Isogeometric analysis on non-matching segmentation: discontinuous Galerkin techniques and efficient solvers

DOI10.1007/s12190-019-01252-3zbMath1427.65404OpenAlexW2924374056MaRDI QIDQ2008058

Ioannis Toulopoulos, Christoph Hofer, Ulrich Langer

Publication date: 22 November 2019

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12190-019-01252-3

zbMATH Keywords

discontinuous Galerkin methodsisogeometric analysiselliptic diffusion problemsheterogeneous diffusion coefficientsIETI-DP domain decomposition solversmultipatch domain representationsnon-matching interface parametrizations

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) 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)

Related Items

IETI-DP methods for discontinuous Galerkin multi-patch isogeometric analysis with T-junctions ⋮ A IETI-DP method for discontinuous Galerkin discretizations in isogeometric analysis with inexact local solvers ⋮ Analysis of discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods ⋮ The INTERNODES method for the treatment of non-conforming multipatch geometries in isogeometric analysis ⋮ Discontinuous Galerkin isogeometric analysis for segmentations generating overlapping regions ⋮ Overlapping additive Schwarz preconditioners for isogeometric collocation discretizations of linear elasticity ⋮ Discontinuous Galerkin Isogeometric Analysis of Elliptic Diffusion Problems on Segmentations with Gaps ⋮ Convergence theory for IETI-DP solvers for discontinuous Galerkin isogeometric analysis that is explicit in \(h\) and \(p\)

Uses Software

• G+Smo
• IETI

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method
• Finite and boundary element tearing and interconnecting solvers for multiscale problems
• Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries
• IETI -- isogeometric tearing and interconnecting
• Discontinuous Galerkin isogeometric analysis of elliptic problems on segmentations with non-matching interfaces
• Isogeometric analysis and applications 2014. Selected papers based on the presentations at the IGAA 2014, Annweiler am Trifels, Germany, April 7--10, 2014
• Planar domain parameterization with THB-splines
• Parallelization of continuous and discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods
• Analysis of multipatch discontinuous Galerkin IgA approximations to elliptic boundary value problems
• Isogeometric mortar methods
• Theory and practice of finite elements.
• Dual-primal isogeometric tearing and interconnecting solvers for multipatch dG-Iga equations
• Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization
• Low-rank space-time decoupled isogeometric analysis for parabolic problems with varying coefficients
• BDDC methods for discontinuous Galerkin discretization of elliptic problems
• Nitsche's method for two and three dimensional NURBS patch coupling
• The Isogeometric Segmentation Pipeline
• Discontinuous Galerkin Isogeometric Analysis of Elliptic Diffusion Problems on Segmentations with Gaps
• A Nitsche-type formulation and comparison of the most common domain decomposition methods in isogeometric analysis
• 3-D FETI-DP Preconditioners for Composite Finite Element-Discontinuous Galerkin Methods
• Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations
• Raytcho Lazarov - 60
• Analysis of discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods
• Isogeometric Analysis
• Mathematical analysis of variational isogeometric methods
• A FETI-DP Preconditioner for a Composite Finite Element and Discontinuous Galerkin Method
• Discontinuous Galerkin isogeometric analysis for segmentations generating overlapping regions
• A practical guide to splines.