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We explore a class of splitting schemes employing implicit-explicit (IMEX) time-stepping to achieve accurate and energy-stable solutions for thin-film equations and Cahn-Hilliard models with variable mobility. This splitting method…
The Computational Singular Perturbation (CSP) method of Lam and Goussis is an iterative method to reduce the dimensionality of systems of ordinary differential equations with multiple time scales. In [J. Nonlin. Sci., to appear], the…
A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit…
The incompressible smoothed particle hydrodynamics method (ISPH) is a numerical method widely used for accurately and efficiently solving flow problems with free surface effects. However, to date there has been little mathematical…
In numerical time-integration with implicit-explicit (IMEX) methods, a within-step adaptable decomposition called residual balanced decomposition is introduced. With this decomposition, the requirement of a small enough residual in the…
We present a new strategy for solving stiff ODEs with explicit methods. By adaptively taking a small number of stabilizing small explicit time steps when necessary, a stiff ODE system can be stabilized enough to allow for time steps much…
When evolving in time the solution of a hyperbolic partial differential equation, it is often desirable to use high order strong stability preserving (SSP) time discretizations. These time discretizations preserve the monotonicity…
Process Management Systems (PMSs) are currently more and more used as a supporting tool for cooperative processes in pervasive and highly dynamic situations, such as emergency situations, pervasive healthcare or domotics/home automation.…
In this paper, we propose a multirate iterative scheme with multiphysics finite element method for a fluid-saturated poroelasticity model. Firstly, we reformulate the original model into a fluid coupled problem to apply the multiphysics…
Unconditionally stable implicit time-marching methods are powerful in solving stiff differential equations efficiently. In this work, a novel framework to handle stiff physical terms implicitly is proposed. Both physical and numerical…
In the near future, massively parallel computing systems will be necessary to solve computation intensive applications. The key bottleneck in massively parallel implementation of numerical algorithms is the synchronization of data across…
High order strong stability preserving (SSP) time discretizations are advantageous for use with spatial discretizations with nonlinear stability properties for the solution of hyperbolic PDEs. The search for high order strong stability…
We develop a multirate timestepper for semi-implicit solutions of the unsteady incompressible Navier-Stokes equations (INSE) based on a recently-developed multidomain spectral element method (SEM). For {\em incompressible} flows, multirate…
Consistent splitting schemes are among the most accurate pressure segregation methods, incurring no splitting errors or spurious boundary conditions. Nevertheless, their theoretical properties are not yet fully understood, especially when…
When the singular values of the evolution operator are all smaller or all greater than one, stable integration algorithms are obtained either by explicit or implicit methods. When the singular spectrum mixes greater and smaller than one…
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…
Large-scale multiphysics simulations are computationally challenging due to the coupling of multiple processes with widely disparate time scales. The advent of exascale computing systems exacerbates these challenges, since these enable ever…
Explicit stabilized methods are an efficient alternative to implicit schemes for the time integration of stiff systems of differential equations in large dimension. In this paper, we derive explicit stabilized integrators of orders one and…
The initialization process of a novel power system transient simulation scheme for stability studies is put forward, by further developing a "time-domain harmonic power-flow algorithm". The initialization process is formulated as an…
Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…