Related papers: Convergence rate for numerical computation of the …
Non-equilibrium Green's function theory and related methods are widely used to describe transport phenomena in many-body systems, but they often require a costly inversion of a large matrix. We show here that the shift-invert Lanczos method…
In this manuscript, we develop an efficient algorithm to evaluate the azimuthal Fourier components of the Green's function for the Helmholtz equation in cylindrical coordinates. A computationally efficient algorithm for this modal Green's…
Green's function of the problem describing steady forward motion of bodies in an open ocean in the framework of the linear surface wave theory (the function is often referred to as Kelvin's wave source potential) is considered. Methods for…
Learning the Green's function using deep learning models enables to solve different classes of partial differential equations. A practical limitation of using deep learning for the Green's function is the repeated computationally expensive…
This paper is devoted to show a discrete adaptive finite element approximation result for the isotropic two-dimensional Griffith energy arising in fracture mechanics. The problem is addressed in the geometric measure theoretic framework of…
We present useful connections between the finite difference and the finite element methods for a model boundary value problem. We start from the observation that, in the finite element context, the interpolant of the solution in one…
We build upon a recent theoretical breakthrough by employing novel algorithms to accurately compute the fractions $F_p$ of all closed walks on the infinite square lattice whose the last erased loop corresponds is any one of the $762, 207,…
This paper presents an extended version of the article [Franz, S., Kopteva, N.: J. Differential Equations, 252 (2012)]. The main improvement compared to the latter is in that here we additionally estimate the mixed second-order derivative…
We consider the interpolation problem with the inverse multiquadric radial basis function. The problem usually produces a large dense linear system that has to be solved by iterative methods. The efficiency of such methods is strictly…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
In present work, we explore and experiment an alternative approach of studying resonance properties in finite volume. By analytic continuing finite lattice size $L$ into complex plane, the oscillating behavior of finite volume Green's…
Structure and coordinate dependence of the reflected wave, as well as boundary conditions for quasi-particles of graphene and the two dimensional electron gas in sheets with abrupt lattice edges are obtained and analyzed by the Green's…
We analyze random resistor networks through a study of lattice Green's functions in arbitrary dimensions. We develop a systematic disorder perturbation expansion to describe the weak disorder regime of such a system. We use this formulation…
Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of…
We revisit the Fourier transform of a Hankel function, of considerable importance in the theory of knife edge diffraction. Our approach is based directly upon the underlying Bessel equation, which admits manipulation into an alternate…
We present a new method for calculating the Green functions for a lattice scalar field theory in $D$ dimensions with arbitrary potential $V(\phi)$. The method for non-perturbative evaluation of Green functions for $D \! = \! 1$ is…
A modified Green operator is proposed as an improvement of Fourier-based numerical schemes commonly used for computing the electrical or thermal response of heterogeneous media. Contrary to other methods, the number of iterations necessary…
We present a general formula for the particular solution of an inhomogeneous linear difference equation with variable coefficients. The answer is expressed as a weighted sum of fundamental solutions of the associated linear difference…
The main problem in theoretical analysis of structures with strong confinement is the fact that standard mathematical tools: differential equations and Fourier's transformations are no longer applicable. In this paper we have demonstrated…
A new method for the stabilization of the sign problem in the Green Function Monte Carlo technique is proposed. The method is devised for real lattice Hamiltonians and is based on an iterative ''stochastic reconfiguration'' scheme which…