Zobrazeno 1 - 10
of 215
pro vyhledávání: '"Lazarov, Raytcho"'
The survey is devoted to numerical solution of the fractional equation $A^\alpha u=f$, $0 < \alpha <1$, where $A$ is a symmetric positive definite operator corresponding to a second order elliptic boundary value problem in a bounded domain $\Omega$ i
Externí odkaz:
http://arxiv.org/abs/2010.02717
In this paper we consider one particular mathematical problem of this large area of fractional powers of self-adjoined elliptic operators, defined either by Dunford-Taylor-like integrals or by the representation through the spectrum of the elliptic o
Externí odkaz:
http://arxiv.org/abs/1910.13865
Here we study theoretically and compare experimentally an efficient method for solving systems of algebraic equations, where the matrix comes from the discretization of a fractional diffusion operator. More specifically, we focus on matrices obtained
Externí odkaz:
http://arxiv.org/abs/1905.08155
Over the past few decades, there has been substantial interest in evolution equations that involving a fractional-order derivative of order $\alpha\in(0,1)$ in time, due to their many successful applications in engineering, physics, biology and finan
Externí odkaz:
http://arxiv.org/abs/1805.11309
We discuss, study, and compare experimentally three methods for solving the system of algebraic equations $\mathbb{A}^\alpha \bf{u}=\bf{f}$, $0< \alpha <1$, where $\mathbb{A}$ is a symmetric and positive definite matrix obtained from finite differenc
Externí odkaz:
http://arxiv.org/abs/1805.00711
In this paper, we develop and study algorithms for approximately solving the linear algebraic systems: $\mathcal{A}_h^\alpha u_h = f_h$, $ 0< \alpha <1$, for $u_h, f_h \in V_h$ with $V_h$ a finite element approximation space. Such problems arise in f
Externí odkaz:
http://arxiv.org/abs/1803.10055
We present and analyze a space-time Petrov-Galerkin finite element method for a time-fractional diffusion equation involving a Riemann-Liouville fractional derivative of order $\alpha\in(0,1)$ in time and zero initial data. We derive a proper weak fo
Externí odkaz:
http://arxiv.org/abs/1707.08057
Autor:
Lazarov, Raytcho, Vabishchevich, Petr
We consider the homogeneous equation ${\mathcal A} u=0$, where ${\mathcal A}$ is a symmetric and coercive elliptic operator in $H^1(\Omega)$ with $\Omega$ bounded domain in ${{\mathbb R}}^d$. The boundary conditions involve fractional power $\alpha$,
Externí odkaz:
http://arxiv.org/abs/1702.06477
In this paper we consider efficient algorithms for solving the algebraic equation ${\mathcal A}^\alpha {\bf u}={\bf f}$, $0< \alpha <1$, where ${\mathcal A}$ is a symmetric and positive definite matrix obtained form finite difference or finite elemen
Externí odkaz:
http://arxiv.org/abs/1612.04846
We apply geometric multigrid methods for the finite element approximation of flow problems governed by Darcy and Brinkman systems used in modeling highly heterogeneous porous media. The method is based on divergence-conforming discontinuous Galerkin
Externí odkaz:
http://arxiv.org/abs/1602.04858