Hybrid Nitsche for distributed computing

2025/04/07 by Gustafsson, Tom, Hannukainen, Antti, Kohonen, Vili +1
#65F55 #65N30 #65N55 #65Y05 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2504.05036

Abstract

We extend the distributed finite element method of [1], built upon model order reduction, to arbitrary polynomial degree using a hybrid Nitsche scheme. This new method considerably simplifies the transformation of the finite element system to the reduced basis for large problems. We prove that the error of the reduced Nitsche solution converges optimally with respect to the approximation order of the finite element spaces and linearly with respect to the dimension reduction parameter ε. Numerical tests with nontrivial tetrahedral meshes using second-degree polynomial bases support the theoretical results.

Citations

• Distributed finite element solution using model order reduction
• Nitsche's Finite Element Method for Model Coupling in Elasticity
• Optimal local approximation spaces for parabolic problems
• Randomized Numerical Linear Algebra: Foundations & Algorithms
• Multiscale-Spectral GFEM and Optimal Oversampling
• Hybridized CutFEM for Elliptic Interface Problems
• Randomized Oversampling for Generalized Multiscale Finite Element Methods
• Optimal Local Approximation Spaces for Generalized Finite Element\n Methods with Application to Multiscale Problems
• Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions
• Multidimensional binary search trees used for associative searching

Related

• Distributed finite element solution using model order reduction
• A Nitsche Hybrid multiscale method with non-matching grids
• A Nitsche-eXtended finite element method for distributed optimal control problems of elliptic interface equations
• Substructuring Preconditioners for an h-p Nitsche-type method
• Data-driven Stabilization of Nitsche's Method