Related papers: Automatic differentiation for performing the Cauch…
We equip a high-order continuous Galerkin discretization of a general hyperbolic problem with a nonlinear stabilization term and introduce a new methodology for enforcing preservation of invariant domains. The amount of shock-capturing…
The active flux (AF) method is a compact high-order finite volume method originally proposed for solving hyperbolic conservation laws, in which cell averages and point values at cell interfaces are evolved simultaneously. This paper…
The successes of deep learning, variational inference, and many other fields have been aided by specialized implementations of reverse-mode automatic differentiation (AD) to compute gradients of mega-dimensional objectives. The AD…
Thermodynamic and flash equilibrium calculations are the cornerstones of simulation process calculations. The iterative approach, a widely used nonlinear problem-solving technique, relies on derivative calculations throughout the procedure…
In this paper, a compact and high order ADER (Arbitrary high order using DERivatives) scheme using the simple HWENO method (ADER-SHWENO) is proposed for hyperbolic conservation laws. The newly-developed method employs the Lax-Wendroff…
Algorithmic differentiation (AD) is a set of techniques that provide partial derivatives of computer-implemented functions. Such a function can be supplied to state-of-the-art AD tools via its source code, or via an intermediate…
Modelers use automatic differentiation (AD) of computation graphs to implement complex Deep Learning models without defining gradient computations. Stochastic AD extends AD to stochastic computation graphs with sampling steps, which arise…
In this paper we establish best approximation type error estimates for the fully discrete Galerkin solutions of the time-dependent Stokes problem using the stream-function formulation. For the time discretization we use the discontinuous…
In its application to the modeling of a mineral separation process, we propose the numerical analysis of the Cahn-Hilliard equation by employing spacetime discretizations of the automatic variationally stable finite element (AVS-FE) method.…
In this article, a finite element Galerkin method is applied to the Kelvin-Voigt viscoelastic fluid model, when its forcing function is in $L^{\infty}(\bL^2)$. Some new {\it a priori} bounds for the velocity as well as for the pressure are…
We propose a class of weighted compact central (WCC) schemes for solving hyperbolic conservation laws. The linear version can be considered as a high-order extension of the central Lax-Friedrichs (LxF) scheme and the central conservation…
Ptychography, a coherent diffraction imaging technique, has become an indispensable tool in materials characterization, biological imaging, and nanostructure analysis due to its capability for high-resolution, lensless reconstruction of…
We present a novel implicit scheme for the numerical solution of time-dependent conservation laws. The core idea of the presented method is to exploit and approximate the mixed spatial-temporal derivative of the solution that occurs…
We present an efficient and accurate grid method for solving the time-dependent Schr\"{o}dinger equation of atomic systems interacting with intense laser pulses. As usual, the angular part of the wave function is expanded in terms of…
A singularly perturbed reaction-diffusion problem posed on the unit square in $\mathbb{R}^2$ is solved numerically by a local discontinuous Galerkin (LDG) finite element method. Typical solutions of this class of 2D problems exhibit…
The paper develops high-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamical (RHD) equations, built on the local Lax-Friedrich splitting, the WENO reconstruction, the…
This paper considers the reliability of automatic differentiation (AD) for neural networks involving the nonsmooth MaxPool operation. We investigate the behavior of AD across different precision levels (16, 32, 64 bits) and convolutional…
We present a novel quasi-conservative arbitrary high order accurate ADER discontinuous Galerkin (DG) method allowing to efficiently use a non-conservative form of the considered partial differential system, so that the governing equations…
We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include…
Classical reverse-mode automatic differentiation (AD) imposes only a small constant-factor overhead in operation count over the original computation, but has storage requirements that grow, in the worst case, in proportion to the time…