相关论文: Multi-dimensional filtering: Reducing the dimensio…

Higher-order accuracy (order of $k+1$ in the $L^2$ norm) is one of the well known beneficial properties of the discontinuous Galerkin (DG) method. Furthermore, many studies have demonstrated the superconvergence property (order of $2k+1$ in…

Convolving the output of Discontinuous Galerkin (DG) computations with symmetric Smoothness-Increasing Accuracy-Conserving (SIAC) filters can improve both smoothness and accuracy. To extend convolution to the boundaries, several one-sided…

This article considers the application of Smoothness-Increasing Accuracy-Conserving (SIAC) filtering for the non-linear stabilization of discontinuous Galerkin (DG) discretizations via entropy correction. Upon constructing discrete filters…

This article establishes the usefulness of the Smoothness-Increasing Accuracy-Increasing (SIAC) filter for reducing the errors in the mean and variance for a wave equation with uncertain coefficients solved via generalized polynomial chaos…

Convolving the output of Discontinuous Galerkin (DG) computations using spline filters can improve both smoothness and accuracy of the output. At domain boundaries, these filters have to be one-sided. Recently, position-dependent…

We theoretically analyze the superconvergence of the upwind discontinuous Galerkin (DG) method for both the steady-state and time-dependent radiative transfer equation (RTE), and apply the Smooth-Increasing Accuracy-Conserving (SIAC)…

We present a hybrid filter that is only applied to the approximation at the final time and allows for reducing errors away from a shock as well as near a shock. It is designed for discontinuous Galerkin approximations to PDEs and combines a…

We propose the Bayesian smoothness-increasing accuracy-conserving (SIAC) filter -- a hierarchical Bayesian extension of the existing deterministic SIAC filter. The SIAC filter is a powerful numerical tool for removing high-frequency noise…

We build a multi-element variant of the smoothness increasing accuracy conserving (SIAC) shock capturing technique proposed for single element spectral methods by Wissink et al. (B.W. Wissink, G.B. Jacobs, J.K. Ryan, W.S. Don, and E.T.A.…

The simulation of plasma physics is computationally expensive because the underlying physical system is of high dimensions, requiring three spatial dimensions and three velocity dimensions. One popular numerical approach is Particle-In-Cell…

In this article we introduce Line Smoothness-Increasing Accuracy-Conserving Multi-Resolution Analysis\linebreak (LSIAC-MRA). This is a procedure for exploiting convolution kernel post-processors for obtaining more accurate multi-dimensional…

The smoothing technique of Savitzky and Golay is extended to data defined on multidimensional meshes. A smoothness-increasing accuracy-conserving (SIAC) filter is defined that is suitable for use with finite-element computation.

We consider the problem of high-dimensional filtering of state-space models (SSMs) at discrete times. This problem is particularly challenging as analytical solutions are typically not available and many numerical approximation methods can…

The joint bilateral filter, which enables feature-preserving signal smoothing according to the structural information from a guidance, has been applied for various tasks in geometry processing. Existing methods either rely on a static…

Linear wave equations sourced by a Dirac delta distribution $\delta(x)$ and its derivative(s) can serve as a model for many different phenomena. We describe a discontinuous Galerkin (DG) method to numerically solve such equations with…

We introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. Following an approach already proposed for the Hamilton-Jacobi equations by other authors, we aim at reducing the spurious oscillations…

3D Gaussian Splatting has revolutionized neural rendering with real-time performance. However, scaling this approach to large scenes using Level-of-Detail methods faces critical challenges: inefficient serial traversal consuming over 60\%…

The Discontinuous Galerkin (DG) method applied to hyperbolic differential equations outputs weakly-linked polynomial pieces. Post-processing these pieces by Smoothness-Increasing Accuracy-Conserving (SIAC) convolution with B-splines can…

We develop reliable a posteriori error estimators for fully discrete Runge-Kutta discontinuous Galerkin approximations of nonlinear convection-diffusion systems endowed with a convex entropy in multiple spatial dimensions on the flat torus…

Nonlinear/non-Gaussian filtering has broad applications in many areas of life sciences where either the dynamic is nonlinear and/or the probability density function of uncertain state is non-Gaussian. In such problems, the accuracy of the…