Related papers: An iterative Monte Carlo method to solve nonlinear…
This article describes Monte-Carlo algorithms for charged systems using constrained updates for the electric field. The method is generalized to treat inhomogeneous dielectric media, electrolytes via the Poisson-Boltzmann equation and…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
This paper presents a methodology for constructing iterative schemes of any order of convergence for solving nonlinear systems of equations. It also provides formulas for the order of convergence of any iterative schemes constructed using…
Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
We use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients. In this approach, all required expectations are approximated by a Monte Carlo method. The…
In this article we offer some modification of Monte-Carlo method for multiple parametric integral computation and solving of a linear integral Fredholm equation of a second kind (well posed problem). We prove that the rate of convergence of…
We present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise…
A three-point iterative method for solving scalar non-linear equations was selected and then adapted to solve systems of non-linear equations. Subsequently, by applying Taylor's theorem to functions of $\R^{n}$ in $\R^{n}$, it is shown that…
A quantum Monte Carlo method combining update of the loop algorithm with the global flip of the world line is proposed as an efficient method to study the magnetization process in an external field, which has been difficult because of…
Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance,…
Diagrammatic Monte Carlo approach is applied to a problem of a single spin-down fermion resonantly interacting with the sea of ideal spin-up fermions. On one hand, we develop a generic, sign-problem tolerant, method of exact numerical…
We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit…
In this work, we develop a novel Monte Carlo method for solving the electromagnetic scattering problem. The method is based on a formal solution of the scattering problem as a modified Born series whose coefficients are found by a conformal…
This paper proposes a Sequential Monte Carlo approach for the Bayesian estimation of mixed causal and noncausal models. Unlike previous Bayesian estimation methods developed for these models, Sequential Monte Carlo offers extensive…
A new algorithm for Monte Carlo calculation of the double exchange model is studied. The algorithm is commonly applicable to wide classes of strongly correlated electron systems which involve itinerant electrons coupled with…
A Monte Carlo method is presented to evaluate quantum states with many particles moving in the continuum. The scattering state is generated at each time by a Monte Carlo random sampling algorithm. The same calculation are repeated until the…
Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue…