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1. Full Text Adaptive mesh refinement strategies in isogeometric analysis— A computational comparison
by Hennig, Paul and Kästner, Markus and Morgenstern, Philipp and Peterseim, Daniel
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 04/2017, Volume 316, pp. 424 - 448
We explain four variants of an adaptive finite element method with cubic splines and compare their performance in simple elliptic model problems. The methods... 
Isogeometric analysis | T-splines | Adaptive mesh refinement | Truncated hierarchical B-splines | POLYNOMIAL SPLINES | DEFINITION | DESIGN | LOCAL REFINEMENT | SUITABLE T-SPLINES | LINEAR INDEPENDENCE | HIERARCHICAL REFINEMENT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | FINITE-ELEMENT-METHOD | Mathematics - Numerical Analysis
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2. Full Text The role of Bézier extraction in adaptive isogeometric analysis: Local refinement and hierarchical refinement
by de Borst, R and Chen, L
International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 02/2018, Volume 113, Issue 6, pp. 999 - 1019
We present 2 adaptive refinement techniques, namely, adaptive local refinement and adaptive hierarchical refinement, for isogeometric analysis. An element‐wise... 
hierarchical T‐splines | Bézier extraction | LR T‐splines | adaptive refinement | isogeometric analysis | LR T-splines | hierarchical T-splines | POLYNOMIAL SPLINES | MESHES | Bezier extraction | CAD | T-SPLINES | NURBS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | LR B-SPLINES | Solution space | Splines | Mathematical analysis | Adaptive algorithms
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3. Full Text Local refinement of analysis-suitable T-splines
by Scott, M.A and Li, X and Sederberg, T.W and Hughes, T.J.R
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 03/2012, Volume 213-216, pp. 206 - 222
We develop a local refinement algorithm for analysis-suitable T-splines which does not produce excessive propagation of control points. We then demonstrate its... 
Isogeometric analysis | T-splines | Bézier extraction | Local refinement | Bezier extraction | CAD | MESH | FLUID-STRUCTURE INTERACTION | NONLINEAR ELASTICITY | NURBS | CONTINUITY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | Analysis | Algorithms
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4. Full Text A 3D common-refinement method for non-matching meshes in partitioned variational fluid–structure analysis
by Li, Yulong and Law, Yun Zhi and Joshi, Vaibhav and Jaiman, Rajeev K
Journal of Computational Physics, ISSN 0021-9991, 12/2018, Volume 374, pp. 163 - 187
We present a three-dimensional (3D) common-refinement method for non-matching unstructured meshes between non-overlapping subdomains of incompressible... 
Nonlinear iterative force correction | Fluid–structure interaction | Partitioned staggered | Petrov–Galerkin finite element | Non-matching meshes | 3D common-refinement | CONSERVATIVE LOAD-TRANSFER | TRANSFER ALGORITHMS | OVERLAYING SURFACE MESHES | AITKENS PROCESS | Petrov-Galerkin finite element | FORMULATION | PHYSICS, MATHEMATICAL | Fluid-structure interaction | SCHEME | PROJECTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MASS | SOLID INTERFACE | CONVERGENCE | Turbulence | Analysis | Methods
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5. Full Text Truncated hierarchical Catmull–Clark subdivision with local refinement
by Wei, Xiaodong and Zhang, Yongjie and Hughes, Thomas J.R and Scott, Michael A
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 07/2015, Volume 291, pp. 1 - 20
In this paper we present a new method termed (THCCS), which generalizes truncated hierarchical B-splines to control grids of arbitrary topology. THCCS basis... 
Isogeometric analysis | Truncation mechanism | Local refinement | Extraordinary nodes | Catmull–Clark subdivision | Hierarchical B-splines | Catmull-Clark subdivision | POLYNOMIAL SPLINES | T-SPLINE | DESIGN | MESHES | LINEAR INDEPENDENCE | NURBS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | FINITE-ELEMENT-ANALYSIS | SURFACES | Partitions | Subdivisions | Basis functions | Unity | Preserves | Benchmarking | Continuity | Topology
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6. Full Text A hierarchical approach to adaptive local refinement in isogeometric analysis
by Vuong, A.-V and Giannelli, C and Jüttler, B and Simeon, B
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 2011, Volume 200, Issue 49, pp. 3554 - 3567
► We present hierarchical adaptive local refinements for isogeometric analysis. ► The theoretical properties of the spline space ensure key requirements. ► The... 
Isogeometric analysis | Adaptivity | Local refinement | Hierarchical B-splines | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MESHES | ENGINEERING, MULTIDISCIPLINARY | APPROXIMATION | SPLINES | Finite element method | Permissible error | Partitions | Computer simulation | Unity | Mathematical analysis | Splines | Mathematical models
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7. Full Text ADER-WENO finite volume schemes with space–time adaptive mesh refinement
by Dumbser, Michael and Zanotti, Olindo and Hidalgo, Arturo and Balsara, Dinshaw S
Journal of Computational Physics, ISSN 0021-9991, 09/2013, Volume 248, pp. 257 - 286
We present the first high order one-step ADER-WENO finite volume scheme with adaptive mesh refinement (AMR) in multiple space dimensions. High order spatial... 
Hyperbolic conservation laws | Adaptive mesh refinement (AMR) | Time accurate local timestepping | MHD equations | ADER approach | Space–time adaptive grids | High order WENO reconstruction | Euler equations | Local space–time DG predictor | Space-time adaptive grids | Local space-time DG predictor | GENERALIZED RIEMANN PROBLEM | TANG VORTEX SYSTEM | EFFICIENT IMPLEMENTATION | FLUID-DYNAMICS | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | HIGH-ORDER | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | Analysis | Algorithms
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8. Full Text Red--green refinement of simplicial meshes in d dimensions
by Jörg Grande
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2019, Volume 88, Issue 316, pp. 751 - 782
The local red-green mesh refinement of consistent, simplicial meshes in d dimensions is considered. We give a constructive solution to the green closure... 
Red-green refinement | Local mesh refinement | Green closure | Simplicial meshes | Kuhn triangulation | simplicial meshes | MATHEMATICS, APPLIED | red-green refinement | green closure | FINITE-ELEMENT METHODS
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9. Full Text GRChombo: Numerical relativity with adaptive mesh refinement
by Clough, Katy and Figueras, Pau and Finkel, Hal and Kunesch, Markus and Lim, Eugene A and Tunyasuvunakool, Saran and Argonne National Lab. (ANL), Argonne, IL (United States)
Classical and Quantum Gravity, ISSN 0264-9381, 12/2015, Volume 32, Issue 24, pp. 245011 - 245044
In this work, we introduce GRChombo: a new numerical relativity code which incorporates full adaptive mesh refinement (AMR) using block structured... 
numerical, general relativity, adaptive mesh | numerical | WAVES | GRAVITATIONAL COLLAPSE | PHYSICS, MULTIDISCIPLINARY | EVOLUTIONS | FIELD | ASTRONOMY & ASTROPHYSICS | adaptive mesh | EQUATIONS | general relativity | BLACK-HOLES | PHYSICS, PARTICLES & FIELDS | Einstein equations | Hierarchies | Mathematical analysis | Numerical relativity | Formalism | Quantum gravity | Standards | Stands | Physics - General Relativity and Quantum Cosmology
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10. Full Text Adaptive isogeometric analysis by local h-refinement with T-splines
by Dörfel, Michael R and Jüttler, Bert and Simeon, Bernd
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 2010, Volume 199, Issue 5, pp. 264 - 275
Isogeometric analysis based on non-uniform rational B-splines (NURBS) as basis functions preserves the exact geometry but suffers from the drawback of a... 
Isogeometric analysis | Adaptivity | T-splines | A posteriori error estimation | CAD | NURBS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MESHES | ENGINEERING, MULTIDISCIPLINARY
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11. Full Text Tree-based solvers for adaptive mesh refinement code FLASH - I: Gravity and optical depths
by Wünsch, R and Walch, S and Dinnbier, F and Whitworth, A
Monthly Notices of the Royal Astronomical Society, ISSN 0035-8711, 04/2018, Volume 475, Issue 3, pp. 3393 - 3418
We describe an OctTree algorithm for the MPI parallel, adaptive mesh refinement code FLASH, which can be used to calculate the gas self-gravity, and also the... 
Hydrodynamics | Gravitation | Radiative transfer | ISM: evolution | Galaxies: ISM | MOLECULAR CLOUDS | SILCC PROJECT | radiative transfer | STAR-FORMATION RATE | hydrodynamics | A NUMERICAL CODE | INTERSTELLAR-MEDIUM | COSMOLOGICAL SIMULATIONS | N-BODY SIMULATIONS | FORCE-CALCULATION ALGORITHM | gravitation | galaxies: ISM | RESOLUTION CODE | ASTRONOMY & ASTROPHYSICS | PARTICLE-MESH | Multigrid methods | Adaptive algorithms | Radiation | Diffuse radiation | Boundary conditions | Radiation transport | Algorithms | Mathematical analysis | Optical analysis | Solvers | Grid refinement (mathematics) | Acceptance criteria | Acceptance tests
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12. Full Text Block-based adaptive mesh refinement for fluid–structure interactions in incompressible flows
by Liu, Cheng and Hu, Changhong
Computer Physics Communications, ISSN 0010-4655, 11/2018, Volume 232, pp. 104 - 123
In this study, an immersed boundary (IB) approach on the basis of moving least squares (MLS) interpolation is proposed for analyzing the dynamic response of a... 
MLS interpolation | CIP-CSL | Adaptive mesh | Fluid–structure interaction | Immersed boundary method | Incompressible flows | UNSTEADY AERODYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | BODIES | NUMERICAL SIMULATIONS | PLATES | PHYSICS, MATHEMATICAL | Fluid-structure interaction | Specific gravity | Analysis
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13. Full Text Adjoint-based error estimation and adaptive mesh refinement for the RANS and k– ω turbulence model equations
by Hartmann, Ralf and Held, Joachim and Leicht, Tobias
Journal of Computational Physics, ISSN 0021-9991, 2011, Volume 230, Issue 11, pp. 4268 - 4284
In this article we present the extension of the error estimation and goal-oriented mesh refinement approach from laminar to turbulent flows, which are governed... 
Discontinuous Galerkin method | Error estimation | Turbulent flows | Goal-oriented mesh refinement
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14. Full Text A high order special relativistic hydrodynamic and magnetohydrodynamic code with space–time adaptive mesh refinement
by Zanotti, Olindo and Dumbser, Michael
Computer Physics Communications, ISSN 0010-4655, 03/2015, Volume 188, pp. 110 - 127
We present a high order one-step ADER–WENO finite volume scheme with space–time adaptive mesh refinement (AMR) for the solution of the special relativistic... 
Magnetohydrodynamics | High order ADER–WENO finite volume scheme | Time-accurate local time stepping (LTS) | Space–time adaptive mesh refinement (AMR) | Special relativity | Space-time adaptive mesh refinement (AMR) | ADER-WENO finite volume scheme | High order | EQUATIONS | ESSENTIALLY NONOSCILLATORY SCHEMES | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | High order ADER-WENO finite volume scheme | SIMULATIONS | FLOWS | EXACT RIEMANN SOLVER | UNSTRUCTURED MESHES | HYPERBOLIC CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | SHOCK CAPTURING SCHEMES | Mechanical engineering | Algorithms | Wave propagation | Computational fluid dynamics | Mathematical analysis | Fluid flow | Magnetohydrodynamic equations | Hydrodynamics | Mathematical models | Runge-Kutta method | Galerkin methods
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