An object‐oriented geometric engine design for discontinuities in unfitted/immersed/enriched finite element methods

Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Numerical and other methods in solid mechanics (74Sxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)

Cites Work

Unnamed Item
Hierarchical interface-enriched finite element method: an automated technique for mesh-independent simulations
An enrichment scheme for solidification problems
Stable generalized finite element method (SGFEM)
A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries
3D hierarchical interface-enriched finite element method: implementation and applications
An adaptive mesh rezoning scheme for moving boundary flows and fluid--structure interaction
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
Modeling mixed-mode dynamic crack propagation using finite elements: Theory and applications
Constrained Delaunay triangulations
A deforming finite element method for analysis of alloy solidification problems
Two-dimensional incompressible Navier-Stokes calculations in complex-shaped moving domains
The partition of unity finite element method: basic theory and applications
Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria.
Structural optimization using sensitivity analysis and a level-set method.
Modeling quasi-static crack growth with the extended finite element method. I: Computer implementation
Crack propagation modelling using an advanced remeshing technique
Stable GFEM (SGFEM): improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics
Solving thermal and phase change problems with the extended finite element method
A level set method for structural topology optimization.
Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
ALE finite element computations of fluid-structure interaction problems
New algorithms for virtual reconstruction of heterogeneous microstructures
A stable discontinuity-enriched finite element method for 3-D problems containing weak and strong discontinuities
The stable XFEM for two-phase flows
On tailoring fracture resistance of brittle structures: a level set interface-enriched topology optimization approach
An interface-enriched generalized finite element formulation for locking-free coupling of non-conforming discretizations and contact
Fully decoupling geometry from discretization in the Bloch-Floquet finite element analysis of phononic crystals
Higher-order conformal decomposition FEM (CDFEM)
On the stability and interpolating properties of the hierarchical interface-enriched finite element method
A coupling interface method for elliptic interface problems
Fast algorithms for intersection of non-matching grids using Plücker coordinates
Stable generalized finite element method and associated iterative schemes; application to interface problems
A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics
Recent progress in robust and quality Delaunay mesh generation
An eXtended Finite Element Method/Lagrange multiplier based approach for fluid-structure interaction
An interface-enriched generalized FEM for problems with discontinuous gradient fields
Improvements of explicit crack surface representation and update within the generalized finite element method with application to three-dimensional crack coalescence
A conformal decomposition finite element method for arbitrary discontinuities on moving interfaces
A new formulation for imposing Dirichlet boundary conditions on non-matching meshes
CutFEM: Discretizing geometry and partial differential equations
The XFEM for nonlinear thermal and phase change problems
Continuum-discontinuum modelling of shear bands
Three-dimensional immersed finite element methods for electric field simulation in composite materials
Radial basis functions and level set method for structural topology optimization
Two-scale shear band evolution by local partition of unity
A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries
Imposing Dirichlet boundary conditions in the extended finite element method
An Extended Finite Element Method for Two-Phase Fluids
Enhancement of fixed‐grid methods towards complex fluid–structure interaction applications
An extended finite element method with analytical enrichment for cohesive crack modeling
A conformal decomposition finite element method for modeling stationary fluid interface problems
A new fast finite element method for dislocations based on interior discontinuities
An adaptive remeshing strategy for flows with moving boundaries and fluid–structure interaction
Two-scale method for shear bands: thermal effects and variable bandwidth
A corrected XFEM approximation without problems in blending elements
hp-Generalized FEM and crack surface representation for non-planar 3-D cracks
Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
Fitted and Unfitted Finite-Element Methods for Elliptic Equations with Smooth Interfaces
A general methodology for structural shape optimization problems using automatic adaptive remeshing
THE PARTITION OF UNITY METHOD
Geometric Level Set Methods in Imaging, Vision, and Graphics
An arbitrary Lagrangian Eulerian finite-element approach for fluid-structure interaction phenomena
On the construction of blending elements for local partition of unity enriched finite elements
An enriched finite element method and level sets for axisymmetric two-phase flow with surface tension
L<scp>EVEL</scp> S<scp>ET</scp> M<scp>ETHODS FOR</scp> F<scp>LUID</scp> I<scp>NTERFACES</scp>
Survey of meshless and generalized finite element methods: A unified approach
Extended finite element method for three-dimensional crack modelling
Isogeometric Analysis
An immersed finite element space and its approximation capability
A hybrid extended finite element/level set method for modeling phase transformations
On the design of CGAL a computational geometry algorithms library
Efficient Implementation of Finite Element Methods on Nonmatching and Overlapping Meshes in Three Dimensions
A finite element method for crack growth without remeshing
TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator
Dislocations by partition of unity
A generalized finite element method for the simulation of three-dimensional dynamic crack propagation.
Modeling holes and inclusions by level sets in the extended finite element method