A Particle-Partition of Unity Method Part V: Boundary Conditions

By Michael Griebel, M. Schweitzer. 2003

161 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/4d80b80cac35709293e52c689af18aff869f6d87

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

On Approximation in Meshless Methods (2005, background): “Determining Cinv can be formulated as an eigenvalue problem, and a numerical scheme that works well has been proposed in [51,96].”
Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods (2012, methodology): “Although efforts were made towards providing a lower bound on the stabilization parameter, notably, in the work of Griebel and Schweitzer [25], their approach required the solution of an eigenvalue problem, making it expensive for evolving interfaces.”
The extended/generalized finite element method: An overview of the method and its applications (2010, unknown): “Theoretical investigations that give insight on how the enrichment works in the partition of unity context are found in Babuška et al. [12, 13] and Schweitzer [156].”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “Convergence of linear FEM and linear RKPM in a second order PDE with a smooth solution convergence by using an eigenvalue problem (Griebel and Schweitzer 2003a).”
A Nitsche‐type formulation and comparison of the most common domain decomposition methods in isogeometric analysis (2014, methodology): “The related stabilization parameter is mesh-dependent and can be obtained by the solution of a generalized eigenvalue problem over the interface DOFs, as proposed in [40].”
On methods for stabilizing constraints over enriched interfaces in elasticity (2009, methodology): “It has been shown [15] that a minimum ! exists that will guarantee positive definiteness of the bilinear form associated with Nitsche’s method.”
Robust imposition of Dirichlet boundary conditions on embedded surfaces (2012, background): “Although C1 may be computed globally (see [27, 28]), for problems with evolving interfaces, this necessitates the solution of a large eigenvalue problem at every time step and thus adds significantly to the computational expense.”
A robust Nitsche's formulation for interface problems with spline‐based finite elements (2015, methodology): “Both global [16] and element level [17, 18] calculations have been employed to obtain suitable parameters.”
Imposing Dirichlet boundary conditions with Nitsche's method and spline‐based finite elements (2010, methodology): “For this convergence study, we also compared our results to those obtained using the global approach for the eigenvalue problem suggested by Griebel and Schweitzer [10].”