Search results for "Uncertain data"
showing 6 items of 6 documents
SAVU: A Statistical Approach for Uncertain Data in Dynamics of Axially Moving Materials
2012
In physics and engineering problems, model input is never exact. The effect of small uncertainties on the solution is thus an important question. In this study, a direct statistical-visual approach to approximate the solution set is investigated in the context of axially moving materials. The multidimensional probability distribution for the input uncertainties is assumed known. It is considered as a deterministic object, which is then mapped through the model. The resulting probability density of the model output is visualized. The proposed system consists of three non-trivial parts, which are briefly discussed: a multidimensional sampler, a density estimator, and a high dynamic range (HDR…
On the Reliability of Error Indication Methods for Problems with Uncertain Data
2012
This paper is concerned with studying the effects of uncertain data in the context of error indicators, which are often used in mesh adaptive numerical methods. We consider the diffusion equation and assume that the coefficients of the diffusion matrix are known not exactly, but within some margins (intervals). Our goal is to study the relationship between the magnitude of uncertainty and reliability of different error indication methods. Our results show that even small values of uncertainty may seriously affect the performance of all error indicators.
Two-Sided Estimates of the Solution Set for the Reaction–Diffusion Problem with Uncertain Data
2009
We consider linear reaction–diffusion problems with mixed Dirichlet–Neumann–Robin conditions. The diffusion matrix, reaction coefficient, and the coefficient in the Robin boundary condition are defined with an uncertainty which allow bounded variations around some given mean values. A solution to such a problem cannot be exactly determined (it is a function in the set of “possible solutions” formed by generalized solutions related to possible data). The problem is to find parameters of this set. In this paper, we show that computable lower and upper bounds of the diameter (or radius) of the set can be expressed throughout problem data and parameters that regulate the indeterminacy range. Ou…
A Problem Structuring Method
1991
Given a formal definition of problem and a formal definition of system, the equivalence between both concepts is studied. Considering a problem as a 3-tuple , where D is the set of possible data, R is the set of possible results, and P the set of conditions of the problem, classes of problems are constructed as combinations of types of data, types of results and types of conditions. For example, data can be either literal or numerical, either with uncertainty or not; conditions can be determined by rules, tables, equations, it may have uncertainty, etc. As a case of application it is outlined how some of the most common problems (knowledge representation, search, reasoning and planning, etc…
Errors Generated by Uncertain Data
2014
In this chapter, we study effects caused by incompletely known data. In practice, the data are never known exactly, therefore the results generated by a mathematical model also have a limited accuracy. Then, the whole subject of error analysis should be treated in a different manner, and accuracy of numerical solutions should be considered within a framework of a more complicated scheme, which includes such notions as maximal and minimal distances to the solution set and its radius.
A Simulation Based Analysis of an Multi Objective Diffusive Load Balancing Algorithm
2018
In this paper, we presented a further development of our research on developing an optimal software-hardware mapping framework. We used the Petri Net model of the complete hardware and software High Performance Computing (HPC) system running a Computational Fluid Dynamics (CFD) application, to simulate the behaviour of the proposed diffusive two level multi-objective load-balancing algorithm. We developed an meta-heuristic algorithm for generating an approximation of the Pareto-optimal set to be used as reference. The simulations showed the advantages of this algorithm over other diffusive algorithms: reduced computational and communication overhead and robustness due to low dependence on u…