Verification on the Ensemble of Independent Numerical Solutions

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

“…A separate area of application of a generalized computational experiment can be a comparative assessment of the accuracy of numerical methods. Similar attempts are presented in [2,15] devoted to the problem of accuracy estimation with the help of the ensemble of solutions. According to [2,15], if a researcher is able to calculate the same problem using several numerical methods with different computational properties, in particular, different approximation orders, then in some cases one can estimate the neighborhood of the approximate solution containing the exact solution (exact solution enclosure).…”

“…Similar attempts are presented in [2,15] devoted to the problem of accuracy estimation with the help of the ensemble of solutions. According to [2,15], if a researcher is able to calculate the same problem using several numerical methods with different computational properties, in particular, different approximation orders, then in some cases one can estimate the neighborhood of the approximate solution containing the exact solution (exact solution enclosure). If an ensemble of numerical solutions can be divided into clusters of "accurate" and "inaccurate" solutions, then the error ranking of values can be performed using an a posteriori analysis of the distances between the numerical solutions.…”

“…In a practical sense, this makes it possible to reveal hidden dependences of valuable functionals on the determining parameters of the problem, similar to the above formulas. This work continues a series of works devoted to the development and implementation of a generalized computational experiment for various classes of computational aerodynamics problems [2,3,[9][10][11][12][13][14][15][16][17].…”

Generalized Computational Experiment and Visual Analysis of Multidimensional Data

“…In a practical sense, this makes it possible to reveal hidden dependences of valuable functionals on the determining parameters of the problem, similar to the above formulas. This work continues a series of works devoted to the development and implementation of a generalized computational experiment for various classes of computational aerodynamics problems [3][4][5][6][7][8][9][10][11][12][13][14]. Despite the fact that there are very few works devoted to the development of a generalized computational experiment, the development of such experiments is gradually taking place in many areas.…”

“…Also, such a formal formulation allows numerical study of optimization analysis problems, when the inverse problem is solved at each point of the grid partition of the multidimensional space of the determining parameters. Both types of similar problems are considered in a series of papers [3][4][5][6][7][8][9][10][11][12][13][14]. The only way to effectively carry out a generalized numerical experiment is applying of parallel computations.…”