Stereo images of error surfaces in problems of numerical methods verification

Андреев, С. В.; Bondarev, A. E.; Bondareva, N.A.

doi:10.26583/sv.12.2.12

Cited by 7 publications

(11 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…3) when choosing a criterion, automatically change a color of remaining criteria based on a level of similarity with the selected one;  automatic reordering of alternatives depending on a level of similarity with the focusable alternative;  automatic reordering of criteria depending on a level of similarity with the focusable criterion;  in case of using the three-dimensional visualization method of criteria's correlation, provide an ability to customize a scales of a level of similarity for automatic grouping of criteria. It is also possible to improve the quality of visual analytics of images obtained by the methods discussed above by using autostereoscopic displays, which make it possible to increase the efficiency of perception of three-dimensional images [11].…”

Section: Visual Analytics Of Three-dimensional Images Of Multicriterimentioning

confidence: 99%

Application of Visual Analytics Methods to Reduce the Dimensionality of Decision-making Problems

Zakharova¹,

Korostelyov²

2020

View full text Add to dashboard Cite

The article discusses the possibilities and approaches to the use of visual analytics methods to reduce the dimension of decision-making problems. The main directions of reducing the dimension of the decision-making problem, as well as increasing its information content using three-dimensional visualization methods are highlighted: filtering alternatives, grouping and ranking criteria. The application of several methods of visualization of choice set and criteria set are considered: histograms with grouping by alternatives, histograms with grouping by criteria, correlation surfaces of criteria. The advantages and disadvantages of visualization methods are highlighted in relation to solving the problem of reducing the dimension of choice set and criteria set. The basic principles of increasing the efficiency of visual analytics of three-dimensional images for decision-making problem in order to reduce its dimension are noted. A description of an experiment on visual analytics of three-dimensional images is given on the example of the problem of choosing an optimal solver OpenFOAM (out of three alternatives) based on 24 results of computational experiments of supersonic flow around a cone with different initial parameters. It is noted that with the help of visual analytics, it was possible to find an error in one of the computational experiments, to reduce the number of alternatives to two, and the number of criteria to five, which made it possible to apply traditional decision-making methods to this problem and choose the optimal solver.

show abstract

Section: Visual Analytics Of Three-dimensional Images Of Multicriterimentioning

confidence: 99%

Application of Visual Analytics Methods to Reduce the Dimensionality of Decision-making Problems

Zakharova¹,

Korostelyov²

2020

View full text Add to dashboard Cite

show abstract

“…1), when focusing on a specific alternative, automatically change a color of remaining alternatives based on a level of similarity with the selected one (for example, by applying a gradient); • in the case of visualization of criteria as a single image (Fig. 2) It is also possible to improve the quality of visual analytics of images obtained by the methods discussed above by using autostereoscopic displays [11].…”

Section: Visual Analytics Of Stereometric Images Of Multi-criteria Almentioning

confidence: 99%

Methods for Construction and Research Stereometric Visual Images of Multi-criteria Alternatives

Zakharova

Korostelyov

2020

Proceedings of the 30th International Conference on Computer Graphics and Machine Vision (GraphiCon 2020). Part 2

View full text Add to dashboard Cite

The article discusses methods for constructing and research stereometric visual images of multi-criteria alternatives. The difficulty of applying traditional decision-making methods when choosing the best alternative in the case of decision-making tasks with a large dimension is noted. Methods are proposed for reducing the dimension of a decision-making problem by constructing stereometric visual images that describe choice set and criteria set. The tasks of visual analytics are highlighted in the course of reducing the dimension of the decisionmaking task: grouping and ranking criteria, pairwise comparison and filtering of alternatives. A description of the methods for constructing stereometric visual images of multi-criteria alternatives based on histograms of alternatives and criteria is given. Also describes a method for constructing surface of the criteria's correlation. Using the developed method of alternatives visualization as a single image enables their visual filtering. The application method of the criteria visualization as a single image in combination with the construction and analysis of surface of the criteria's correlation allows for the grouping and ranking of criteria. The experiment is described on the application of the proposed methods for constructing and studying stereometric visual images of multi-criteria alternatives using the example of the problem of choosing the best OpenFoam solver, with the help of which estimates of the accuracy of calculating the inviscid flow around the cone were obtained. It is shown how, due to the above visualization methods, it is possible to reduce the count of criteria by several times.

show abstract

“…One of the most expressive and visual forms of visualization is the construction of stereo animations of the results of numerical studies. A similar construction of stereo images for this task was carried out and described in [22]. Fig.…”

Section: The Example Of Verification Problemmentioning

confidence: 99%

Generalized computational experiment in the problems of numerical methods verification

Alekseev

Bondarev

Kuvshinnikov

2020

CPT2020 the 8th International Scientific Conference on Computing in Physics and Technology Proceedings

View full text Add to dashboard Cite

This work is devoted to the application of a generalized computational experiment for a comparative assessment of numerical methods accuracy. The construction of a generalized computational experiment is based on the simultaneous solution using parallel computations in a multitasking mode of a basic problem with different input parameters, obtaining results in the form of multidimensional data volumes and their visual analysis. This approach can be effective in problems of verification of numerical methods. A comparative assessment of the accuracy for solvers of the open software package OpenFOAM is carried out. The classic inviscid problem of oblique shock wave is used as a basic task. Variations of the key parameters of the problem — the Mach number and angle of attack — are considered. An example of constructing error surfaces is given when the solvers of the OpenFOAM software package are compared. The concept of an error index is introduced as an integral characteristic of deviations from the exact solution for each solver in the class of problems under consideration. The surfaces of deviations from the exact solution in the L2 norm, constructed for each solver, together with the calculated error indices, make it possible to obtain a complete picture of the accuracy of the solvers under consideration for the class of problems defined by the ranges of variation of the Mach number and angle of attack.

show abstract

Stereo images of error surfaces in problems of numerical methods verification

Cited by 7 publications

References 9 publications

Application of Visual Analytics Methods to Reduce the Dimensionality of Decision-making Problems

Application of Visual Analytics Methods to Reduce the Dimensionality of Decision-making Problems

Methods for Construction and Research Stereometric Visual Images of Multi-criteria Alternatives

Generalized computational experiment in the problems of numerical methods verification

Contact Info

Product

Resources

About