Discretization Methods and Iterative Solvers Based on Domain Decomposition

By Barbara I. Wohlmuth. Lecture Notes in Computational Science and Engineering, 2001

432 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/5a5fde8e47d6cd9ecab896e003841b21470a0184

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Citations in the corpus

Two dimensional mortar contact methods for large deformation frictional sliding (2005, methodology): “Although large deformation formulation of contact problems based on node-to-surface strategies has been commonplace for quite some time (see, e.g., References [16, 17] and the recent monograph [7]), efforts in the literature to generally treat large deformation contact problems using mortar element ”
Isogeometric contact: a review (2014, neutral): “[106] B.”
A contact searching algorithm including bounding volume trees applied to finite sliding mortar formulations (2007, methodology): “Since such suitable spaces can be shown to satisfy appropriate inf–sup conditions (see [ 7 ]), we have the significant advantage that the mortar method satisfies Babuska– Brezzi stability conditions as well, at least for linear elastic problems in small deformations (see [8] for an early discussion ”
A BDDC ALGORITHM FOR A MIXED FORMULATION OF FLOW IN POROUS MEDIA (2005, neutral): “These results were originally given in [24, 21, 23].”
An eXtended Finite Element Method/Lagrange multiplier based approach for fluid-structure interaction (2008, methodology): “For the problem at hand, we adopt the Mortar methods for non-matching grids [6,7] and [46].”
Additive manufacturing in construction: A review on processes, applications, and digital planning methods (2019, methodology): “6) [144,145], by decomposing the domain with the Mortar method [146,147], and by homogenizing heterogeneous structures [148,149].”
Scalable TFETI algorithm for the solution of multibody contact problems of elasticity (2009, background): “The solution of auxiliary linear problems in the inner loop may be improved by standard preconditioners [58] and may be adapted to the mortar discretization [59].”
A dual mortar approach for 3D finite deformation contact with consistent linearization (2010, background): “Under the assumption that (1) c is compactly embedded in (1)\ (1) u , we obtain W(1) =H1/2( (1) c ) and M=H−1/2( (1) c ), see [14].”
Efficient simulation of multi‐body contact problems on complex geometries: A flexible decomposition approach using constrained minimization (2009, background): “(10) Note that in general (9) is not equivalent to (8) if D is not a diagonal matrix with positive entries.”
A finite deformation mortar contact formulation using a primal–dual active set strategy (2009, neutral): “Then, on the slave side, dual Lagrange multipliers j , j =1,2, are defined to be in the corresponding dual trace space M=H−1/2( (1) c ), see [21].”
A 3D mortar method for solid mechanics (2004, methodology): “Nevertheless, most of the work has been done for 2D although examples of problems using mortar methods on 3D meshes with at surfaces composed of rectangular facets has been demonstrated in References [1, 7].”
A multiscale method with patch for the solution of stochastic partial differential equations with localized uncertainties (2013, background): “For the construction of suitable approximation spaces Mh in the case of non conforming meshes, see [31] and the references therein.”
3D fluid–structure-contact interaction based on a combined XFEM FSI and dual mortar contact approach (2010, background): “Moreover, they are constructed such that a biorthogonality condition as introduced in [14,35, 36 ] holds (for brevity, the discretized slave surface is denoted as � h in the following) �”