Related papers: Cartesian Coordinate, Oblique Boundary, Finite Dif…
The application of suitable numerical boundary conditions for hyperbolic conservation laws on domains with complex geometry has become a problem with certain difficulty that has been tackled in different ways according to the nature of the…
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…
In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…
By employing non-equispaced grid points near boundaries, boundary-optimized upwind finite-difference operators of orders up to nine are developed. The boundary closures are constructed within a diagonal-norm summation-by-parts (SBP)…
We show that a generalised sparse grid combination technique which combines multi-variate extrapolation of finite difference solutions with the standard combination formula lifts a second order accurate scheme on regular meshes to a fourth…
In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with…
Interpolating scaling functions give a faithful representation of a localized charge distribution by its values on a grid. For such charge distributions, using a Fast Fourier method, we obtain highly accurate electrostatic potentials for…
A new approximation method for inverting the Poisson's equation is presented for a continuously distributed and finite-sized source in an unbound domain. The advantage of this image multipole method arises from its ability to place the…
We present a real-space adaptive-coordinate method, which combines the advantages of the finite-difference approach with the accuracy and flexibility of the adaptive coordinate method. The discretized Kohn-Sham equations are written in…
An expandable local and parallel two-grid finite element scheme based on superposition principle for elliptic problems is proposed and analyzed in this paper by taking example of Poisson equation. Compared with the usual local and parallel…
Imposition methods of interface conditions for the second-order wave equation with non-conforming grids is considered. The spatial discretization is based on high order finite differences with summation-by-parts properties. Previously…
We present a simple numerical algorithm for solving elliptic equations where the diffusion coefficient, the source term, the solution and its flux are discontinuous across an irregular interface. The algorithm produces second-order accurate…
Calculating dynamical diffraction patterns for X-ray topography and similar x-ray scattering-imaging techniques require the numerical integration of the Takagi-Taupin equations. This is usually performed with a simple second order finite…
We propose numerical schemes that enable the application of particle methods for advection problems in general bounded domains. These schemes combine particle fields with Cartesian tensor product splines and a fictitious domain approach.…
The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by…
We solve Poisson's equation using new multigrid algorithms that converge rapidly. The novel feature of the 2D and 3D algorithms are the use of extra diagonal grids in the multigrid hierarchy for a much richer and effective communication…
A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics of molecules in solvent. The proposed method used an implicit…
We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…
We present an extension to the Poisson-Boltzmann model where the dipolar features of solvent molecules are taken explicitly into account. The formulation is derived at mean-field level and can be extended to any order in a systematic…
Elliptic partial differential equations are important both from application and analysis points of views. In this paper we apply the Closest Point Method to solving elliptic equations on general curved surfaces. Based on the closest point…