Rémi Abgrall,Yongle Liu,Philipp Öffner
Rémi Abgrall
In this paper, we provide a few new properties of Active Flux (AF)/Point-Average-Moment PolynomiAl-interpreted (PamPa) schemes. First, we show, in full generality, that the AF/PamPa schemes can be interpreted in such a way that the disconti...
Linearly Implicit Finite Element Methods Approximating the Solution to the Nonlinear Schrödinger Equation with a Schamel-Type Nonlinearity [0.03%]
具有Schamel型非线性的非线性Schrödinger方程的解的隐式有限元方法逼近
Panagiotis Paraschis,Georgios E Zouraris
Panagiotis Paraschis
We consider an initial- and Dirichlet boundary- value problem for a nonlinear Schrödinger equation of the form u t = i Δ u + i V u + i μ | u | β u + f over [ 0 , T ] × Ω , where T > 0 , Ω ⊂ R ...
Fully Well-Balanced Methods for Schwarzschild-Euler Equation in Gullstrand-Painlevé Coordinates [0.03%]
广义厄恩斯特方程的完全平衡方法在GP坐标系下的应用
Ernesto Pimentel-García,Samuel Santos-Pérez,Isabel Cordero-Carrión et al.
Ernesto Pimentel-García et al.
We present a comprehensive formulation of the general-relativistic Euler equations in Gullstrand-Painlevé coordinates, providing a description of fluid dynamics that remains regular across the Schwarzschild event horizon. After establishin...
Inf-Sup Stable Space-Time Discretization of the Wave Equation Based on a First-Order-In-Time Variational Formulation [0.03%]
基于一阶时间变分公式构建的波动方程空间-时间稳定离散格式
Matteo Ferrari,Ilaria Perugia,Enrico Zampa
Matteo Ferrari
In this paper, we present a conforming space-time discretization of the wave equation based on a first-order-in-time variational formulation. Our method extends the scheme of French and Peterson (1996), incorporating exponential weights in ...
Matrix-Free Inexact Preconditioning Techniques for Isogeometric Tensor-Product Discretizations [0.03%]
Isogeometric分数阶偏微分方程的矩阵自由近似预条件技术研究
Michał Ł Mika,René R Hiemstra,Dominik Schillinger
Michał Ł Mika
We propose a matrix-free inexact preconditioning strategy for elliptic partial differential equations discretized by the isogeometric Galerkin method on tensor-product spline spaces. We base our preconditioner on an approximation of the dis...
A Robust Finite Element Method for Linearized Magnetohydrodynamics on General Domains [0.03%]
一般区域线性化磁流体动力学的鲁棒有限元方法
L Beirão da Veiga,C Lovadina,M Trezzi
L Beirão da Veiga
We generalize and improve the finite element method for linearized Magnetohydrodynamics introduced in (Beirão da Veiga et al., SIAM J. Numer. Anal. 62(4):1539-1564 (2024)). The main novelty is that the proposed scheme is able to handle als...
Vanja Nikolić,Teresa Rauscher
Vanja Nikolić
Harmonic generation plays a crucial role in contrast-enhanced ultrasound, both for imaging and therapeutic applications. However, accurately capturing these nonlinear effects is computationally demanding when using traditional time-domain a...
Fast Numerical Solvers for Parameter Identification Problems in Mathematical Biology [0.03%]
数学生物学中的参数识别问题的快速数值解法研究
Karolína Benková,John W Pearson,Mariya Ptashnyk
Karolína Benková
In this paper, we consider effective discretization strategies and iterative solvers for nonlinear PDE-constrained optimization models of pattern evolution within biological processes. Upon a Sequential Quadratic Programming linearization o...
Inf-sup stable space-time Local Discontinuous Galerkin method for the heat equation [0.03%]
求解热方程的时空局部间断Galerkin方法的稳定性分析
Sergio Gómez,Chiara Perinati,Paul Stocker
Sergio Gómez
We propose and analyze a space-time Local Discontinuous Galerkin method for the approximation of the solution to parabolic problems. The method allows for very general discrete spaces and prismatic space-time meshes. Existence and uniquenes...
Stochastic Conformal Integrators for Linearly Damped Stochastic Poisson Systems [0.03%]
线性阻尼随机泊松系统的随机保辛积分方法
Charles-Edouard Bréhier,David Cohen,Yoshio Komori
Charles-Edouard Bréhier
We propose and study conformal integrators for linearly damped stochastic Poisson systems. We analyse the qualitative and quantitative properties of these numerical integrators: preservation of dynamics of certain Casimir and Hamiltonian fu...