Related papers: Rapid evaluation of Newtonian potentials on planar…
This article presents a high-order accurate numerical method for the evaluation of singular volume integral operators, with attention focused on operators associated with the Poisson and Helmholtz equations in two dimensions. Following the…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
Particular solutions of the Poisson equation can be constructed via Newtonian potentials, integrals involving the corresponding Green's function which in two-dimensions has a logarithmic singularity. The singularity represents a significant…
We present an accurate and efficient method to calculate the gravitational potential of an isolated system in three-dimensional Cartesian and cylindrical coordinates subject to vacuum (open) boundary conditions. Our method consists of two…
Three algorithm are proposed to evaluate volume potentials that arise in boundary element methods for elliptic PDEs. The approach is to apply a modified fast multipole method for a boundary concentrated volume mesh. If $h$ is the meshwidth…
We present an efficient and accurate algorithm for solving the Poisson equation in spherical polar coordinates with a logarithmic radial grid and open boundary conditions. The method employs a divide-and-conquer strategy, decomposing the…
This article presents a new high-order accurate algorithm for finding a particular solution to a linear, constant-coefficient partial differential equation (PDE) by means of a convolution of the volumetric source function with the Green's…
We present an effective harmonic density interpolation method for the numerical evaluation of singular and nearly singular Laplace boundary integral operators and layer potentials in two and three spatial dimensions. The method relies on…
The modified Poisson-Boltzmann (MPB) equations are often used to describe equilibrium particle distribution of ionic systems. In this paper, we propose a fast algorithm to solve MPB equations with the self Green's function as the self…
We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a volume potential and a double layer potential. Rather than…
We present a simple yet accurate method to compute the adjoint double layer potential, which is used to solve the Neumann boundary value problem for Laplace's equation in three dimensions. An expansion in curvilinear coordinates leads us to…
We introduce an efficient way, called Newton algorithm, to study arbitrary ideals in C[[x,y]], using a finite succession of Newton polygons. We codify most of the data of the algorithm in a useful combinatorial object, the Newton tree. For…
The accurate and efficient evaluation of potentials is of great importance for the numerical solution of partial differential equations. When the integration domain of the potential is irregular and is discretized by an unstructured mesh,…
We introduce an accurate and efficient method for a class of nonlocal potential evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipolar potentials. Our method is based on a Gaussian-sum approximation…
We calculate electrostatic potential landscapes for an external probe charge in the presence of a set of metallic islands. Our numerical calculation in three dimensions (3D)uses an efficient grid relaxation technique. The well-known…
This paper describes a node relocation algorithm based on nonlinear optimization which delivers excellent results for both unstructured and structured plane triangle meshes over convex as well as non-convex domains with high curvature. The…
With the aid of Hensel Lemma, we refine the 2-adic Newton polygon algorithm proposed by Magron, Koprowski, and Vaccon at ISSAC 2023 to express computationally a given positive univariate polynomial with rational coefficients as a sum of…
We present a fast, direct and adaptive Poisson solver for complex two-dimensional geometries based on potential theory and fast multipole acceleration. More precisely, the solver relies on the standard decomposition of the solution as the…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
This study proposes a Newton based multiple objective optimization algorithm for hyperparameter search. The first order differential (gradient) is calculated using finite difference method and a gradient matrix with vectorization is formed…