相关论文: A robust solver for H(curl) convection-diffusion a…

For embedded boundary electromagnetics using the Dey-Mittra algorithm, a special grad-div matrix constructed in this work allows use of multigrid methods for efficient inversion of Maxwell's curl-curl matrix. Efficient curl-curl inversions…

A convection-diffusion problem with a large shift in space is considered. Numerical analysis of high order finite element methods on layer-adapted Duran type meshes, as well as on coarser Duran type meshes in places where weak layers…

Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal…

Local graph clustering and the closely related seed set expansion problem are primitives on graphs that are central to a wide range of analytic and learning tasks such as local clustering, community detection, nodes ranking and feature…

In this work, the author developed a multiple scattering model for heterogeneous elastic continua with strong property fluctuation and obtained the exact solution to the dispersion equation derived from the Dyson equation under the…

The histogram estimator of a discrete probability mass function often exhibits undesirable properties related to zero probability estimation both within the observed range of counts and outside into the tails of the distribution. To…

This paper develops and analyzes a general iterative framework for solving parameter-dependent and random convection-diffusion problems. It is inspired by the multi-modes method of [7,8] and the ensemble method of [20] and extends those…

The development of simple and fast hypergraph spectral methods has been hindered by the lack of numerical algorithms for simulating heat diffusions and computing fundamental objects, such as Personalized PageRank vectors, over hypergraphs.…

The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…

In many practical applications of numerical methods a substantial increase in efficiency can be obtained by using local grid refinement, since the solution is generally smooth in large parts of the domain and large gradients occur only…

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression…

We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. We modify the classical algorithm by introducing a new…

The Hodge decomposition provides a very powerful mathematical method for the analysis of 2D and 3D vector fields. It states roughly that any vector field can be $L^2$-orthogonally decomposed into a curl-free, divergence-free, and a harmonic…

The topic of these notes could be easily expanded into a full one-semester course. Nevertheless, we shall try to give some flavour along with theoretical bases of spectral and pseudo-spectral methods. The main focus is made on Fourier-type…

This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…

This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…

Smoothing a signal based on local neighborhoods is a core operation in machine learning and geometry processing. On well-structured domains such as vector spaces and manifolds, the Laplace operator derived from differential geometry offers…

This paper considers the existence of local and global-in-time strong solutions to the advection-diffusion equation with variable coefficients on an evolving surface with a boundary. We apply both the maximal $L^p$-in-time regularity for…

This paper is devoted to the design and analysis of a numerical algorithm for approximating solutions of a degenerate cross-diffusion system, which models particular instances of taxis-type migration processes under local sensing…

The convolution quadrature method originally developed for the Riemann-Liouville fractional calculus is extended in this work to the Hadamard fractional calculus by using the exponential type meshes. Local truncation error analysis is…