solution is expressed as a layer potential; however, the error in its evaluation grows large near the…
We consider three problems for the Helmholtz equation in interior and exterior domains in R^d (d=2,3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem. We derive…
In this paper, we prove the existence of a classical solution to a Neumann boundary problem for Hessian equations in uniformly convex domain. The methods depend upon the established of a priori derivative estimates up to second order. So we…
In this paper, we present a stochastic method for the simulation of Laplace's equation with a mixed boundary condition in planar domains that are polygonal or bounded by circular arcs. We call this method the Reflected Walk-on-Spheres…
We consider the Dirichlet-to-Neumann mapping and the Neumann problem for the Laplace operator on a torus, given in toroidal coordinates. The Dirichlet-to-Neumann mapping is expressed with respect to series expansions in toroidal harmonics…
A piecewise continuous biharmonic problem in domains with corner points and a corresponding Schwarz type boundary value problem for monogenic functions in a commutative biharmonic algebra are considered. A method for reducing the problems…
A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition…
In Boundary Element Method, Green's function with no boundary conditions is used for solving Laplace's equation with Dirichlet boundary condition. To determine the gradient of solution on the boundary, we need to solve the boundary integral…
A spectral method is described for solving coupled elliptic problems on an interior and an exterior domain. The method is formulated and tested on the two-dimensional interior Poisson and exterior Laplace problems, whose solutions and their…
A non-singular formulation of the boundary integral method (BIM) is presented for the Laplace equation whereby the well-known singularities that arise from the fundamental solution are eliminated analytically. A key advantage of this…
Writing the boundary integral equation for an exterior problem of elasticity is subordinate so far to hypotheses on the asymptotical behaviour at infinity of solutions. The sufficient conditions met in the literature are too restrictive and…
A new transform-based approach is presented that can be used to solve mixed boundary value problems for Laplace's equation in non-convex and other planar domains, specifically the so-called Lipschitz domains. This work complements Crowdy…