Construction of a Generalized Computational Experiment and Visual Analysis of Multidimensional Data

Bondarev, A. E.; Галактионов, В. А.

doi:10.30987/graphicon-2019-2-117-121

Cited by 2 publications

(3 citation statements)

References 13 publications

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“…The geometric theory of multidimensional interpolation can also be used to solve other engineering problems of modeling and visualization multi-factor processes and phenomena [20][21][22][23][24][25][26][27][28][29][30].…”

Section: Resultsmentioning

confidence: 99%

About one method of numeral decision of differential equalizations in partials using geometric interpolants

Konopatskiy

Voronova

Бездитный

et al. 2020

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

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The article presents a new vision of the process of approximating the solution of differential equations based on the construction of geometric objects of multidimensional space incident to nodal points, called geometric interpolants, which have pre-defined differential characteristics corresponding to the original differential equation. The incidence condition for a geometric interpolant to nodal points is provided by a special way of constructing a tree of a geometric model obtained on the basis of the moving simplex method and using special arcs of algebraic curves obtained on the basis of Bernstein polynomials. A fundamental computational algorithm for solving differential equations based on geometric interpolants of multidimensional space is developed. It includes the choice and analytical description of the geometric interpolant, its coordinate-wise calculation and differentiation, the substitution of the values of the parameters of the nodal points and the solution of the system of linear algebraic equations. The proposed method is used as an example of solving the inhomogeneous heat equation with a linear Laplacian, for approximation of which a 16-point 2-parameter interpolant is used. The accuracy of the approximation was estimated using scientific visualization by superimposing the obtained surface on the surface of the reference solution obtained on the basis of the variable separation method. As a result, an almost complete coincidence of the approximation solution with the reference one was established.

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Section: Resultsmentioning

confidence: 99%

About one method of numeral decision of differential equalizations in partials using geometric interpolants

Konopatskiy

Voronova

Бездитный

et al. 2020

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

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show abstract

“…A large number of different applications of a generalized computational experiment are described in detail in [4][5][6][7][8][9][10][11][12][13][14]. The concept of a generalized computational experiment was applied to a wide range of both model and practical problems.…”

Section: Generalized Computational Experimentsmentioning

confidence: 99%

“…The concept, basic methods and approaches of a generalized computational experiment, as well as a number of software tools for its implementation were developed in Keldysh Institute of Applied Mathematics RAS. The main aspects of constructing a generalized computational experiment and examples of its implementation are described in detail in [4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

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

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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.

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Construction of a Generalized Computational Experiment and Visual Analysis of Multidimensional Data

Cited by 2 publications

References 13 publications

About one method of numeral decision of differential equalizations in partials using geometric interpolants

About one method of numeral decision of differential equalizations in partials using geometric interpolants

Generalized computational experiment in the problems of numerical methods verification

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