Related papers: Exact propagation without analytical solutions
This paper investigates a system of nonlinear reaction-diffusion equations modeling the industrial synthesis of ammonia. By applying Lie group analysis, we construct self-similar solutions and derive a reduced system of ordinary…
A new approach for integration of motion in many-body systems of interacting polyatomic molecules is proposed. It is based on splitting time propagation of pseudo-variables in a modified phase space, while the real translational and…
We introduce a micro-macro parareal algorithm for the time-parallel integration of multiscale-in-time systems. The algorithm first computes a cheap, but inaccurate, solution using a coarse propagator (simulating an approximate slow…
In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drift terms. Upon noting that the effective diffusion matrix can…
In this paper we consider the numerical solutions for a class of jump diffusions with Markovian switching. After briefly reviewing necessary notions, a new jump-adapted efficient algorithm based on the Euler scheme is constructed for…
The Gillespie algorithm and its extensions are commonly used for the simulation of chemical reaction networks. A limitation of these algorithms is that they have to process and update the system after every reaction, requiring significant…
We introduce a novel paradigm for learning non-parametric drift and diffusion functions for stochastic differential equation (SDE). The proposed model learns to simulate path distributions that match observations with non-uniform time…
We present a unified treatment of the Fourier spectra of spherically symmetric nonlocal diffusion operators. We develop numerical and analytical results for the class of kernels with weak algebraic singularity as the distance between source…
This paper discusses new simulation algorithms for stochastic chemical kinetics that exploit the linearity of the chemical master equation and its matrix exponential exact solution. These algorithms make use of various approximations of the…
Researchers have employed stochastic simulations to determine the validity of their theoretical findings and to study analytically intractable spreading dynamics. In both cases, the correctness and efficiency of the simulation algorithm are…
In this paper, we present a numerical approach to solve the McKean-Vlasov equations, which are distribution-dependent stochastic differential equations, under some non-globally Lipschitz conditions for both the drift and diffusion…
In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…
Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…
The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation…
Implementing multicomponent diffusion models in reacting-flow simulations is computationally expensive due to the challenges involved in calculating diffusion coefficients. Instead, mixture-averaged diffusion treatments are typically used…
An overview of the author's papers on the new approach to the Brownian coagulation theory and its generalization to the diffusion-limited reaction rate theory is presented. The traditional diffusion approach of the Smoluchowski theory for…
Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…
We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
In this study, we propose a unified, general framework for the direct discontinuous Galerkin methods. In the new framework, the antiderivative of the nonlinear diffusion matrix is not needed. This allows a simple definition of the numerical…