Related papers: A fast spectral method for electrostatics in doubl…
Spectral methods for solving partial differential equations (PDEs) and stochastic partial differential equations (SPDEs) often use Fourier or polynomial spectral expansions on either uniform and non-uniform grids. However, while very widely…
We present a new high-order accurate spectral element solution to the two-dimensional scalar Poisson equation subject to a general Robin boundary condition. The solution is based on a simplified version of the shifted boundary method…
We present a multiscale finite element method for a diffusion problem with rough and high contrast coefficients. The construction of the multiscale finite element space is based on the localized orthogonal decomposition methodology and it…
Poisson-Boltzmann theory is the cornerstone for soft matter electrostatics. We provide novel exact analytical solutions to this non-linear mean-field approach, for the diffuse layer of ions in the vicinity of a planar or a cylindrical…
We propose a spectral solver for the Poisson equation on a square domain, achieving optimal complexity through the ultraspherical spectral method and the alternating direction implicit (ADI) method. Compared with the state-of-the-art…
This work investigates two physics-based models that simulate the non-linear partial differential algebraic equations describing an electric double layer supercapacitor. In one model the linear dependence between electrolyte concentration…
Standard Ewald sums, which calculate e.g. the electrostatic energy or the force in periodically closed systems of charged particles, can be efficiently speeded up by the use of the Fast Fourier Transformation (FFT). In this article we…
With the aim of describing bound and continuum states for diatomic molecules, we develop and implement a spectral method that makes use of Generalized Sturmian Functions (GSF) in prolate spheroidal coordinates. In order to master all…
In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic…
A spectral formulation of the boundary integral equation method for antiplane problems is presented. The boundary integral equation method relates the slip and the shear stress at an interface between two half-planes. It involves evaluating…
A weakly conducting liquid droplet immersed in another leaky dielectric liquid can exhibit rich dynamical behaviors under the effect of an applied electric field. Depending on material properties and field strength, the nonlinear coupling…
Spectral methods are well suited for solving hydrodynamic problems in which the self-gravity of the flow needs to be considered. Because Poisson's equation is linear, the numerical solution for the gravitational potential for each…
In this article we develop an algorithm for the efficient simulation of electrolytes in the presence of physical boundaries. In previous work the Discrete Ion Stochastic Continuum Overdamped Solvent (DISCOS) algorithm was derived for triply…
We present a Cartesian cut-cell finite-volume method for sharp-interface two-phase diffusion problems in static geometries. The formulation follows a two-fluid approach: independent diffusion equations are discretized in each phase on a…
Two-dimensional (2D) electronic materials are of significant technological interest due to their exceptional properties and broad applicability in engineering. The transition from nanoscale physics, that dictates their stable…
We study the elastic time-harmonic wave scattering problems on unbounded domains with boundaries composed of finite collections of disjoints finite open arcs (or cracks) in two dimensions. Specifically, we present a fast spectral Galerkin…
We consider the Brans-Dicke Reissner-Nordstrom spacetime in isotropic coordinates and the electrostatic field of an electric point charge placed outside its surface of inversion. We treat the static electric point charge as a linear…
Singularly perturbed differential equations with a Dirac delta function yield discontinuous solutions. Therefore, careful consideration is required when using numerical methods to solve these equations because of the Gibbs phenomenon. A…
The speed of sound in two-phase pipe flow systems is often several orders of magnitude greater than the travelling speed of hydraulic information (volume fractions.) Dynamically simulating such flows requires resolution of acoustic and…
We address periodic-image errors arising from the use of periodic boundary conditions to describe systems that do not exhibit full three-dimensional periodicity. The difference between the periodic potential, as straightforwardly obtained…