相关论文: A multi-domain spectral method for scalar and vect…
We find all spectral type differential equations satisfied by the symmetric generalized ultraspherical polynomials which are orthogonal on the interval [-1,1] with respect to the classical symmetric weight function for the Jacobi…
We present a new numerical method for the isometric embedding of 2-geometries specified by their 2-metrics in three dimensional Euclidean space. Our approach is to directly solve the fundamental embedding equation supplemented by six…
We introduce an algebraic multiscale method for two--dimensional problems. The method uses the generalized multiscale finite element method based on the quadrilateral nonconforming finite element spaces. Differently from the…
The interaction of particles in an electrolytic medium can be calculated by solving the Poisson equation inside the solutes and the linearized Poisson--Boltzmann equation in the solvent, with suitable boundary conditions at the interfaces.…
The Dirichlet-Neumann method is a common domain decomposition method for nonoverlapping domain decomposition and the method has been studied extensively for linear elliptic equations. However, for nonlinear elliptic equations, there are…
We develop a fast method for computing the electrostatic energy and forces for a collection of charges in doubly-periodic slabs with jumps in the dielectric permittivity at the slab boundaries. Our method achieves spectral accuracy by using…
In this work a spectral theory for 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation is developed. Spectral data for such solutions are defined (following Hitchin and Bobenko) and the space of spectral…
This paper introduces general methodologies for constructing closed-form solutions to linear constant-coefficient partial differential equations (PDEs) with polynomial right-hand sides in two and three spatial dimensions. Polynomial…
Second-order self-force calculations will be critical for modelling extreme-mass-ratio inspirals, and they are now known to have high accuracy even for binaries with mass ratios $\sim 1:10$. Many of the challenges facing these calculations…
In this paper, we provide a new routine to employ the Nash-Moser iteration technique to analyze the local and global properties of positive solutions to the equation $$\Delta_pv + a|\nabla v|^qv^r =0$$ on a complete Riemannian manifold with…
In this article using Nehari manifold method we study the multiplicity of solutions of the following nonlocal elliptic system involving variable exponents and concave-convex nonlinearities: \begin{equation*} \;\;\; \begin{array}{rl}…
In this article, we study numerical approximation of eigenvalue problems of the Schr\"{o}dinger operator $\displaystyle -\Delta u + \frac{c^2}{|x|^2}u$. There are three stages in our investigation: We start from a ball of any dimension, in…
We describe a multidomain spectral-tau method for solving the three-dimensional helically reduced wave equation on the type of two-center domain that arises when modeling compact binary objects in astrophysical applications. A global…
This article concerns optimal estimates for non-homogeneous degenerate elliptic equation with source functions in borderline spaces of integrability. We deliver sharp H\"older continuity estimates for solutions to $p$-degenerate elliptic…
We analyze the spectrum of the operator $\Delta^{-1} [\nabla \cdot (K\nabla u)]$, where $\Delta$ denotes the Laplacian and $K=K(x,y)$ is a symmetric tensor. Our main result shows that this spectrum can be derived from the spectral…
The Neumann--Neumann method is a commonly employed domain decomposition method for linear elliptic equations. However, the method exhibits slow convergence when applied to semilinear equations and does not seem to converge at all for…
The stability of a differentially rotating fluid subject to its own gravity is a problem with applications across wide areas of astrophysics--from protoplanetary discs (PPDs) to entire galaxies. The shearing box formalism offers a…
Calculating the spectral function of two dimensional systems is arguably one of the most pressing challenges in modern computational condensed matter physics. While efficient techniques are available in lower dimensions, two dimensional…
We propose subspace methods for 3-parameter eigenvalue problems. Such problems arise when separation of variables is applied to separable boundary value problems; a particular example is the Helmholtz equation in ellipsoidal and…
This paper discusses the spectral collocation method for numerically solving nonlocal problems: one dimensional space fractional advection-diffusion equation; and two dimensional linear/nonlinear space fractional advection-diffusion…