Search results for "Discretization"
showing 10 items of 237 documents
Multiscale model approach for magnetization dynamics simulations
2016
Simulations of magnetization dynamics in a multiscale environment enable the rapid evaluation of the Landau-Lifshitz-Gilbert equation in a mesoscopic sample with nanoscopic accuracy in areas where such accuracy is required. We have developed a multiscale magnetization dynamics simulation approach that can be applied to large systems with spin structures that vary locally on small length scales. To implement this, the conventional micromagnetic simulation framework has been expanded to include a multiscale solving routine. The software selectively simulates different regions of a ferromagnetic sample according to the spin structures located within in order to employ a suitable discretization…
Controlled time integration for the numerical simulation of meteor radar reflections
2016
We model meteoroids entering the Earth[U+05F3]s atmosphere as objects surrounded by non-magnetized plasma, and consider efficient numerical simulation of radar reflections from meteors in the time domain. Instead of the widely used finite difference time domain method (FDTD), we use more generalized finite differences by applying the discrete exterior calculus (DEC) and non-uniform leapfrog-style time discretization. The computational domain is presented by convex polyhedral elements. The convergence of the time integration is accelerated by the exact controllability method. The numerical experiments show that our code is efficiently parallelized. The DEC approach is compared to the volume …
Stochastic Galerkin method for cloud simulation
2018
AbstractWe develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model parameters and initial or boundary conditions. The developed stochastic Galerkin method combines the space-time approximation obtained by a suitable finite volume method with a spectral-type approximation based on the generalized polynomial chaos expansion in the stochastic space. The resulting numerical scheme yields a second-order accurate approximation in both space and time and exponential convergence in the stochastic space. Our numerical results…
On numerical broadening of particle size spectra: a condensational growth study using PyMPDATA 1.0
2021
Abstract. The work discusses the diffusional growth in particulate systems such as atmospheric clouds. It focuses on the Eulerian modeling approach in which the evolution of the probability density function describing the particle size spectrum is carried out using a fixed-bin discretization. The numerical diffusion problem inherent to the employment of the fixed-bin discretization is scrutinized. The work focuses on the applications of MPDATA family of numerical schemes. Several MPDATA variants are explored including: infinite-gauge, non-oscillatory, third-order-terms and recursive antidiffusive correction (double pass donor cell, DPDC) options. Methodology for handling coordinate transfor…
A Fractional-Order Control Approach to Ramp Tracking with Memory-Efficient Implementation
2020
We investigate the fractional-order (FO) control of arbitrary order LTI systems. We show that, for ramp tracking or input disturbance rejection, it is advantageous to include an FO integrator to the open-loop if we have to increase the order of integration further than one. With the lower phase-loss of the FO integrator it is easier to guarantee a desired phase margin. Furthermore the flat phase response around the crossover-frequency (iso-damping property) can be achieved for a wider frequency range such that the closed-loop is more robust wrt. amplitude and phase margins. The drawback of the FO approach is the increased implementation effort and the algebraic decay, which slows down the t…
A Hierarchical Learning Scheme for Solving the Stochastic Point Location Problem
2012
Published version of a chapter in the book: Advanced Research in Applied Artificial Intelligence. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-31087-4_78 This paper deals with the Stochastic-Point Location (SPL) problem. It presents a solution which is novel in both philosophy and strategy to all the reported related learning algorithms. The SPL problem concerns the task of a Learning Mechanism attempting to locate a point on a line. The mechanism interacts with a random environment which essentially informs it, possibly erroneously, if the unknown parameter is on the left or the right of a given point which also is the current guess. The first pioneering work […
Dynamic coarse-graining fills the gap between atomistic simulations and experimental investigations of mechanical unfolding
2017
We present a dynamic coarse-graining technique that allows to simulate the mechanical unfolding of biomolecules or molecular complexes on experimentally relevant time scales. It is based on Markov state models (MSM), which we construct from molecular dynamics simulations using the pulling coordinate as an order parameter. We obtain a sequence of MSMs as a function of the discretized pulling coordinate, and the pulling process is modeled by switching among the MSMs according to the protocol applied to unfold the complex. This way we cover seven orders of magnitude in pulling speed. In the region of rapid pulling we additionally perform steered molecular dynamics simulations and find excellen…
A study on time discretization and adaptive mesh refinement methods for the simulation of cancer invasion: The urokinase model
2016
In the present work we investigate a model that describes the chemotactically and proteolytically driven tissue invasion by cancer cells. The model is a system of advection-reaction-diffusion equations that takes into account the role of the serine protease urokinase-type plasminogen activator. The analytical and numerical study of such a system constitutes a challenge due to the merging, emerging, and traveling concentrations that the solutions exhibit. Classical numerical methods applied to this system necessitate very fine discretization grids to resolve these dynamics in an accurate way. To reduce the computational cost without sacrificing the accuracy of the solution, we apply adaptive…
Low-cost scalable discretization, prediction and feature selection for complex systems
2019
The introduced data-driven tool allows simultaneous feature selection, model inference, and marked cost and quality gains.
New exact methods for the time-invariant berth allocation and quay crane assignment problem
2019
Abstract Efficient management of operations in seaport container terminals has become a critical issue, due to the increase in maritime traffic and the strong competition between ports. In this paper we focus on two seaside operational problems: the Berth Allocation Problem and the Quay Crane Assignment Problem, which are considered in an integrated way. For the continuous BACAP problem with time-invariant crane assignment we propose a new mixed integer linear model in which the vessels can be moored at any position on the quay, not requiring any quay discretization. The model is enhanced by adding several families of valid inequalities. The resulting model is able to solve instances with u…