Related papers: A parallel fast multipole method for a space-time …
Nonlinear parabolic equations are frequently encountered in applications and efficient approximating techniques for their solution are of great importance. In order to provide an effective scheme for the temporal approximation of such…
Massively parallel computer architectures create new opportunities for the performance of long-timescale molecular dynamics (MD) simulations. Here, we introduce the path-accelerated molecular dynamics (PAMD) method that takes advantage of…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
Parallel-in-time methods are developed to accelerate the direct-adjoint looping procedure. Particularly, we utilize the Paraexp algorithm, previously developed to integrate equations forward in time, to accelerate the direct-adjoint looping…
As has been shown in our previous work, the parallel-in-time direct inverse (ParaDIn) method introduced by Yamaleev and Paudel in (arXiv: 2406.00878v1, 2024) imposes some constraint on the maximum number of time levels, $N_t$, that can be…
In this paper, we propose and analyze a new semi-implicit stochastic multiscale method for the radiative heat transfer problem with additive noise fluctuation in composite materials. In the proposed method, the strong nonlinearity term…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
This paper proposes a higher-order multiscale computational method for nonlinear thermo-electric coupling problems of composite structures, which possess temperature-dependent material properties and nonlinear Joule heating. The innovative…
This paper proposes an efficient parallelised computation of field/circuit coupled systems co-simulated with the Waveform Relaxation (WR) technique. The main idea of the introduced approach lies in application of the parallel-in-time method…
In this paper, a hybrid quasi-static atomistic simulation method at finite temperature is developed, which combines the advantages of MD for thermal equilibrium and atomic-scale finite element method (AFEM) for efficient equilibration. Some…
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…
We present a simplified analog quantum simulation protocol for preparing quantum states that embed solutions of parabolic partial differential equations, including the heat, Black-Scholes and Fokker-Planck equations. The key idea is to…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
In this paper, we propose a fast multipole method (FMM) for 3-D linearized Poisson-Boltzmann (PB) equation in layered media. The main framework of the algorithm is analogous to the FMM for Helmholtz and Laplace equation in layered media…
A computer simulation has to be fast to be helpful, if it is employed to study the behavior of a multicomponent dynamic system. This paper discusses modeling concepts and algorithmic techniques useful for creating such fast simulations.…
In this paper, we explore how numerical calculations can be accelerated by implementing several numerical methods of fractional-order systems using parallel computing techniques. We investigate the feasibility of parallel computing…
We present a new time-stepping algorithm for nonlinear PDEs that exhibit scale separation in time. Our scheme combines asymptotic techniques (which are inexpensive but can have insufficient accuracy) with parallel-in-time methods (which,…
We consider the problem of intelligent and efficient task allocation mechanism in large-scale mobile edge computing (MEC), which can reduce delay and energy consumption in a parallel and distributed optimization. In this paper, we study the…
An efficient computational scheme devised for investigations of ground state properties of the electronically correlated systems is presented. As an example, $(H_{2})_{n}$ chain is considered with the long-range electron-electron…
In the present paper we propose a reduced temperature non-equilibrium model for simulating multicomponent flows with inter-phase heat transfer, diffusion processes (including the viscosity and the heat conduction) and external energy…