Related papers: Spectral Methods for capillary surfaces described …
Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a pseudodifferential representation of the Dirac equation along with a simple Fourier-basis technique. Owing to the presence of…
In this paper, we study the forced mean curvature flows and the prescribed mean curvature equations of both graphs and level-sets with capillary-type boundary conditions on a $C^3$ bounded domain, which is not necessarily convex. We prove a…
We describe an adaptive version of a method for generating valid naturally curved quadrilateral meshes. The method uses a guiding field, derived from the concept of a cross field, to create block decompositions of multiply connected two…
Over the last years, deep learning methods have become an increasingly popular choice to solve tasks from the field of inverse problems. Many of these new data-driven methods have produced impressive results, although most only give point…
Chebyshev pseudospectral (PS) methods are reported to provide highly accurate solution using polynomial approximation. Use of polynomial basis functions in PS algorithms limits the formulation to univariate systems constraining it to tensor…
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the…
Obtaining high-quality particle distributions for stable and accurate particle-based simulations poses significant challenges, especially for complex geometries. We introduce a preprocessing technique for 2D and 3D geometries, optimized for…
Spectral methods are renowned for their high accuracy and efficiency in solving partial differential equations. The Fourier pseudo-spectral method is limited to periodic domains and suffers from Gibbs oscillations in non-periodic problems.…
Recently, the efficient numerical solution of Hamiltonian problems has been tackled by defining the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Their derivation relies on the expansion of…
The normal mode model is important in computational atmospheric acoustics. It is often used to compute the atmospheric acoustic field under a harmonic point source. Its solution consists of a set of discrete modes radiating into the upper…
The present study describes, first, an efficient algorithm for computing capillary-gravity solitary waves solutions of the irrotational Euler equations with a free surface and, second, provides numerical evidences of the existence of an…
In the context of topological insulators, the shallow-water model was recently shown to exhibit an anomalous bulk-edge correspondence. For the model with a boundary, the parameter space involves both longitudinal momentum and boundary…
We propose to augment standard grid-based fluid solvers with pointwise divergence-free velocity interpolation, thereby ensuring exact incompressibility down to the sub-cell level. Our method takes as input a discretely divergence-free…
We investigate the geometric implications of spectral curvature bounds, extending classical rigidity results in scalar curvature geometry to the spectral setting. By systematically employing the warped $\mu$-bubble method, we show…
We introduce a method-of-lines formulation of the closest point method, a numerical technique for solving partial differential equations (PDEs) defined on surfaces. This is an embedding method, which uses an implicit representation of the…
To enhance the ability of neural networks to extract local point cloud features and improve their quality, in this paper, we propose a multiscale graph generation method and a self-adaptive graph convolution method. First, we propose a…
Point cloud reconstruction from raw point cloud has been an important topic in computer graphics for decades, especially due to its high demand in modeling and rendering applications. An important way to solve this problem is establishing a…
Reaction-Diffusion equations can present solutions in the form of traveling waves. Such solutions evolve in different spatial and temporal scales and it is desired to construct numerical methods that can adopt a spatial refinement at…
Self-adjoint operators on infinite-dimensional spaces with continuous spectra are abundant but do not possess a basis of eigenfunctions. Rather, diagonalization is achieved through spectral measures. The SpecSolve package [SIAM Rev., 63(3)…
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…