Search results for "Applied Mathematics"
showing 10 items of 4379 documents
On the application of the generalized means to construct multiresolution schemes satisfying certain inequalities proving stability
2021
Multiresolution representations of data are known to be powerful tools in data analysis and processing, and they are particularly interesting for data compression. In order to obtain a proper definition of the edges, a good option is to use nonlinear reconstructions. These nonlinear reconstruction are the heart of the prediction processes which appear in the definition of the nonlinear subdivision and multiresolution schemes. We define and study some nonlinear reconstructions based on the use of nonlinear means, more in concrete the so-called Generalized means. These means have two interesting properties that will allow us to get associated reconstruction operators adapted to the presence o…
Molecular dynamics simulations in hybrid particle-continuum schemes: Pitfalls and caveats
2017
Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations typically pose a computational bottleneck, which we investigate in detail in this study. We find that it is preferable to simulate many small systems as opposed to a few large systems, and that a choice of a simple isokinetic thermostat is typically sufficient while thermostats such as Lowe-Andersen allow for simulations at elevated viscosity. We discuss suitable choices for time steps and finite-size effects which arise in the limit of very small simulation bo…
(Approximate) Low-Mode Averaging with a new Multigrid Eigensolver
2015
We present a multigrid based eigensolver for computing low-modes of the Hermitian Wilson Dirac operator. For the non-Hermitian case multigrid methods have already replaced conventional Krylov subspace solvers in many lattice QCD computations. Since the $\gamma_5$-preserving aggregation based interpolation used in our multigrid method is valid for both, the Hermitian and the non-Hermitian case, inversions of very ill-conditioned shifted systems with the Hermitian operator become feasible. This enables the use of multigrid within shift-and-invert type eigensolvers. We show numerical results from our MPI-C implementation of a Rayleigh quotient iteration with multigrid. For state-of-the-art lat…
Two new sum-of-sinusoids-based methods for the efficient generation of multiple uncorrelated rayleigh fading waveforms
2009
Article from the journal: IEEE Transactions on Wireless Communications Publisher's version: http://dx.doi.org/10.1109/twc.2009.080769 This paper deals with the design of a set of multiple uncorrelated Rayleigh fading waveforms. The Rayleigh fading waveforms are mutually uncorrelated, but each waveform is correlated in time. The waveforms are generated by using the deterministic sum-of-sinusoids (SOS) channel modeling principle. Two new closed-form solutions are presented for the computation of the model parameters. Analytical and numerical results show that the resulting deterministic SOS-based channel simulator fulfills all main requirements imposed by the reference model with given correl…
Performance and Delay Analysis of Hybrid ARQ With Incremental Redundancy Over Double Rayleigh Fading Channels
2014
In this paper, we study the performance of hybrid automatic repeat request (HARQ) with incremental redundancy over double Rayleigh channels, a common model for the fading amplitude of vehicle-to-vehicle communication systems. We inves- tigate the performance of HARQ from an information theoretic perspective. Analytical expressions are derived for the -outage capacity, the average number of transmissions, and the average transmission rate of HARQ with incremental redundancy assum- ing a maximum number of HARQ rounds. Moreover, we evaluate the delay experienced by Poisson arriving packets for HARQ with incremental redundancy. We provide analytical expressions for the expected waiting time, th…
Mesh-adaptive methods for viscous flow problem with rotation
2007
In this paper, new functional type a posteriori error estimates for the viscous flow problem with rotating term are presented. The estimates give guaranteed upper bounds of the energy norm of the error and provide reliable error indication. We describe the implementation of the adaptive finite element methods (AFEM) in the framework of the functional type estimates proposed. Computational properties of the estimates are investigated on series of numerical examples.
Computational Homogenization of Heterogeneous Materials by a Novel Hybrid Numerical Scheme
2020
The Virtual Element Method (VEM) is a recent numerical technique capable of dealing with very general polygonal and polyhedral mesh elements, including irregular or non-convex ones. Because of this feature, the VEM ensures noticeable simplification in the data preparation stage of the analysis, especially for problems whose analysis domain features complex geometries, as in the case of computational micro-mechanics problems. The Boundary Element Method (BEM) is a well known, extensively used and effective numerical technique for the solution of several classes of problems in science and engineering. Due to its underlying formulation, the BEM allows reducing the dimensionality of the proble…
An introduction to knowledge computing
2014
This paper deals with the challenges related to self-management and evolution of massive knowledge collections. We can assume that a self-managed knowledge graph needs a kind of a hybrid of: an explicit declarative self-knowledge (as knowledge about own properties and capabilities) and an explicit procedural self-knowledge (as knowledge on how to utilize own properties and the capabilities for the self-management).We offer an extension to a traditional RDF model of describing knowledge graphs according to the Semantic Web standards so that it will also allow to a knowledge entity to autonomously perform or query from remote services different computational executions needed. We also introdu…
Path Integral approach via Laplace’s method of integration for nonstationary response of nonlinear systems
2019
In this paper the nonstationary response of a class of nonlinear systems subject to broad-band stochastic excitations is examined. A version of the Path Integral (PI) approach is developed for determining the evolution of the response probability density function (PDF). Specifically, the PI approach, utilized for evaluating the response PDF in short time steps based on the Chapman–Kolmogorov equation, is here employed in conjunction with the Laplace’s method of integration. In this manner, an approximate analytical solution of the integral involved in this equation is obtained, thus circumventing the repetitive integrations generally required in the conventional numerical implementation of …
Dynamic Spectrum Reservation for CR Networks in the Presence of Channel Failures: Channel Allocation and Reliability Analysis
2018
[EN] Providing channel access opportunities for new service requests and guaranteeing continuous connections for ongoing flows until service completion are two challenges for service provisioning in wireless networks. Channel failures, which are typically caused by hardware and software failures or/and by intrinsic instability in radio transmissions, can easily result in network performance degradation. In cognitive radio networks (CRNs), secondary transmissions are inherently vulnerable to connection breaks due to licensed users' arrivals as well as channel failures. To explore the advantages of channel reservation on performance improvement in error-prone channels, we propose and analyze …