We consider large linear systems arising from the isogeometric discretization of the Poisson problem on a single-patch domain. The numerical solution of such systems is considered a challenging task, particularly when the degree of the splines employed as basis functions is high. We consider a preconditioning strategy which is based on the solution of a Sylvester-like equation at each step of an iterative solver. We show that this strategy, which fully exploits the tensor structure that underlies isogeometric problems, is robust with respect to both mesh size and spline degree, although it may suffer from the presence of complicated geometry or coefficients. We consider two popular solvers for the Sylvester equation, a direct one and an iterative one, and we discuss in detail their implementation and efficiency for 2D and 3D problems on single-patch or conforming multi-patch NURBS geometries. Numerical experiments for problems with different domain geometries are presented, which demonstrate the potential of this approach.
Isogeometric multi-patch preconditioner for time-dependent electromagnetic problems
École Polytechnique Fédérale Lausanne（洛桑联邦理工学院）；Università di Pavia（帕维亚大学）；Istituto di Matematica Applicata e Tecnologie Informatiche “E. Magenes” del CNR（意大利国家研究委员会应用数学与信息技术研究所（E. Magenes））；Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）；Galician Centre for Mathematical Research and Technology（加利西亚数学研究与技术中心）
Robust preconditioning and error estimates for optimal control of the convection-diffusion-reaction equation with limited observation in Isogeometric analysis
Robust Preconditioning for Space-Time Isogeometric Analysis of Parabolic Evolution Problems
Johannes Kepler University（约翰内斯·开普勒大学）；Institute of Computational Mathematics, Johannes Kepler University（约翰内斯·开普勒大学计算数学研究所）；Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences（奥地利科学院约翰·拉顿计算与应用数学研究所）
Scalable multigrid methods for immersed finite element methods and immersed isogeometric analysis
Eindhoven University of Technology（埃因霍温理工大学）；University of Colorado Boulder（科罗拉多大学博尔德分校）；German Aerospace Center (DLR)（德国航空航天中心）；Walt Disney Animation Studios（华特迪士尼动画工作室）
The cost of continuity: performance of iterative solvers on isogeometric finite elements
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Consejo Nacional de Investigaciones Científicas y Técnicas（阿根廷国家科学研究委员会）；The University of the Basque Country UPV/EHU（巴斯克地区大学）；Ikerbasque（伊卡巴斯克基金会）
Parallel matching-based AMG preconditioners for elliptic equations discretized by IgA
National Research Council of Italy (CNR)（意大利国家研究委员会）；Institute for Applied Computing “Mauro Picone” (IAC)（毛罗·皮切纳应用计算研究所）；University of Pisa（比萨大学）；University of Rome “Tor Vergata”（罗马托维尔加塔大学）
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）
