Related papers: Asymptotic analysis for close evaluation of layer …
The double-layer potential plays an important role in solving boundary value problems for elliptic equations. All the fundamental solutions of the generalized bi-axially symmetric Helmholtz equation were known, and only for the first one…
The manuscript describes a quadrature rule that is designed for the high order discretization of boundary integral equations (BIEs) using the Nystr\"{o}m method. The technique is designed for surfaces that can naturally be parameterized…
This is the second of two papers devoted to the asymptotic behavior of solutions to the incompressible Navier-Stokes equations in a half-space with point vortex initial data. A major difficulty stems from the interaction between the point…
A general framework for determining fundamental bounds in nanophotonics is introduced in this paper. The theory is based on convex optimization of dual problems constructed from operators generated by electromagnetic integral equations. The…
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…
Treatment of fields near domain boundaries is a long-standing problem in signal processing that has come into renewed focus following recent efforts in convolution-based multiscale coarse-graining and in machine-learned parameterizations…
In this paper, we investigate single and double layer potentials mapping boundary data to interior functions of a domain at high frequency $\lambda^2\to\infty$. For single layer potentials, we find that the…
A semilinear reaction-diffusion two-point boundary value problem, whose second-order derivative is multiplied by a small positive parameter $\eps^2$, is considered. It can have multiple solutions. An asymptotic expansion is constructed for…
We study the asymptotic diffusion processes with (generally nonlocal) open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be…
A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of…
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…
This paper is concerned with problems of scattering of time-harmonic acoustic waves by a two-layered medium with a non-locally perturbed boundary (called a rough boundary in this paper) in two dimensions, where a Dirichlet or impedance…
The Lagrange mesh method is a very simple procedure to accurately solve eigenvalue problems starting from a given nonrelativistic or semirelativistic two-body Hamiltonian with local or nonlocal potential. We show in this work that it can be…
We develop a finite element method for the Laplace-Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced…
We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the dependance of Neumann eigenvalues of the perturbed Laplacian with…
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…
Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…
For multispecies ions, we study boundary layer solutions of charge conserving Poisson-Boltzmann (CCPB) equations [50] (with a small parameter \k{o}) over a finite one-dimensional (1D) spatial domain, subjected to Robin type boundary…
In terms of layer potential methods, this paper is devoted to study the $L^2$ boundary value problems for nonhomogeneous elliptic operators with rapidly oscillating coefficients in a periodic setting. Under a low regularity assumption on…
The double-layer potential plays an important role in solving boundary value problems for elliptic equations, and in the study of which for a certain equation, the properties of the fundamental solutions of the given equation are used. All…