Dmytro Sytnyk

Medeea Horvat, Stephan B. Lunowa, Dmytro Sytnyk et al.

Intracranial aneurysms are the leading cause of hemorrhagic stroke. One of the established treatment approaches is the embolization induced by coil insertion. However, the prediction of treatment and subsequent changed flow characteristics in the aneurysm is still an open problem. In this work, we present an approach based on a patient-specific geometry and parameters including a coil representation as inhomogeneous porous medium. The model consists of the volume-averaged Navier-Stokes equations for a non-Newtonian blood rheology. We solve these equations using a problem-adapted lattice Boltzmann method and present a comparison between fully-resolved and volume-averaged simulations. The results indicate the validity of the model. Overall, this workflow allows for patient specific assessment of the flow due to potential treatment.

Dmytro Sytnyk

An extension of sinc interpolation on $\mathbb{R}$ to the class of algebraically decaying functions is developed in the paper. Similarly to the classical sinc interpolation we establish two types of error estimates. First covers a wider class of functions with the algebraic order of decay on $\mathbb{R}$. The second type of error estimates governs the case when the order of function's decay can be estimated everywhere in the horizontal strip of complex plane around $\mathbb{R}$. The numerical examples are provided.

Dmytro Sytnyk

We present a new parallel numerical method for solving the non-stationary Schrödinger equation with linear nonlocal condition and time-dependent potential which does not commute with the stationary part of the Hamiltonian. The given problem is discretized in-time using a polynomial-based collocation scheme. We establish the conditions on the existence of solution to the discretized problem, estimate the accuracy of the discretized solution and propose the method how this solution can be approximately found in an efficient parallel manner.

Vitalii Vasylyk, Dmytro Sytnyk

The $m$-point nonlocal problem for the first order differential equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified provided that the operator coefficient $A$ is strongly positive and some existence and uniqueness conditions are fulfilled. This algorithm is based on representations of operator functions by a Dunford-Cauchy integral along a hyperbola enveloping the spectrum of $A$ and on the proper quadratures involving short sums of resolvents. The efficiency of the proposed algorithms is demonstrated by numerical examples.