Related papers: Adaptive time-stepping for aggregation-shattering …
Phase-field models of fatigue are capable of reproducing the main phenomenology of fatigue behavior. However, phase-field computations in the high-cycle fatigue regime are prohibitively expensive, due to the need to resolve spatially the…
Strong stability preserving (SSP) Runge-Kutta methods are often desired when evolving in time problems that have two components that have very different time scales. Where the SSP property is needed, it has been shown that implicit and…
The convergence of a family of AMF-Runge-Kutta methods (in short AMF-RK) for the time integration of evolutionary Partial Differential Equations (PDEs) of Advection Diffusion Reaction type semi-discretized in space is considered. The…
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…
Time series, as frequently the case in neuroscience, are rarely stationary, but often exhibit abrupt changes due to attractor transitions or bifurcations in the dynamical systems producing them. A plethora of methods for detecting such…
We present two types of meta-algorithm that can greatly improve the accuracy of existing algorithms for integrating the equations of motion of dynamical systems. The first meta-algorithm takes an integrator that is time-symmetric only for…
In this paper we demonstrate a simple heuristic adaptive restart technique that can dramatically improve the convergence rate of accelerated gradient schemes. The analysis of the technique relies on the observation that these schemes…
Numerical solutions to fractional differential equations can be extremely computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In finite difference…
A coercivity property of temporal convolution operators is an essential tool in the analysis of time-dependent boundary integral equations and their space and time discretisations. It is known that this coercivity property is inherited by…
A mixed accuracy framework for Runge--Kutta methods presented in [Grant, JSC 2022] has been shown to speed up the computation in diagonally implicit Runge--Kutta (DIRK) methods by using less expensive low accuracy approaches for the…
In this paper, we present an efficient numerical method to address a thermodynamically consistent gas flow model in porous media involving compressible gas and deformable rock. The accurate modeling of gas flow in porous media often poses…
This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…
The growing share of intermittent renewable energy sources, storage technologies, and the increasing degree of so-called sector coupling necessitates optimization-based energy system models with high temporal and spatial resolutions, which…
The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant…
Exponential Runge--Kutta methods have shown to be competitive for the time integration of stiff semilinear parabolic PDEs. The current construction of stiffly accurate exponential Runge--Kutta methods, however, relies on a convergence…
We study a discrete-time random feature method for nonlinear, time-dependent partial differential equations. In contrast to continuous-time formulations that treat time as an additional input variable, the method advances the solution step…
Time-fractional parabolic equations with a Caputo time derivative of order $\alpha\in(0,1)$ are discretised in time using collocation methods, which assume that the Caputo derivative of the computed solution is piecewise-polynomial. For…
The computational effort for the evaluation of numerical simulations based on e.g. the finite-element method is high. Metamodels can be utilized to create a low-cost alternative. However the number of required samples for the creation of a…
We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle…
We present the formulation and optimization of a Runge-Kutta-type time-stepping scheme for solving the shallow water equations, aimed at substantially increasing the effective allowable time-step over that of comparable methods. This…