A simple and efficient preconditioning scheme for Heaviside enriched XFEM
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Publication:487861
DOI10.1007/s00466-014-1063-8zbMath1311.74124arXiv1312.6092OpenAlexW2001525771MaRDI QIDQ487861
David Makhija, Kurt Maute, Alireza Doostan, Christapher Lang
Publication date: 23 January 2015
Published in: Computational Mechanics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1312.6092
Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)
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Cites Work
- Unnamed Item
- Unnamed Item
- Extended stochastic FEM for diffusion problems with uncertain material interfaces
- A uniformly well-conditioned, unfitted Nitsche method for interface problems
- Levelset based fluid topology optimization using the extended finite element method
- Stable generalized finite element method (SGFEM)
- Subdivision-stabilised immersed b-spline finite elements for moving boundary flows
- Imposing essential boundary conditions in mesh-free methods
- Modelling dendritic solidification with melt convection using the extended finite element method
- Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
- Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements
- A computational approach to handle complex microstructure geometries.
- On some techniques for approximating boundary conditions in the finite element method
- The stable XFEM for two-phase flows
- Simulation of the flow of a viscoelastic fluid around a stationary cylinder using an extended finite element method
- A finite element method for the simulation of strong and weak discontinuities in solid mechanics
- A cut finite element method for a Stokes interface problem
- Density and level set-XFEM schemes for topology optimization of 3-D structures
- A Modified Finite Volume Approximation of Second-Order Elliptic Equations with Discontinuous Coefficients
- A multiple level set approach to prevent numerical artefacts in complex microstructures with nearby inclusions within XFEM
- A robust preconditioning technique for the extended finite element method
- Nitsche’s method for general boundary conditions
- The extended/generalized finite element method: An overview of the method and its applications
- Improved implementation and robustness study of the X-FEM for stress analysis around cracks
- An Extended Finite Element Method for Two-Phase Fluids
- An embedded Dirichlet formulation for 3D continua
- A corrected XFEM approximation without problems in blending elements
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- Structured extended finite element methods for solids defined by implicit surfaces
- Finite cover method for linear and non-linear analyses of heterogeneous solids
- The extended finite element method (XFEM) for solidification problems
- Balancing domain decomposition for problems with large jumps in coefficients
- A finite element method for crack growth without remeshing
- Modeling holes and inclusions by level sets in the extended finite element method
- Analysis of an extended pressure finite element space for two-phase incompressible flows