Sequential Approximation of Functions in Sobolev Spaces Using Random SamplesCommunications on Applied Mathematics and Computation - Tập 1 - Trang 449-466 - 2019
Kailiang Wu, Dongbin Xiu
We present an iterative algorithm for approximating an unknown function sequentially using random samples of the function values and gradients. This is an extension of the recently developed sequential approximation (SA) method, which approximates a target function using samples of function values only. The current paper extends the development of the SA methods to the Sobolev space and allows the...... hiện toàn bộ
The Hermite-Taylor Correction Function Method for Maxwell’s EquationsCommunications on Applied Mathematics and Computation - - Trang 1-25 - 2023
Yann-Meing Law, Daniel Appelö
The Hermite-Taylor method, introduced in 2005 by Goodrich et al. is highly efficient and accurate when applied to linear hyperbolic systems on periodic domains. Unfortunately, its widespread use has been prevented by the lack of a systematic approach to implementing boundary conditions. In this paper we present the Hermite-Taylor correction function method (CFM), which provides exactly such a syst...... hiện toàn bộ
PrefaceCommunications on Applied Mathematics and Computation - - Trang 1-2 - 2023
Qing Nie, Chi-Wang Shu, Yulong Xing, Yong-Tao Zhang
Failure-Informed Adaptive Sampling for PINNs, Part II: Combining with Re-sampling and Subset SimulationCommunications on Applied Mathematics and Computation - - Trang 1-22 - 2023
Zhiwei Gao, Tao Tang, Liang Yan, Tao Zhou
This is the second part of our series works on failure-informed adaptive sampling for physic-informed neural networks (PINNs). In our previous work (SIAM J. Sci. Comput. 45: A1971–A1994), we have presented an adaptive sampling framework by using the failure probability as the posterior error indicator, where the truncated Gaussian model has been adopted for estimating the indicator. Here, we prese...... hiện toàn bộ
A Semi-Lagrangian Spectral Method for the Vlasov–Poisson System Based on Fourier, Legendre and Hermite PolynomialsCommunications on Applied Mathematics and Computation - Tập 1 - Trang 333-360 - 2019
Lorella Fatone, Daniele Funaro, Gianmarco Manzini
In this work, we apply a semi-Lagrangian spectral method for the Vlasov–Poisson system, previously designed for periodic Fourier discretizations, by implementing Legendre polynomials and Hermite functions in the approximation of the distribution function with respect to the velocity variable. We discuss second-order accurate-in-time schemes, obtained by coupling spectral techniques in the space–ve...... hiện toàn bộ
An Unconventional Divergence Preserving Finite-Volume Discretization of Lagrangian Ideal MHDCommunications on Applied Mathematics and Computation - - Trang 1-55 - 2023
Walter Boscheri, Raphaël Loubère, Pierre-Henri Maire
We construct an unconventional divergence preserving discretization of updated Lagrangian ideal magnetohydrodynamics (MHD) over simplicial grids. The cell-centered finite-volume (FV) method employed to discretize the conservation laws of volume, momentum, and total energy is rigorously the same as the one developed to simulate hyperelasticity equations. By construction this moving mesh method ensu...... hiện toàn bộ
A Multi-physics Methodology for Four States of MatterCommunications on Applied Mathematics and Computation - Tập 2 - Trang 487-514 - 2019
Louisa Michael, Stephen T. Millmore, Nikolaos Nikiforakis
We propose a numerical methodology for the simultaneous numerical simulation of four states of matter: gas, liquid, elastoplastic solids, and plasma. The distinct, interacting physical processes are described by a combination of compressible, inert, and reactive forms of the Euler equations, multi-phase equations, elastoplastic equations, and resistive MHD equations. Combinations of systems of equ...... hiện toàn bộ