arXiv subjects

Naum M. Khutoryansky

Publications and source records attributed to Naum M. Khutoryansky.

2 recordsLinked to original sources

arXiv2019

Explicit Stencil Computation Schemes Generated by Poisson's Formula for the 2D Wave Equation

A new approach to building explicit time-marching stencil computation schemes for the transient 2D acoustic wave equation is implemented. It is based on using Poisson's formula and its three time level modification combined with polynomial stencil interpolation of the solution at each time-step and exact integration. The time-stepping algorithm consists of two explicit stencil computation procedures: a first time-step procedure incorporating the initial conditions and a two-step scheme for the second and next time-steps. Three particular explicit stencil schemes (with five, nine and 13 space points) are constructed using this approach. Their stability regions are presented. Accuracy advantages of the new schemes in comparison with conventional finite-difference schemes are demonstrated by simulation using an exact benchmark solution.

math.NA↗

arXiv2017

Exact Time Domain Solutions of 1-D Transient Dynamic Piezoelectric Problems with Nonlinear Damper Boundary Conditions

Novel exact solutions of one-dimensional transient dynamic piezoelectric problems for thickness polarized layers and disks, or length polarized rods, are obtained. The solutions are obtained using a time domain Green's function method that leads to an exact analytical recursive procedure which is applicable for a wide variety of boundary conditions including nonlinear cases. A nonlinear damper boundary condition is considered in more detail. The corresponding nonlinear relationship between stresses and velocities at a current time moment is used in the recursive procedure. In addition to the exact recursive procedure that is effective for calculations, some new practically important explicit exact solutions are presented. Several examples of the time behavior of the output electric potential difference are given to illustrate the effectiveness of the proposed exact approach.

math.NA↗