Related papers: Additive Polynomial Time Integrators, Part I: Fram…

We describe the ARKODE library of one-step time integration methods for ordinary differential equation (ODE) initial-value problems (IVPs). In addition to providing standard explicit and diagonally implicit Runge--Kutta methods, ARKODE also…

Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…

Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were proposed and analyzed in [8]. These specially designed methods use reduced precision or the implicit computations and full…

Rational methods are intended to time integrate linear homogeneous problems. However, their scope can be extended so as to cover linear nonhomogeneous problems. In this paper the integration of semilinear problems is considered. The…

Dielectric elastomers are increasingly studied for their potential in soft robotics, actuators, and haptic devices. Under time-dependent loading, they dissipate energy via viscous deformation and friction in electric polarization. However,…

This paper deals with the application of probabilistic time integration methods to semi-explicit partial differential-algebraic equations of parabolic type and its semi-discrete counterparts, namely semi-explicit differential-algebraic…

Implicit-explicit Runge-Kutta (IMEX-RK) time discretization methods are very popular when solving stiff kinetic equations. In [21], an asymptotic analysis shows that a specific class of high-order IMEX-RK schemes can accurately capture the…

Rational exponential integrators (REXI) are a class of numerical methods that are well suited for the time integration of linear partial differential equations with imaginary eigenvalues. Since these methods can be parallelized in time (in…

We propose a novel numerical method for the solution of the shallow water equations in different regimes of the Froude number making use of general polygonal meshes. The fluxes of the governing equations are split such that advection and…

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…

We reconsider the variational derivation of symplectic partitioned Runge-Kutta schemes. Such type of variational integrators are of great importance since they integrate mechanical systems with high order accuracy while preserving the…

We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…

In a previous paper, a technique was suggested to avoid order reduction with any explicit exponential Runge-Kutta method when integrating initial boundary value nonlinear problems with time-dependent boundary conditions. In this paper, we…

Peer methods are a comprehensive class of time integrators offering numerous degrees of freedom in their coefficient matrices that can be used to ensure advantageous properties, e.g. A-stability or super-convergence. In this paper, we show…

Fast and accurate solutions of time-dependent partial differential equations (PDEs) are of pivotal interest to many research fields, including physics, engineering, and biology. Generally, implicit/semi-implicit schemes are preferred over…

Railway Wireless Power Transfer (WPT) is a promising non-contact power supply solution, but constructing prototypes for controller testing can be both costly and unsafe. Real-time hardware-in-the-loop simulation is an effective and secure…

We propose a kernel compression method for solving Distributed-Order (DO) Fractional Partial Differential Equations (DOFPDEs) at the cost of solving corresponding local-in-time PDEs. The key concepts are (1) discretization of the integral…

This paper introduces BFEMP, a new approach for monolithically coupling the Material Point Method (MPM) with the Finite Element Method (FEM) through barrier energy-based particle-mesh frictional contact using a variational time-stepping…

Solving partial differential equations (PDEs) with highly oscillatory solutions on complex domains remains a challenging and important problem. High-frequency oscillations and intricate geometries often result in prohibitively expensive…

This paper studies fixed-step convergence of implicit-explicit general linear methods. We focus on a subclass of schemes that is internally consistent, has high stage order, and favorable stability properties. Classical, index-1…