Related papers: THE CONVERGENCE OF CHAOTIC INTEGRALS
The paper is devoted to the numerical solutions of fractional PDEs based on its probabilistic interpretation, that is, we construct approximate solutions via certain Monte Carlo simulations. The main results represent the upper bound of…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
Hamiltonian Monte Carlo (or hybrid Monte Carlo) with partial momentum refreshment explores the state space more slowly than it otherwise would due to the momentum reversals which occur on proposal rejection. These cause trajectories to…
A Monte Carlo method for the collisional guiding-center Fokker-Planck kinetic equation is derived to include the effects of background magnetic-field nonuniformity. It is shown that, in the limit of a homogeneous magnetic field, the…
We combine a generic method for finding fast orthogonal transforms for a given quasi-Monte Carlo integration problem with the multilevel Monte Carlo method. It is shown by example that this combined method can vastly improve the efficiency…
Monte Carlo simulation, experiment and continuum theory are used to examine the anchoring exhibited by a nematic liquid crystal at a patterned substrate comprising a periodic array of rectangles that, respectively, promote vertical and…
Equilibrium systems evolve according to Detailed Balance (DB). This principe guided development of the Monte-Carlo sampling techniques, of which Metropolis-Hastings (MH) algorithm is the famous representative. It is also known that DB is…
A novel linear integration rule called $\textit{control neighbors}$ is proposed in which nearest neighbor estimates act as control variates to speed up the convergence rate of the Monte Carlo procedure on metric spaces. The main result is…
We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…
We report on what seems to be an intriguing connection between variable integration time and partial velocity refreshment of Ideal Hamiltonian Monte Carlo samplers, both of which can be used for reducing the dissipative behavior of the…
This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits both nonlocal and nonlinear behaviour making the numerical…
We developed a Monte Carlo simulation method to calculate incoherent Thomson scattering spectra in high temperature plasmas. The basic idea is to treat the entire scattering process as the superposition of individual photon-electron…
A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest-order of these algorithms reduces to the $n$-fold way algorithm. These algorithms are applied to study the escape…
Bootstrapping was designed to randomly resample data from a fixed sample using Monte Carlo techniques. However, the original sample itself defines a discrete distribution. Convolutional methods are well suited for discrete distributions,…
The main subject to study in this paper are properties of the sequence of reversely iterated segments. Especially, we will examine properties of chaotic behavior of the sequence of measures of corresponding segments. Our results are not…
Time-fractional parabolic equations with a Caputo time derivative are considered. For such equations, we explore and further develop the new methodology of the a-posteriori error estimation and adaptive time stepping proposed in [7]. We…
Monte Carlo (MC) methods for numerical integration seem to be embarassingly parallel on first sight. When adaptive schemes are applied in order to enhance convergence however, the seemingly most natural way of replicating the whole job on…
The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement…
In order to find the equilibrium geometries of molecules and solids and to perform ab initio molecular dynamics, it is necessary to calculate the forces on the nuclei. We present a correlated sampling method to efficiently calculate…