Overlapping Multipatch Isogeometric Method with Minimal Stabilization

DOI10.1137/19M1306750zbMath1475.65185arXiv1912.06400MaRDI QIDQ5857840

Xiaodong Wei, Pablo Antolin, Riccardo Puppi, Annalisa Buffa

Publication date: 8 April 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.06400

zbMATH Keywords

Boolean operationstrimmingunionstabilized methodsoverlapping meshesisogeometric methods

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20) Fictitious domain methods for boundary value problems involving PDEs (65N85)

Related Items (6)

Robust numerical integration on curved polyhedra based on folded decompositions ⋮ Analysis-aware defeaturing: Problem setting and a posteriori estimation ⋮ Immersed boundary-conformal isogeometric method for linear elliptic problems ⋮ A reconstructed discontinuous approximation on unfitted meshes to \(H(\mathrm{curl})\) and \(H(\mathrm{div})\) interface problems ⋮ Volumetric embedded entities for the isogeometric analysis of complex structures ⋮ Stabilized isogeometric formulation of the Stokes problem on overlapping patches

Uses Software

• Igatools
• IETI
• IRIT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geometric modeling, isogeometric analysis and the finite cell method
• Solid T-spline construction from boundary representations for genus-zero geometry
• Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method
• Conformal solid T-spline construction from boundary T-spline representations
• Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries
• IETI -- isogeometric tearing and interconnecting
• Isogeometric analysis of trimmed NURBS geometries
• Volumetric parameterization and trivariate B-spline fitting using harmonic functions
• Robustness of isogeometric structural discretizations under severe mesh distortion
• \(n\)-widths, sup-infs, and optimality ratios for the \(k\)-version of the isogeometric finite element method
• Isogeometric analysis for trimmed CAD surfaces
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• From geometric design to numerical analysis: a direct approach using the finite cell method on constructive solid geometry
• On the numerical integration of trimmed isogeometric elements
• Isogeometric mortar methods
• Analysis in computer aided design: nonlinear isogeometric B-Rep analysis of shell structures
• Isogeometric analysis for CSG models
• Variationally consistent isogeometric analysis of trimmed thin shells at finite deformations, based on the STEP exchange format
• Multimesh finite element methods: solving PDEs on multiple intersecting meshes
• Isogeometric analysis on V-reps: first results
• Explicit dynamic isogeometric B-rep analysis of penalty-coupled trimmed NURBS shells
• Overlapping multi-patch structures in isogeometric analysis
• Volumetric spline parameterization for isogeometric analysis
• Condition number analysis and preconditioning of the finite cell method
• Smart octrees: accurately integrating discontinuous functions in 3D
• Improved conditioning of isogeometric analysis matrices for trimmed geometries
• Isogeometric dual mortar methods for computational contact mechanics
• Multigrid solvers for immersed finite element methods and immersed isogeometric analysis
• On the stability of the $L^2$ projection in $H^1(\Omega)$
• On Quasi-Interpolation Operators in Spline Spaces
• An Algorithm for Non-Matching Grid Projections with Linear Complexity
• A finite element method for domain decomposition with non-matching grids
• A finite element method on composite grids based on Nitsche's method
• Isogeometric Analysis
• Mathematical analysis of variational isogeometric methods
• A Minimal Stabilization Procedure for Isogeometric Methods on Trimmed Geometries
• A priori error for unilateral contact problems with Lagrange multipliers and isogeometric analysis
• Igatools: An Isogeometric Analysis Library

This page was built for publication: Overlapping Multipatch Isogeometric Method with Minimal Stabilization