相关论文: Continuous-stage Runge-Kutta-Nystr\"Om methods

The paper develops high order accurate Runge-Kutta discontinuous local evolution Galerkin (RKDLEG) methods on the cubed-sphere grid for the shallow water equations (SWEs). Instead of using the dimensional splitting method or solving…

Reducing bit-widths of weights, activations, and gradients of a Neural Network can shrink its storage size and memory usage, and also allow for faster training and inference by exploiting bitwise operations. However, previous attempts for…

This paper introduces a nonlinear conjugate gradient method (NCGM) for addressing the robust counterpart of uncertain multiobjective optimization problems (UMOPs). Here, the robust counterpart is defined as the minimum across objective-wise…

We present a method to construct a continuous extension (otherwise known as dense output) for a numerical routine in the special case of the numerical solution being a scalar-valued function exhibiting rapid oscillations. Such cases call…

Singly-TASE operators for the numerical solution of stiff differential equations were proposed by Calvo et al. in J.Sci. Comput. 2023 to reduce the computational cost of Runge-Kutta-TASE (RKTASE) methods when the involved linear systems are…

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…

Variational space-time formulations for Partial Differential Equations have been of great interest in the last decades. While it is known that implicit time marching schemes have variational structure, the Galerkin formulation of explicit…

Resummation methods using continued functions are implemented to converge divergent series appearing in perturbation problems related to continuous phase transitions in field theories. In some cases, better convergence properties are…

We develop two new sets of stable, rank-adaptive Dynamically Orthogonal Runge-Kutta (DORK) schemes that capture the high-order curvature of the nonlinear low-rank manifold. The DORK schemes asymptotically approximate the truncated singular…

Many control, optimization, and learning algorithms rely on discretizations of continuous-time contracting systems, where preservation of contractivity under numerical integration is key for stability, robustness, and reliable fixed-point…

In practical computation with Runge--Kutta methods, the stage equations are not satisfied exactly, due to roundoff errors, algebraic solver errors, and so forth. We show by example that propagation of such errors within a single step can…

This paper extends the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulations on a rotating coordinate frame. The kinetic equation with the inclusion of centrifugal and Coriolis acceleration is used in the…

While a diverse collection of continual learning (CL) methods has been proposed to prevent catastrophic forgetting, a thorough investigation of their effectiveness for processing sequential data with recurrent neural networks (RNNs) is…

In this chapter, we investigate recently proposed nonlinear conjugate gradient (NCG) methods for shape optimization problems. We briefly introduce the methods as well as the corresponding theoretical background and investigate their…

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…

In this article, the construction and implementation of a seventh order weighted essentially non-oscillatory scheme is reported for hyperbolic conservation laws. Local smoothness indicators are constructed based on $L_{1}$-norm, where a…

Spectral Clustering is a popular technique to split data points into groups, especially for complex datasets. The algorithms in the Spectral Clustering family typically consist of multiple separate stages (such as similarity matrix…

A simple alternative to the conjugate gradient(CG) method is presented; this method is developed as a special case of the more general iterated Ritz method (IRM) for solving a system of linear equations. This novel algorithm is not based on…

The class of stochastic Runge-Kutta methods for stochastic differential equations due to R\"o{\ss}ler is considered. Coefficient families of diagonally drift-implicit stochastic Runge-Kutta (DDISRK) methods of weak order one and two are…

This paper considers random graph approach to simulate irreversible step-growth polymerization. We study generalization of approach developed by Kryven~I. by introducing different types of bonds each with its own weight representing…