The Surrogate Matrix Methodology: A Priori Error Estimation

DOI10.1137/18M1226580zbMath1435.65022arXiv1902.07333OpenAlexW3101523096MaRDI QIDQ5204013

Daniel Drzisga, Brendan Keith, Barbara I. Wohlmuth

Publication date: 9 December 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.07333

zbMATH Keywords

finite element methodsmatrix-freelow ordera priori analysisgeometric multigridsurrogate numerical methods

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Numerical interpolation (65D05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Parallel numerical computation (65Y05) Complexity and performance of numerical algorithms (65Y20)

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Cites Work

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• A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
• Efficient nonlinear solvers for nodal high-order finite elements in 3D
• Coupled variational formulations of linear elasticity and the DPG methodology
• A scalable, matrix-free multigrid preconditioner for finite element discretizations of heterogeneous Stokes flow
• Tetrahedral grid refinement
• The surrogate matrix methodology: low-cost assembly for isogeometric analysis
• A generic interface for parallel cell-based finite element operator application
• A two-scale approach for efficient on-the-fly operator assembly in massively parallel high performance multigrid codes
• Parallel Octree-Based Finite Element Method for Large-Scale Earthquake Ground Motion Simulation
• Hierarchical hybrid grids: data structures and core algorithms for multigrid
• Towards Textbook Efficiency for Parallel Multigrid
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• A scalable multi-level preconditioner for matrix-free µ-finite element analysis of human bone structures
• Element-by-element linear and nonlinear solution schemes
• Finite Element Approximation of the p-Laplacian
• A Stencil Scaling Approach for Accelerating Matrix-Free Finite Element Implementations
• Curved Elements in the Finite Element Method. I
• Stencil Scaling for Vector-Valued PDEs on Hybrid Grids With Applications to Generalized Newtonian Fluids