相关论文: Boundary-integral method for poloidal axisymmetric…
Green's function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs). However, in most cases, Green's function is difficult to compute. The troubles arise in the following…
This paper presents a re-formulation of the boundary integral method (BIM) for the Debye-Huckel model of molecular and colloidal electrostatics that removes the mathematical singularities that have been accepted as an intrinsic part of the…
This paper introduces a novel class of indirect boundary integral equation (BIE) formulations for the solution of electromagnetic scattering problems involving smooth perfectly electric conductors (PECs) in three-dimensions. These…
We analyze the well posedness of certain field-only boundary integral equations (BIE) for frequency domain electromagnetic scattering from perfectly conducting spheres. Starting from the observations that (1) the three components of the…
This work presents an unfitted boundary algebraic equation (BAE) method for solving three-dimensional elliptic partial differential equations on complex geometries using finite difference on structured meshes. We demonstrate that replacing…
In this paper, I develop a boundary element method for axisymmetric acoustic radiation and propagation problems in a subsonic uniform flow. This formulation uses the axisymmetric convected Green's function independent of the flow direction…
This paper introduces a novel boundary integral equation (BIE) method for the numerical solution of problems of planewave scattering by periodic line arrays of two-dimensional penetrable obstacles. Our approach is built upon a direct BIE…
A key issue in the solution of partial differential equations via integral equation methods is the evaluation of possibly singular integrals involving the Green's function and its derivatives multiplied by simple functions over discretized…
For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation…
This paper presents a novel boundary integral equation (BIE) formulation for the two-dimensional time-harmonic water-waves problem. It utilizes a complex-scaled Laplace's free-space Green's function, resulting in a BIE posed on the infinite…
This paper is concerned with the problem of an acoustic wave scattering in a locally perturbed periodic structure. As the total wavefield is non-quasi-periodic, effective truncation techniques are pursued for high-accuracy numerical…
In this manuscript, we develop an efficient algorithm to evaluate the azimuthal Fourier components of the Green's function for the Helmholtz equation in cylindrical coordinates. A computationally efficient algorithm for this modal Green's…
We present an unfitted boundary algebraic equation (BAE) method for solving elliptic partial differential equations in complex geometries. The method employs lattice Green's functions on infinite regular grids combined with discrete…
The dyadic Green's function of the inhomogeneous vector Helmholtz equation describes the field pattern of a single frequency point source. It appears in the mathematical description of many areas of electromagnetism and optics including…
This paper is the direct-formulation companion to [Burbano-Gallegos, P\'erez-Arancibia, and Turc, ESAIM: M2AN, 60(1):273--315, 2026], which developed indirect combined-field-only boundary integral equations (BIEs) for time-harmonic…
Starting with a mathematical boundary value problem for the magnetic vector potential in an axisymmetric cylindrical coordinate system, we derive a general solution for any arbitrary current distribution using the method of Green's…
The demagnetization field in micromagnetism is given as the gradient of a potential which solves a partial differential equation (PDE) posed in R^d. In its most general form, this PDE is supplied with continuity condition on the boundary of…
In this paper, we consider the boundary integral equation (BIE) method for solving the exterior Neumann boundary value problems of elastic and thermoelastic waves in three dimensions based on the Fredholm integral equations of the first…
In this paper, we consider band-structure calculations governed by the Helmholtz or Maxwell equations in piecewise homogeneous periodic materials. Methods based on boundary integral equations are natural in this context, since they…
Green's function characterizes a partial differential equation (PDE) and maps its solution in the entire domain as integrals. Finding the analytical form of Green's function is a non-trivial exercise, especially for a PDE defined on a…