Related papers: An Efficient Second-Order Accurate and Continuous …
We present here the first systematic treatment of the problems posed by the visualization and analysis of large-scale, parallel adaptive mesh refinement (AMR) simulations on an Eulerian grid. When compared to those obtained by constructing…
In this paper we explore acceleration techniques for large scale nonconvex optimization problems with special focuses on deep neural networks. The extrapolation scheme is a classical approach for accelerating stochastic gradient descent for…
We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
Deep learning-based bilateral grid processing has emerged as a promising solution for image enhancement, inherently encoding spatial and intensity information while enabling efficient full-resolution processing through slicing operations.…
In his article "Powerlist: A Structure for Parallel Recursion" Jayadev Misra wrote: "Many data parallel algorithms - Fast Fourier Transform, Batcher's sorting schemes and prefix sum - exhibit recursive structure. We propose a data…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second…
The advent of robust, reliable and accurate higher order Godunov schemes for many of the systems of equations of interest in computational astrophysics has made it important to understand how to solve them in multi-scale fashion. This is so…
We generalize the interpolative separable density fitting (ISDF) method, used for compressing the four-index electron repulsion integral (ERI) tensor, to incorporate adaptive real space grids for potentially highly localized single-particle…
Most existing point cloud upsampling methods have roughly three steps: feature extraction, feature expansion and 3D coordinate prediction. However,they usually suffer from two critical issues: (1)fixed upsampling rate after one-time…
This paper presents a super-resolution method based on gradient-based adaptive interpolation. In this method, in addition to considering the distance between the interpolated pixel and the neighboring valid pixel, the interpolation…
We detail how to use Newton's method for distortion-based curved $r$-adaption to a discrete high-order metric field while matching a target geometry. Specifically, we combine two terms: a distortion measuring the deviation from the target…
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…
Splitting and merging are long standing issues in PIC codes. I propose a novel algorithm devoted to exact splitting for Particle-In-Cell (PIC) codes relying on Adaptive Mesh Refinement (AMR) grids. AMR grids have - by definition - a…
In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline based interpolation method for spectral codes is presented. The theory links the order of the…
In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based method that,…
A trigonometric interpolation algorithm for non-periodic functions has been recently proposed and applied to study general ordinary differential equation (ODE). This paper enhances the algorithm to approximate functions in $2$-dim space.…
Obtainable computational efficiency is evaluated when using an Adaptive Mesh Refinement (AMR) strategy in time accurate simulations governed by sets of conservation laws. For a variety of 1D, 2D, and 3D hydro- and magnetohydrodynamic…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…