Efficient Iterative Arbitrary High-Order Methods: an Adaptive Bridge Between Low and High Order [0.03%]
高效迭代任意高阶方法：低阶与高阶之间的自适应桥梁
Lorenzo Micalizzi,Davide Torlo,Walter Boscheri
Lorenzo Micalizzi
We propose a new paradigm for designing efficient p-adaptive arbitrary high-order methods. We consider arbitrary high-order iterative schemes that gain one order of accuracy at each iteration and we modify them to match the accuracy achieve...
A New Efficient Explicit Deferred Correction Framework: Analysis and Applications to Hyperbolic PDEs and Adaptivity [0.03%]
一个新的高效的显式延迟校正框架：分析及在双曲型偏微分方程和自适应方法中的应用
Lorenzo Micalizzi,Davide Torlo
Lorenzo Micalizzi
The deferred correction (DeC) is an iterative procedure, characterized by increasing the accuracy at each iteration, which can be used to design numerical methods for systems of ODEs. The main advantage of such framework is the automatic wa...
Piecewise Acoustic Source Imaging with Unknown Speed of Sound Using a Level-Set Method [0.03%]
基于水平集方法的声源图像重建算法
Guanghui Huang,Jianliang Qian,Yang Yang
Guanghui Huang
We investigate the following inverse problem: starting from the acoustic wave equation, reconstruct a piecewise constant passive acoustic source from a single boundary temporal measurement without knowing the speed of sound. When the amplit...
An Arbitrarily High Order and Asymptotic Preserving Kinetic Scheme in Compressible Fluid Dynamic [0.03%]
一种具有任意高阶和渐近保持性质的可压缩流体动力学粒子输运chemes方法
Rémi Abgrall,Fatemeh Nassajian Mojarrad
Rémi Abgrall
We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics, both in time and space, which include the relaxation schemes by Jin and Xin. These methods can use the CFL number larger o...
L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation [0.03%]
Caputo-Hadamard时间分数阶扩散方程的L1/LDG方法
Zhen Wang
Zhen Wang
In this paper, a class of discrete Gronwall inequalities is proposed. It is efficiently applied to analyzing the constructed L1/local discontinuous Galerkin (LDG) finite element methods which are used for numerically solving the Caputo-Hada...
A Combination of Residual Distribution and the Active Flux Formulations or a New Class of Schemes That Can Combine Several Writings of the Same Hyperbolic Problem: Application to the 1D Euler Equations [0.03%]
残差分布与主动通量公式的一种组合或一种新的方案类：应用于一维欧拉方程
R Abgrall
R Abgrall
We show how to combine in a natural way (i.e., without any test nor switch) the conservative and non-conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different classes of schemes: the...
Von Neumann Stability Analysis of DG-Like and P N P M-Like Schemes for PDEs with Globally Curl-Preserving Evolution of Vector Fields [0.03%]
DG-like和P_N_P_M-like方案的微分方程的稳定性分析（矢量场全局保旋演化）
Dinshaw S Balsara,Roger Käppeli
Dinshaw S Balsara
This paper examines a class of involution-constrained PDEs where some part of the PDE system evolves a vector field whose curl remains zero or grows in proportion to specified source terms. Such PDEs are referred to as curl-free or curl-pre...