Explicit implementation strategy of high order edge finite elements and Schwarz preconditioning for the time-harmonic Maxwell's equations
Université Côte d’Azur（蔚蓝海岸大学）；CNRS（法国国家科学研究中心）；LJAD（约瑟夫·拉格朗日实验室）；University of Strathclyde（斯特拉斯克莱德大学）；UPMC Univ Paris 6（巴黎第六大学皮埃尔和玛丽·居里大学）；LJLL（拉格朗日分析与偏微分方程实验室）
In this paper we focus on high order finite element approximations of the electric field combined with suitable preconditioners, to solve the time-harmonic Maxwell's equations in waveguide configurations. The implementation of high order curl-conforming finite elements is quite delicate, especially in the three-dimensional case. Here, we explicitly describe an implementation strategy, which has been embedded in the open source finite element software FreeFem++ (http://www.freefem.org/ff++/). In particular, we use the inverse of a generalized Vandermonde matrix to build a basis of generators in duality with the degrees of freedom, resulting in an easy-to-use but powerful interpolation operator. We carefully address the problem of applying the same Vandermonde matrix to possibly differently oriented tetrahedra of the mesh over the computational domain. We investigate the preconditioning for Maxwell's equations in the time-harmonic regime, which is an underdeveloped issue in the literature, particularly for high order discretizations. In the numerical experiments, we study the effect of varying several parameters on the spectrum of the matrix preconditioned with overlapping Schwarz methods, both for 2d and 3d waveguide configurations.
Optimized Schwarz preconditioning for SEM based magnetohydrodynamics
Institute for Mathematics Applied to Geosciences, National Center for Atmospheric Research（国家大气研究中心应用数学与地球科学研究所）；Department of Mathematics, Kyungpook National University（庆北大学数学系）
Block Schwarz methods and preconditioning strategies using Generalized locally Toeplitz tools - part I: analysis of the preconditioners and numerical validation
Freezing Calderón: Robust Preconditioning for Maxwell Scattering under Shape Uncertainty
Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez（阿道夫·伊巴涅斯大学工程与科学学院）；Department of Mathematics and Digital Futures, KTH Royal Institute of Technology（瑞典皇家理工学院数学与数字未来系）；Inria Chile（法国国家信息与自动化研究所智利分部）
An example of explicit implementation strategy and preconditioning for the high order edge finite elements applied to the time-harmonic Maxwell's equations
Nonlinear Preconditioning: How to use a Nonlinear Schwarz Method to Precondition Newton's Method
University of Strathclyde（斯特拉斯克莱德大学）；Université de Genève（日内瓦大学）；Université Nice Sophia Antipolis（尼斯索菲亚安蒂波利斯大学）；Inria（法国国家数字科学研究所）；Hong Kong Baptist University（香港浸会大学）
A domain decomposition preconditioning for the integral equation formulation of the inverse scattering problem
我们提出了区域分解预处理器的解决方案的积分方程制定的正、逆声散射问题的点散射体。我们研究了正问题和反问题，并提出了预处理技术，以加快迭代求解器。对于前向散射问题，我们扩展了{ \em“A restricted additive Schwarz preconditioner for general sparse线性系“，SIAM Journal on Scientific Computing，21（1999），pp. 792--797}，到积分方程。我们结合这个区域分解预条件与低秩校正，这是很容易构建，形成一个新的预条件。对于逆散射问题，我们使用的前向问题的预处理器作为一个积木构建一个预处理器的高斯-牛顿海森。我们提出的数值结果表明，这两个预处理策略的性能。
Domain decomposition preconditioning for the high-frequency time-harmonic Maxwell equations with absorption
Sorbonne Université, Université Paris-Diderot SPC, CNRS, Inria, Laboratoire Jacques-Louis Lions（索邦大学，巴黎第七大学SPC，法国国家科学研究中心，法国国家信息与自动化研究所，雅克-路易·利翁斯实验室）；Department of Mathematics and Statistics, University of Strathclyde（斯特拉斯克莱德大学数学与统计系）；Université Côte d’Azur, CNRS, Laboratoire J-A Dieudonné（蔚蓝海岸大学，法国国家科学研究中心，J-A 迪厄多内实验室）；Department of Mathematical Sciences, University of Bath（巴斯大学数学科学系）
Analysis of Block Jacobi/Gauss-Seidel and additive/multiplicative Schwarz preconditioning through the theory of GLT sequences, with applications to domain decomposition discretizations
University of Rome Tor Vergata（罗马托尔维加塔大学）；University Mohammed VI Polytechnic（穆罕默德六世polytechnic大学）；University of Insubria（因苏布里亚大学）；Uppsala University（乌普萨拉大学）
Monolithic and Block Overlapping Schwarz Preconditioners for the Incompressible Navier-Stokes Equations
Delft Institute of Applied Mathematics, Delft University of Technology（代尔夫特理工大学应用数学研究所）；Department of Mathematics and Computer Science, University of Cologne（科隆大学数学与计算机科学系）；Center for Data and Simulation Science, University of Cologne（科隆大学数据与模拟科学中心）
Deflation-accelerated preconditioning of the Poisson-Neumann Schur problem on long domains with a high-order discontinuous element-based collocation method
Cornell University（康奈尔大学）；Applied Research Laboratories（应用研究实验室）
