Isogeometric mortar methods

DOI10.1016/j.cma.2014.09.012zbMath1425.65150arXiv1407.8313OpenAlexW1998777442MaRDI QIDQ1797979

Annalisa Buffa, Ericka Brivadis, Linus Wunderlich, Barbara I. Wohlmuth

Publication date: 22 October 2018

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

Full work available at URL: https://arxiv.org/abs/1407.8313

zbMATH Keywords

isogeometric analysisinf-sup stabilitymortar methodscross point modification

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) 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) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items

Analysis-suitable \(G^1\) multi-patch parametrizations for \(C^1\) isogeometric spaces, Frontiers in Mortar Methods for Isogeometric Analysis, Tree-cotree decomposition of isogeometric mortared spaces in H(curl) on multi-patch domains, Curved node-to-face contact schemes for higher-order finite elements in lumped-mass explicit methods, Easy and efficient preconditioning of the isogeometric mass matrix, INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces, Scaled boundary isogeometric analysis for electrostatic problems, Coupling adaptively refined multi-patch spline discretizations via boundary compatibility, IGA-based multi-index stochastic collocation for random PDEs on arbitrary domains, Overlapping multi-patch structures in isogeometric analysis, An approach to construct a three-dimensional isogeometric model from \(\mu\)-CT scan data with an application to the bridge of a violin, Multi-patch isogeometric analysis for Kirchhoff-Love shell elements, The embedded isogeometric Kirchhoff-Love shell: from design to shape optimization of non-conforming stiffened multipatch structures, Crosspoint modification for multi-patch isogeometric analysis, Nitsche's method for non-conforming multipatch coupling in hyperelastic isogeometric analysis, Weak coupling of nonlinear isogeometric spatial Bernoulli beams, A dual domain decomposition algorithm for the analysis of non-conforming isogeometric Kirchhoff-Love shells, Strong multipatch \(C^1\)-coupling for isogeometric analysis on 2D and 3D domains, Initial solution estimation of one-step inverse isogeometric analysis for sheet metal forming with complex topologies, Interface coupling method for the global-local analysis of heterogeneous models: a second-order homogenization-based strategy, Hierarchical NURBS and a higher-order phase-field approach to fracture for finite-deformation contact problems, Isogeometric dual mortar methods for computational contact mechanics, An efficient and robust rotational formulation for isogeometric Reissner-Mindlin shell elements, Isogeometric analysis and hierarchical refinement for higher-order phase-field models, A posteriori error estimation and adaptivity in non-intrusive couplings between concurrent models, Varying-order NURBS discretization: an accurate and efficient method for isogeometric analysis of large deformation contact problems, Moment preserving local spline projection operators, High order geometric methods with splines: fast solution with explicit time-stepping for Maxwell equations, Two finite element approaches for Darcy and Darcy-Brinkman flow through deformable porous media-mixed method vs. NURBS based (isogeometric) continuity, The weak substitution method - an application of the mortar method for patch coupling in NURBS-based isogeometric analysis, A nonsmooth method for spatial frictional contact dynamics of flexible multibody systems with large deformation, Kirchhoff-Love shell representation and analysis using triangle configuration B-splines, A dual mortar embedded mesh method for internal interface problems with strong discontinuities, Multipatch isogeometric analysis for geometrically exact shell elements using B-bar method and Bézier extraction, Adaptive multi-patch isogeometric phase-field method for quasi-static brittle fracture based on Nitsche's method, A comparison of smooth basis constructions for isogeometric analysis, A neural network finite element method for contact mechanics, Volumetric embedded entities for the isogeometric analysis of complex structures, A fully non-invasive hybrid IGA/FEM scheme for the analysis of localized non-linear phenomena, Adaptively refined multi-patch B-splines with enhanced smoothness, A segmentation-free isogeometric extended mortar contact method, Approximately \(\mathcal{C}^1\) -smooth isogeometric functions on two-patch domains, Smooth multi-patch discretizations in isogeometric analysis, Mixed stress-displacement isogeometric collocation for nearly incompressible elasticity and elastoplasticity, Efficient computation of nonlinear isogeometric elements using the adjoint method and algorithmic differentiation, Isogeometric Bézier dual mortaring: the Kirchhoff-Love shell problem, An updated Lagrangian framework for isogeometric Kirchhoff-Love thin-shell analysis, Blended isogeometric Kirchhoff-Love and continuum shells, Construction of approximate \(C^1\) bases for isogeometric analysis on two-patch domains, Skeleton-stabilized isogeometric analysis: high-regularity interior-penalty methods for incompressible viscous flow problems, A Nitsche-based non-intrusive coupling strategy for global/local isogeometric structural analysis, Skew-symmetric Nitsche's formulation in isogeometric analysis: Dirichlet and symmetry conditions, patch coupling and frictionless contact, An interpolation method for coupling non-conforming patches in isogeometric analysis of vibro-acoustic systems, Biorthogonal splines for optimal weak patch-coupling in isogeometric analysis with applications to finite deformation elasticity, Isogeometric analysis for explicit elastodynamics using a dual-basis diagonal mass formulation, Penalty coupling of non-matching isogeometric Kirchhoff-Love shell patches with application to composite wind turbine blades, A projected super-penalty method for the \(C^1\)-coupling of multi-patch isogeometric Kirchhoff plates, A hybrid isogeometric approach on multi-patches with applications to Kirchhoff plates and eigenvalue problems, Rotation-free Bernstein-Bézier elements for thin plates and shells -- development and validation, Weak imposition of constraints for structural membranes in transient geometrically nonlinear isogeometric analysis on multipatch surfaces, Isogeometric analysis on V-reps: first results, The INTERNODES method for the treatment of non-conforming multipatch geometries in isogeometric analysis, Coupling of non-conforming trimmed isogeometric Kirchhoff-Love shells via a projected super-penalty approach, Discontinuous Galerkin isogeometric analysis of elliptic problems on segmentations with non-matching interfaces, Isogeometric analysis on non-matching segmentation: discontinuous Galerkin techniques and efficient solvers, Space of \(C^2\)-smooth geometrically continuous isogeometric functions on two-patch geometries, Isogeometric continuity constraints for multi-patch shells governed by fourth-order deformation and phase field models, Multipatch isogeometric mortar methods for thick shells, A robust penalty coupling of non-matching isogeometric Kirchhoff-Love shell patches in large deformations, A priori penalty factor determination for (trimmed) NURBS-based shells with Dirichlet and coupling constraints in isogeometric analysis, The Influence of Quadrature Errors on Isogeometric Mortar Methods, Domain Decomposition Methods and Kirchhoff-Love Shell Multipatch Coupling in Isogeometric Analysis, A multi-patch nonsingular isogeometric boundary element method using trimmed elements, Isogeometric Mortar Coupling for Electromagnetic Problems, Coupling non-conforming discretizations of PDEs by spectral approximation of the Lagrange multiplier space, An isogeometric mortar method for the coupling of multiple NURBS domains with optimal convergence rates, A weighted point-based formulation for isogeometric contact, Bloch theorem for isogeometric analysis of periodic problems governed by high-order partial differential equations, An efficient patch-to-patch method for coupling independent finite element subdomains with intersecting interfaces, On the use of NURBS-based discretizations in the scaled boundary finite element method for wave propagation problems, Isogeometric collocation methods for Cosserat rods and rod structures, Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: application to a non-intrusive local enrichment of NURBS patches, Isogeometric analysis with geometrically continuous functions on planar multi-patch geometries, A robust patch coupling method for NURBS-based isogeometric analysis of non-conforming multipatch surfaces, Dual and approximate dual basis functions for B-splines and NURBS -- comparison and application for an efficient coupling of patches with the isogeometric mortar method, Isogeometric Bézier dual mortaring: the enriched Bézier dual basis with application to second- and fourth-order problems, A flexible approach for coupling NURBS patches in rotationless isogeometric analysis of Kirchhoff-Love shells, Explicit isogeometric topology optimization using moving morphable components, A three-field dual mortar method for elastic problems with nonconforming mesh, Isogeometric Bézier dual mortaring: refineable higher-order spline dual bases and weakly continuous geometry, Isogeometric analysis and harmonic stator-rotor coupling for simulating electric machines, Space-Time Multipatch Discontinuous Galerkin Isogeometric Analysis for Parabolic Evolution Problems, A concise frictional contact formulation based on surface potentials and isogeometric discretization, Approximation estimates for isogeometric spaces in multipatch geometries, Comparison of current methods for implementing periodic boundary conditions in multi-scale homogenisation, Overlapping Multipatch Isogeometric Method with Minimal Stabilization, An approximate \(C^1\) multi-patch space for isogeometric analysis with a comparison to Nitsche's method

Uses Software

• GeoPDEs
• IETI

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method
• \textsc{GeoPDEs}: a research tool for isogeometric analysis of PDEs
• Anisotropic NURBS approximation in isogeometric analysis
• Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS
• Isogeometric analysis and domain decomposition methods
• Isogeometric analysis and thermomechanical mortar contact problems
• Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries
• IETI -- isogeometric tearing and interconnecting
• \(n\)-widths, sup-infs, and optimality ratios for the \(k\)-version of the isogeometric finite element method
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• Optimal a priori estimates for higher order finite elements for elliptic interface problems
• An interior point method for isogeometric contact
• A mortar element method for some discretizations of a plate problem
• Superconvergence in Galerkin finite element methods
• An abstract framework for a priori estimates for contact problems in 3D with quadratic finite elements
• The mortar finite element method with Lagrange multipliers
• Nitsche's method for two and three dimensional NURBS patch coupling
• A large deformation frictional contact formulation using NURBS-based isogeometric analysis
• Isogeometric contact analysis using mortar method
• A Nitsche-type formulation and comparison of the most common domain decomposition methods in isogeometric analysis
• The weak substitution method - an application of the mortar method for patch coupling in NURBS-based isogeometric analysis
• ISOGEOMETRIC COLLOCATION METHODS
• Variationally consistent discretization schemes and numerical algorithms for contact problems
• The mortar element method for three dimensional finite elements
• The inf-sup test
• Quasi-Optimal Approximation of Surface Based Lagrange Multipliers in Finite Element Methods
• Biorthogonal bases with local support and approximation properties
• Régularité des solutions d'un problème mêlé Dirichlet–Signorini dans un domaine polygonal plan
• EXTENSION OF THE MORTAR FINITE ELEMENT METHOD TO A VARIATIONAL INEQUALITY MODELING UNILATERAL CONTACT
• A Multigrid Method for the Mortar-Type Morley Element Approximation of a Plate Bending Problem
• Isogeometric Analysis
• Mathematical analysis of variational isogeometric methods
• A Multigrid Algorithm for the Mortar Finite Element Method
• Mixed Finite Element Methods and Applications
• Computational Contact Mechanics
• ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES
• Discretization methods and iterative solvers based on domain decomposition