Numerical Analysis
This document gives guidelines to set up, run, and postprocess correct simulations with the finite element method. It is not an introduction to the method itself, but rather a list of things to check and possible mistakes to watch out for…
We present a local Fourier slice equation that enables local and sparse projection of a signal. Our result exploits that a slice in frequency space is an iso-parameter set in spherical coordinates. Therefore, the projection of suitable…
We propose a new tensor completion method based on tensor trains. The to-be-completed tensor is modeled as a low-rank tensor train, where we use the known tensor entries and their coordinates to update the tensor train. A novel tensor train…
This work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply (Petrov-)Galerkin…
Model order reduction algorithms for large-scale descriptor systems are proposed using balanced truncation, in which symmetry or block skew symmetry (reciprocity) and the positive realness of the original transfer matrix are preserved. Two…
The Met Office's weather and climate simulation code the Unified Model is used for both operational Numerical Weather Prediction and Climate modelling. The computational performance of the model running on parallel supercomputers is a key…
The tensor train decomposition decomposes a tensor into a "train" of 3-way tensors that are interconnected through the summation of auxiliary indices. The decomposition is stable, has a well-defined notion of rank and enables the user to…
New features and enhancements for the SPIKE banded solver are presented. Among all the SPIKE algorithm versions, we focus our attention on the recursive SPIKE technique which provides the best trade-off between generality and parallel…
Reducing hardware overhead of neural networks for faster or lower power inference and training is an active area of research. Uniform quantization using integer multiply-add has been thoroughly investigated, which requires learning many…
This paper discusses stochastic numerical methods of Runge-Kutta type with weak and strong convergences for systems of stochastic differential equations in It\^o form. At the beginning we give a brief overview of the stochastic numerical…
There is resurging interest, in statistics and machine learning, in solvers for ordinary differential equations (ODEs) that return probability measures instead of point estimates. Recently, Conrad et al. introduced a sampling-based class of…
The Colebrook equation $\zeta$ is implicitly given in respect to the unknown flow friction factor $\lambda$; $\lambda=\zeta(Re,\epsilon^*,\lambda)$ which cannot be expressed explicitly in exact way without simplifications and use of…
Low-rank matrix approximations play a fundamental role in numerical linear algebra and signal processing applications. This paper introduces a novel rank-revealing matrix decomposition algorithm termed Compressed Randomized UTV (CoR-UTV)…
We describe a strategy for rigorous arbitrary-precision evaluation of Legendre polynomials on the unit interval and its application in the generation of Gauss-Legendre quadrature rules. Our focus is on making the evaluation practical for a…
An Iterative Reanalysis Approximation (IRA) is integrated with the Moving Morphable Components (MMCs) based topology optimization (IRA-MMC) in this study. Compared with other classical topology optimization methods, the Finite Element (FE)…
In this paper, we propose an eigenvalue analysis -- of system dynamics models -- based on the Mutual Information measure, which in turn will be estimated via the Kernel Density Estimation method. We postulate that the proposed approach…
In this paper, we consider solving a class of nonconvex and nonsmooth problems frequently appearing in signal processing and machine learning research. The traditional alternating direction method of multipliers encounters troubles in both…
We present new algorithms for the randomized construction of hierarchically semi-separable matrices, addressing several practical issues. The HSS construction algorithms use a partially matrix-free, adaptive randomized projection scheme to…
High dimensional data and systems with many degrees of freedom are often characterized by covariance matrices. In this paper, we consider the problem of simultaneously estimating the dimension of the principal (dominant) subspace of these…
Convolutional Neural Networks (CNNs) filter the input data using a series of spatial convolution operators with compactly supported stencils and point-wise nonlinearities. Commonly, the convolution operators couple features from all…