Related papers: Coupled Scheme for Linear and Hamilton-Jacobi Equa…
Stochastic contact Hamiltonian systems are a class of important mathematical models, which can describe the dissipative properties with odd dimensions in the stochastic environment. In this article, we investigate the numerical dynamics of…
The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence. Our results apply…
This paper studies a new class of integration schemes for the numerical solution of semi-explicit differential-algebraic equations of differentiation index 2 in Hessenberg form. Our schemes provide the flexibility to choose different…
The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the…
Solving multiple parametrised related systems is an essential component of many numerical tasks, and learning from the already solved systems will make this process faster. In this work, we propose a novel probabilistic linear solver over…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
Iterative methods for solving large sparse systems of linear equations are widely used in many HPC applications. Extreme scaling of these methods can be difficult, however, since global communication to form dot products is typically…
In this paper, for the first time we propose two linear, decoupled, energy-stable numerical schemes for multi-component two-phase compressible flow with a realistic equation of state (e.g. Peng-Robinson equation of state). The methods are…
Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…
This paper introduces a hybrid numerical scheme for the fuzzy dark matter model: It combines a wave-based approach to solve the Schr\"odinger equation using Fourier continuations with Gram polynomials and a fluid-based approach to solve the…
A splitting scheme for backward doubly stochastic differential equations is proposed. The main idea is to decompose a backward doubly stochastic differential equation into a backward stochastic differential equation and a stochastic…
Simulating charged many-body systems has been a computational demanding task due to the long-range nature of electrostatic interaction. For the multi-scale model of electrolytes which combines the strengths of atomistic/continuum…
We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order finite difference methods in a nonconforming multiblock fashion. The aim is to optimize computational efficiency when complex geometries are…
Two-beam coupling within the field of nonlinear optics, which transfers energy from one light beam to the other under certain conditions, has received considerable attention in inertial confinement fusion (ICF) and plasma optics. To…
A new simulation technique to obtain the synchronized steady-state solutions existing in coupled oscillator systems is presented. The technique departs from a semi-analytical formulation presented in previous works. It extends the model of…
We introduce novel entropy-dissipative numerical schemes for a class of kinetic equations, leveraging the recently introduced scalar auxiliary variable (SAV) approach. Both first and second order schemes are constructed. Since the…
Modified Hamiltonians are used in the field of geometric numerical integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually…
Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms…
In this work we introduce novel numerical schemes for a penalized version of the ternary Cahn-Hilliard system for the purpose of creating accurate and efficient numerical schemes of interfacial dynamics with three components as well as some…
Sliding cable system with frictions is encountered in many engineering applications. Such system is typically characterized by existences of complex and varied motion states of different sliding nodes (pulleys), which leads to significant…