Zub P. Models of barycentric averaging and methods of harmonic functions reconstruction

TThe work is dedicated to elaboration and development of new randomized computational methods adapted to specific problems of harmonic functions reconstruction in orthotropic environment, as well as to construction and computer diagnosing of computational properties of the two-dimensional and three-dimensional cubature Newton-Cotes formulas on the discrete elements. The most attention of the work is paid to the method of barycentric averaging (MBA) in which the accelerated one-step scheme of random walks of the Monte-Carlo method is realized. Among the main results of the work one should mention broadening of the MBA method's application upon orthotropic environments and improving of the computational schemes that include the patterns with non-ideally absorbing and reflecting nodes. Those results reveal new opportunities for modeling various boundary conditions.