Error indicators and adaptive remeshing in large deformation finite element analysis
Finite Elements in Analysis and Design
Special finite element methods for a class of second order elliptic problems with rough coefficients
SIAM Journal on Numerical Analysis
Efficient subdivision of finite-element datasets into consistent tetrahedra
VIS '97 Proceedings of the 8th conference on Visualization '97
A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs
SIAM Journal on Scientific Computing
Locally Adapted Tetrahedral Meshes Using Bisection
SIAM Journal on Scientific Computing
Parallel simulations of three-dimensional cracks using the generalized finite element method
Computational Mechanics
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In this paper, heat transfer problems with sharp spatial gradients are analyzed using the Generalized Finite Element Method with global-local enrichment functions (GFEM gl). With this approach, scale-bridging enrichment functions are generated on the fly, providing specially-tailored enrichment functions for the problem to be analyzed with no a-priori knowledge of the exact solution. In this work, a decomposition of the linear system of equations is formulated for both steady-state and transient heat transfer problems, allowing for a much more computationally efficient analysis of the problems of interest. With this algorithm, only a small portion of the global system of equations, i.e., the hierarchically added enrichments, need to be re-computed for each loading configuration or time-step. Numerical studies confirm that the condensation scheme does not impact the solution quality, while allowing for more computationally efficient simulations when large problems are considered. We also extend the GFEM gl to allow for the use of hexahedral elements in the global domain, while still using tetrahedral elements in the local domain, to allow for automatic localized mesh refinement without the use of constrained approximations. Simulations are run with the use of linear and quadratic hexahedral and tetrahedral elements in the global domain. Convergence studies indicate that the use of a different partition of unity (PoU) in the global (hexahedral elements) and local (tetrahedral elements) domains does not adversely impact the solution quality.