Matrix‐free preconditioning for high‐order H(curl) discretizations

[1]  Timothy C. Warburton,et al.  Low-Order Preconditioning of High-Order Triangular Finite Elements , 2018, SIAM J. Sci. Comput..

[2]  Jan Mandel,et al.  An algebraic theory for multigrid methods for variational problems , 1988 .

[3]  Katharina Kormann,et al.  Fast Matrix-Free Discontinuous Galerkin Kernels on Modern Computer Architectures , 2017, ISC.

[4]  Stefan Vandewalle,et al.  Local Fourier Analysis of Multigrid for the Curl-Curl Equation , 2008, SIAM J. Sci. Comput..

[5]  V. E. Henson,et al.  BoomerAMG: a parallel algebraic multigrid solver and preconditioner , 2002 .

[6]  Rainald Löhner,et al.  Improved error and work estimates for high‐order elements , 2013 .

[7]  Katharina Kormann,et al.  A generic interface for parallel cell-based finite element operator application , 2012 .

[8]  Tzanio V. Kolev,et al.  High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics , 2012, SIAM J. Sci. Comput..

[9]  Martin Kronbichler,et al.  Scalability of high-performance PDE solvers , 2020, Int. J. High Perform. Comput. Appl..

[10]  Martin Kronbichler,et al.  Multigrid for Matrix-Free High-Order Finite Element Computations on Graphics Processors , 2019, ACM Trans. Parallel Comput..

[11]  S. Orszag.  Spectral methods for problems in complex geometries , 1980 .

[12]  Ernest E. Rothman,et al.  Preconditioning Legendre spectral collocation approximations to elliptic problems , 1995 .

[13]  J. Nédélec.  Mixed finite elements in ℝ3 , 1980 .

[14]  Van Emden Henson,et al.  Robustness and Scalability of Algebraic Multigrid , 1999, SIAM J. Sci. Comput..

[15]  Panayot S. Vassilevski,et al.  PARALLEL AUXILIARY SPACE AMG FOR H(curl) PROBLEMS , 2009 .

[16]  Per-Olof Persson,et al.  Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods , 2017, J. Comput. Phys..

[17]  Ludmil T. Zikatanov,et al.  Algebraic multigrid methods * , 2016, Acta Numerica.

[18]  Jed Brown,et al.  Efficient Nonlinear Solvers for Nodal High-Order Finite Elements in 3D , 2010, J. Sci. Comput..

[19]  Luke N. Olson.  Algebraic Multigrid Preconditioning of High-Order Spectral Elements for Elliptic Problems on a Simplicial Mesh , 2007, SIAM J. Sci. Comput..

[20]  Shuai Jiang,et al.  Preconditioning the Mass Matrix for High Order Finite Element Approximation on Triangles , 2019, SIAM J. Numer. Anal..

[21]  Hari Sundar,et al.  Comparison of multigrid algorithms for high‐order continuous finite element discretizations , 2014, Numer. Linear Algebra Appl..

[22]  Peter Monk,et al.  Finite Element Methods for Maxwell's Equations , 2003 .

[23]  Paul F. Fischer,et al.  Hybrid Multigrid/Schwarz Algorithms for the Spectral Element Method , 2005, J. Sci. Comput..

[24]  Thomas A. Manteuffel,et al.  Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes , 2012, J. Comput. Phys..

[25]  Stefano Zampini,et al.  MFEM: a modular finite element methods library , 2019, 1911.09220.

[26]  Jinchao Xu,et al.  Nodal Auxiliary Space Preconditioning in H(curl) and H(div) Spaces , 2007, SIAM J. Numer. Anal..