Related papers: Highly efficient Gauss's law-preserving spectral a…
We present a wavenumber-robust strategy for computing Steklov eigenpairs of the Helmholtz operator $-\Delta -\mu^2$. As the wavenumber $\mu \rightarrow \mu_D$ from below (where $\mu_D^2 $ is a Dirichlet- Laplace eigenvalue of multiplicity…
This paper presents a high-accuracy higher-order multiscale method for solving multi-continuum problems in in highly heterogeneous media. First, microscopic unit cell functions are defined, leading to the derivation of macroscopic…
We study the spectral problems associated with the finite-difference operators $H_N = 2 \cosh(p) + V_N(x)$, where $V_N(x)$ is an arbitrary polynomial potential of degree $N$. These systems can be regarded as a solvable deformation of the…
Maxwell-Amp\`{e}re-Nernst-Planck (MANP) equations were recently proposed to model the dynamics of charged particles. In this study, we enhance a numerical algorithm of this system with deep learning tools. The proposed hybrid algorithm…
We show that by using higher order precision arithmetic, i.e., using floating point types with more significant bits than standard double precision numbers, one may accurately compute eigenvalues for non-normal matrices arising in…
While pseudospectral (PS) methods can feature very high accuracy, they tend to be severely limited in terms of geometric flexibility. Application of global radial basis functions overcomes this, however at the expense of problematic…
Implicit neural representations (INRs) have significantly advanced the field of arbitrary-scale super-resolution (ASSR) of images. Most existing INR-based ASSR networks first extract features from the given low-resolution image using an…
This paper presents a fast and powerful method for the computation of eigenvalue bounds for Hessian matrices $\nabla^2 \varphi(x) $ of nonlinear functions $\varphi: U \subseteq R^n\rightarrow R$ on hyperrectangles $B \subset U$. The method…
Due to its highly oscillating solution, the Helmholtz equation is numerically challenging to solve. To obtain a reasonable solution, a mesh size that is much smaller than the reciprocal of the wavenumber is typically required (known as the…
To solve the Bethe-Salpeter eigenvalue problem with distinct sizes, two efficient methods, called {\Gamma}QR algorithm and {\Gamma}-Lanczos algorithm, are proposed in this paper. Both algorithms preserve the special structure of the initial…
We are interested in the numerical solution of large systems of hyperbolic conservation laws or systems in which the characteristic decomposition is expensive to compute. Solving such equations using finite volumes or Discontinuous Galerkin…
This study proposes an extension of the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulation in an arbitrary Lagrangian-Eulerian (ALE) formulation in unstructured mesh. The ALE method is achieved by subdividing…
The homogenization of eigenvalues of non-Hermitian Maxwell operators is studied by the H-convergence method. It is assumed that the Maxwell systems are equipped with suitable m-dissipative boundary conditions, namely, with Leontovich or…
In this paper, a third-order compact gas-kinetic scheme is firstly proposed for three-dimensional computation for the compressible Euler and Navier-Stokes solutions. The scheme achieves its compactness due to the time-dependent gas…
We consider the 2D quasi-periodic scattering problem in optics, which has been modelled by a boundary value problem governed by Helmholtz equation with transparent boundary conditions. A spectral collocation method and a tensor product…
In this paper, we develop high-order asymptotic preserving (AP) schemes for the BGK equation in a hyperbolic scaling, which leads to the macroscopic models such as the Euler and compressible Navier-Stokes equations in the asymptotic limit.…
The energy dissipation law and maximum bound principle are significant characteristics of the Allen-Chan equation. To preserve discrete counterpart of these properties, the linear part of the target system is usually discretized implicitly,…
This paper considers spectral-difference methods of a high-order of accuracy for solving the one-way wave equation using the Laguerre integral transform with respect to time as the base. In order to provide a high spatial accuracy and…
This paper proposes a new hybrid high-order discretization for the biharmonic problem and the corresponding eigenvalue problem. The discrete ansatz space includes degrees of freedom in $n-2$ dimensional submanifolds (e.g., nodal values in…
Graph-based multi-view spectral clustering methods have achieved notable progress recently, yet they often fall short in either oversimplifying pairwise relationships or struggling with inefficient spectral decompositions in…