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The numerical solution of partial differential equations (PDEs) is essential in computational physics. Over the past few decades, various quantum-based methods have been developed to formulate and solve PDEs. Solving PDEs incur high time…
We describe an asynchronous parallel stochastic coordinate descent algorithm for minimizing smooth unconstrained or separably constrained functions. The method achieves a linear convergence rate on functions that satisfy an essential strong…
This paper presents a novel parallel splitting algorithm for solving quasi-static multiple-network poroelasticity (MPET) equations. By introducing a total pressure variable, the MPET system can be reformulated into a coupled…
To further study the application of waveform relaxation methods in fluid dynamics in actual computation, this paper provides a general theoretical analysis of discrete-time waveform relaxation methods for solving linear DAEs. A class of…
The iterative nature of many discretisation methods for continuous dynamical systems has led to the study of the connections between iterative numerical methods in numerical linear algebra and continuous dynamical systems. Certain…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…
In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…
In this paper, to solve a broad class of complex symmetric linear systems, we recast the complex system in a real formulation and apply the generalized successive overrelaxation (GSOR) iterative method to the equivalent real system. We then…
For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…
In this study, we propose high-order implicit and semi-implicit schemes for solving ordinary differential equations (ODEs) based on Taylor series expansion. These methods are designed to handle stiff and non-stiff components within a…
Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. Although monolithic approaches offer possibly the best solution strategy, they often require ad-hoc preconditioners and…
In this paper, we present a parallel computing method for the coupled-cluster singles and doubles (CCSD) in periodic systems. The CCSD in periodic systems solves simultaneous equations for single-excitation and double-excitation amplitudes.…
Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using…
In this article, we employ the construction of the time-marching Discontinuous Petrov-Galerkin (DPG) scheme we developed for linear problems to derive high-order multistage DPG methods for non-linear systems of ordinary differential…
The method of sub-iteration, which was previously applied to the higher-order coupled cluster amplitude equations, is extended to the case of the coupled cluster $\Lambda$ equations. The sub-iteration procedure for the $\Lambda$ equations…
In this paper, we investigate a sequentially decoupled numerical method for solving the fully coupled quasi-static thermo-poroelasticity problems with nonlinear convective transport. The symmetric interior penalty discontinuous Galerkin…
We introduce a semi-explicit time-stepping scheme of second order for linear poroelasticity satisfying a weak coupling condition. Here, semi-explicit means that the system, which needs to be solved in each step, decouples and hence improves…
The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…
We present a novel method for high-order phase reduction in networks of weakly coupled oscillators and, more generally, perturbations of reducible normally hyperbolic (quasi-)periodic tori. Our method works by computing an asymptotic…