Octree-based integration scheme with merged sub-cells for the finite cell method: application to non-linear problems in 3D

DOI10.1016/j.cma.2022.115565OpenAlexW4298113339MaRDI QIDQ2096813

Márton Petö, Fabian Duvigneau, Wadhah Garhuom, Sascha Eisenträger, Daniel Juhre, Alexander Düster

Publication date: 11 November 2022

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2022.115565

zbMATH Keywords

finite cell methodnon-linear mechanicsembedded domain methodsdiscontinuous integralsoctree integration

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (5)

Boolean finite cell method for multi-material problems including local enrichment of the ansatz space ⋮ Critical time-step size analysis and mass scaling by ghost-penalty for immersogeometric explicit dynamics ⋮ An efficient Cartesian mesh generation strategy for complex geometries ⋮ Robust numerical integration of embedded solids described in boundary representation ⋮ Isogeometric multi-resolution full waveform inversion based on the finite cell method

Uses Software

• FCMLab

Cites Work

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• Numerical integration of discontinuities on arbitrary domains based on moment fitting
• The finite cell method: a review in the context of higher-order structural analysis of CAD and image-based geometric models
• An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces
• The finite cell method for polygonal meshes: poly-FCM
• The finite cell method for linear thermoelasticity
• Efficient finite element methodology based on Cartesian grids: application to structural shape optimization
• Local enrichment of the finite cell method for problems with material interfaces
• Topology optimization using the finite cell method
• Fictitious domain finite element methods using cut elements. II: A stabilized Nitsche method
• Finite and spectral cell method for wave propagation in heterogeneous materials
• Numerical integration of polynomials and discontinuous functions on irregular convex polygons and polyhedrons
• Fictitious domain finite element methods using cut elements. I: A stabilized Lagrange multiplier method
• An unfitted hp-adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry
• An accurate, robust, and easy-to-implement method for integration over arbitrary polyhedra: application to embedded interface methods
• Efficient integration method for fictitious domain approaches
• Theoretical and numerical investigation of the finite cell method
• A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions
• The finite cell method for three-dimensional problems of solid mechanics
• Finite cell method. \(h\)- and \(p\)-extension for embedded domain problems in solid mechanics
• The radial integration method for evaluation of domain integrals with boundary-only discretization.
• The tetrahedral finite cell method for fluids: immersogeometric analysis of turbulent flow around complex geometries
• An extension of the finite cell method using Boolean operations
• The finite cell method for nearly incompressible finite strain plasticity problems with complex geometries
• Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone
• An adaptive version of the immersed boundary method
• An unfitted finite element method, based on Nitsche's method, for elliptic interface problems.
• Small and large deformation analysis with the \(p\)- and B-spline versions of the finite cell method
• Numerical homogenization of heterogeneous and cellular materials utilizing the finite cell method
• Equivalent Legendre polynomials: numerical integration of discontinuous functions in the finite element methods
• Preconditioning immersed isogeometric finite element methods with application to flow problems
• Direct structural analysis of domains defined by point clouds
• Numerical homogenization of hybrid metal foams using the finite cell method
• An eigenvalue stabilization technique to increase the robustness of the finite cell method for finite strain problems
• Efficient cut-cell quadrature based on moment fitting for materially nonlinear analysis
• A prediction method based on the voxel model and the finite cell method for cutting force-induced deformation in the five-axis milling process
• Numerical integration for nonlinear problems of the finite cell method using an adaptive scheme based on moment fitting
• A remeshing strategy for large deformations in the finite cell method
• Non-negative moment fitting quadrature rules for fictitious domain methods
• Condition number analysis and preconditioning of the finite cell method
• Smart octrees: accurately integrating discontinuous functions in 3D
• The finite and spectral cell methods for smart structure applications: transient analysis
• A coupling interface method for elliptic interface problems
• The spectral cell method for wave propagation in heterogeneous materials simulated on multiple GPUs and CPUs
• Phase-field modeling of brittle fracture with multi-level \textit{hp}-FEM and the finite cell method
• Quadrature schemes for arbitrary convex/concave volumes and integration of weak form in enriched partition of unity methods
• A fictitious domain approach with spread interface for elliptic problems with general boundary conditions
• Selective enrichment of moment fitting and application to cut finite elements and cells
• Weakly enforced essential boundary conditions for NURBS-embedded and trimmed NURBS geometries on the basis of the finite cell method
• Highly accurate surface and volume integration on implicit domains by means of moment-fitting
• Numerical analysis of Lamb waves using the finite and spectral cell methods
• Equivalent polynomials for quadrature in Heaviside function enriched elements
• Higher-order accurate integration of implicit geometries
• PERFORMANCE OF DIFFERENT INTEGRATION SCHEMES IN FACING DISCONTINUITIES IN THE FINITE CELL METHOD
• Finite Cell Method: High-Order Structural Dynamics for Complex Geometries
• The extended/generalized finite element method: An overview of the method and its applications
• The immersed boundary method
• On the elimination of quadrature subcells for discontinuous functions in the eXtended Finite-Element Method
• Handbook of Data Compression
• Fixed grid finite elements in elasticity problems
• Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes’ problem
• Non-standard bone simulation: interactive numerical analysis by computational steering

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