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Magnetohydrodynamic (MHD) simulations based on the ideal MHD equations have become a powerful tool for modeling phenomena in a wide range of applications including laboratory, astrophysical, and space plasmas. In general, high-resolution…
Computational Fluid Dynamics (CFD) is a major sub-field of engineering. Corresponding flow simulations are typically characterized by heavy computational resource requirements. Often, very fine and complex meshes are required to resolve…
The aim of this paper is to give a result concerning the stability properties of the solutions of magnetohydrodynamics equations at small but finite Reynolds numbers. These solutions are found using the alpha-effect: this method gives us…
This paper aims to numerically verify the large Reynolds number asymptotic theory of magneto-hydrodynamic (MHD) flows proposed in the companion paper Deguchi (2019). To avoid any complexity associated with the chaotic nature of turbulence…
This report presents three Moving Horizon Estimation (MHE) methods for discrete-time partitioned linear systems, i.e. systems decomposed into coupled subsystems with non-overlapping states. The MHE approach is used due to its capability of…
We study infinite-horizon Discounted Markov Decision Processes (DMDPs) under a generative model. Motivated by the Algorithm with Advice framework Mitzenmacher and Vassilvitskii 2022, we propose a novel framework to investigate how a…
We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and…
Fully realizing the potential of multigrid solvers often requires custom algorithms for a given application model, discretizations and even regimes of interest, despite considerable effort from the applied math community to develop fully…
This article introduces a highly parallel algorithm for molecular dynamics simulations with short-range forces on single node multi- and many-core systems. The algorithm is designed to achieve high parallel speedups for strongly…
Hidden Markov models (HMMs) are popular models to identify a finite number of latent states from sequential data. However, fitting them to large data sets can be computationally demanding because most likelihood maximization techniques…
We present a number of novel algorithms, based on mathematical optimization formulations, in order to solve a homogeneous multiprocessor scheduling problem, while minimizing the total energy consumption. In particular, for a system with a…
To minimise systematic errors in Monte Carlo simulations of charged particles, long range electrostatic interactions have to be calculated accurately and efficiently. Standard approaches, such as Ewald summation or the naive application of…
This paper introduces a novel theoretical framework and a suite of highly efficient, parallelizable algorithms for solving the large-scale multicommodity flow (MCF) feasibility problem. We reframe the classical constraint-satisfaction…
Experiments in predator-prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects.…
Numerical modeling of the intensity and evolution of flood events are affected by multiple sources of uncertainty such as precipitation and land surface conditions. To quantify and curb these uncertainties, an ensemble-based simulation and…
The use of deep learning has become increasingly popular in reduced-order models (ROMs) to obtain low-dimensional representations of full-order models. Convolutional autoencoders (CAEs) are often used to this end as they are adept at…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of…
The macro-element variant of the hybridized discontinuous Galerkin (HDG) method combines advantages of continuous and discontinuous finite element discretization. In this paper, we investigate the performance of the macro-element HDG method…
An accurate algorithm is proposed to improve the prediction of a particle in collision with a moving wall within the direct simulation Monte Carlo (DSMC) framework for the simulation of unsteady rarefied flows. This algorithm is able to…