Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization | Paper Citation Record

Observation a5c256bb-b4d7-4f99-ba3c-436e5a4074f4 · outbound

This paper cites An r-adaptive finite element method using neural networks for parametric self- adjoint elliptic problems.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization An r-adaptive finite element method using neural networks for parametric self- adjoint elliptic problems

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This paper cites Ainsworth and J.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Ainsworth and J

Reference 2

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This paper cites A posteriori error estimation of residual type for anisotropic diffusion-convection-reaction problems.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization A posteriori error estimation of residual type for anisotropic diffusion-convection-reaction problems

Reference 4

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This paper cites Direct and inverse error estimates for finite elements with mesh refinements.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Direct and inverse error estimates for finite elements with mesh refinements

Reference 5

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This paper cites Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?

Reference 6

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This paper cites Bangerth and R.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Bangerth and R

Reference 7

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This paper cites Automatic differentiation in machine learning: A survey.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Automatic differentiation in machine learning: A survey

Reference 8

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This paper cites Iso- geometric analysis: Approximation, stability and error estimates for h-refined meshes.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Iso- geometric analysis: Approximation, stability and error estimates for h-refined meshes

Reference 9

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This paper cites Efficient and modular implicit differentiation.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Efficient and modular implicit differentiation

Reference 10

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This paper cites Good Approximation by Splines with Variable Knots. II.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Good Approximation by Splines with Variable Knots. II

Reference 12

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This paper cites Bradbury, R.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Bradbury, R

Reference 14

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This paper cites Adaptivity with moving grids.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Adaptivity with moving grids

Reference 15

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This paper cites Mathematical Founda- tions of Adaptive Isogeometric Analysis.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Mathematical Founda- tions of Adaptive Isogeometric Analysis

Reference 16

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This paper cites Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method

Reference 17

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Observation b82fcf6f-59f3-4a94-873e-3bcb8e61aa2c · outbound

This paper cites Approximation by finite element functions using local regularization.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Approximation by finite element functions using local regularization

Reference 18

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Reference 19

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Observation a7a0ee02-ac56-4b7f-b663-9d1f0c32b112 · outbound

This paper cites A Posteriori Error Estimation for Highly Indefinite Helmholtz Problems.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization A Posteriori Error Estimation for Highly Indefinite Helmholtz Problems

Reference 20

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Observation 04ce4954-b7c8-4d7e-b554-c56921a0e6d4 · outbound

This paper cites Imposing Dirichlet boundary conditions with Nitsche’s method and spline-based finite elements.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Imposing Dirichlet boundary conditions with Nitsche’s method and spline-based finite elements

Reference 21

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Observation 677e849e-afde-4ef7-93c7-1b030cdaf9fa · outbound

This paper cites New anisotropic a priori error estimates.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization New anisotropic a priori error estimates

Reference 22

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This paper cites Deep reinforcement learning for adaptive mesh refinement.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Deep reinforcement learning for adaptive mesh refinement

Reference 23

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This paper cites Grisvard.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Grisvard

Reference 25

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This paper cites Hinze, R.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Hinze, R

Reference 26

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This paper cites Huang and R.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Huang and R

Reference 27

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Observation b4b053be-4158-4e0f-8c81-d66e94e682e7 · outbound

This paper cites Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement

Reference 28

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This paper cites Ihlenburg.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Ihlenburg

Reference 29

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This paper cites Finite element solution of the Helmholtz equation with high wave number. Part I: The h-version of the FEM.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Finite element solution of the Helmholtz equation with high wave number. Part I: The h-version of the FEM

Reference 30

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This paper cites hp-VPINNs: Variational physics-informed neural networks with domain decomposition.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization hp-VPINNs: Variational physics-informed neural networks with domain decomposition

Reference 31

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This paper cites Adam: A Method for Stochastic Optimization.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Adam: A Method for Stochastic Optimization

Reference 32

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This paper cites Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes

Reference 33

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Reference 34

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This paper cites Isogeometric Residual Minimization Method (iGRM) with direction splitting for non-stationary advection–diffusion problems.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Isogeometric Residual Minimization Method (iGRM) with direction splitting for non-stationary advection–diffusion problems

Reference 35

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This paper cites Energy minimisation using overlapping tensor-product free-knot B-splines.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Energy minimisation using overlapping tensor-product free-knot B-splines

Reference 36

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This paper cites r-Adaptive deep learning method for solving partial differential equations.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization r-Adaptive deep learning method for solving partial differential equations

Reference 37

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Observation 320a9e6e-0a5b-4022-aad6-199e6bdcbbe3 · outbound

This paper cites Finite cell method: h- and p-extension for embedded domain problems in solid mechanics.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Finite cell method: h- and p-extension for embedded domain problems in solid mechanics

Reference 38

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This paper cites A posteriori error estimators for elliptic equations with discontinuous coeffi- cients.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization A posteriori error estimators for elliptic equations with discontinuous coeffi- cients

Reference 39

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This paper cites Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial dif- ferential equations.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial dif- ferential equations

Reference 40

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This paper cites Adaptive optimization of isogeometric multi-patch dis- cretizations using artificial neural networks.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Adaptive optimization of isogeometric multi-patch dis- cretizations using artificial neural networks

Reference 41

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This paper cites Robust Variational Physics-Informed Neural Networks.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Robust Variational Physics-Informed Neural Networks

Reference 42

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This paper cites Goal-oriented adaptivity for a con- forming residual minimization method in a dual discontinuous Galerkin norm.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Goal-oriented adaptivity for a con- forming residual minimization method in a dual discontinuous Galerkin norm

Reference 43

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This paper cites Robust a-posteriori estimator for advection-diffusion-reaction problems.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Robust a-posteriori estimator for advection-diffusion-reaction problems

Reference 44

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Observation 1304001d-a0fa-40cc-a404-eccaeaaa7e30 · outbound

This paper cites Isogeometric colloca- tion: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Isogeometric colloca- tion: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations

Reference 45

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Observation d54a08d0-1d99-4b22-8098-fa06ae709389 · outbound

This paper cites The Finite Cell Method: A review in the context of higher-order structural analysis of CAD and image-based geometric models.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization The Finite Cell Method: A review in the context of higher-order structural analysis of CAD and image-based geometric models

Reference 46

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Reference 47

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This paper cites Finite element interpolation of nonsmooth functions satisfying boundary conditions.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Finite element interpolation of nonsmooth functions satisfying boundary conditions

Reference 48

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Observation 74b3aad6-74c6-4f03-a70f-2046629760a3 · outbound

This paper cites Implicit Neu- ral Representations with Periodic Activation Functions.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Implicit Neu- ral Representations with Periodic Activation Functions

Reference 49

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This paper cites M2N: Mesh Movement Networks for PDE Solvers.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization M2N: Mesh Movement Networks for PDE Solvers

Reference 50

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This paper cites Deep Fourier Residual method for solv- ing time-harmonic Maxwell’s equations.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Deep Fourier Residual method for solv- ing time-harmonic Maxwell’s equations

Reference 51

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This paper cites A Deep Fourier Residual method for solving PDEs using neural networks.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization A Deep Fourier Residual method for solving PDEs using neural networks

Reference 52

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This paper cites A Deep Double Ritz method (D 2RM) for solving partial differential equations using neural networks.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization A Deep Double Ritz method (D 2RM) for solving partial differential equations using neural networks

Reference 53

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This paper cites Robust a posteriori error estimates for stationary convection-diffusion equa- tions.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Robust a posteriori error estimates for stationary convection-diffusion equa- tions

Reference 54

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Observation 9eccd1c4-1644-4c04-adb2-f4367fa5773d · outbound

This paper cites Robust a posteriori error estimators for a singularly perturbed reaction-diffusion equation.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Robust a posteriori error estimators for a singularly perturbed reaction-diffusion equation

Reference 55

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This paper cites Verf¨ urth.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Verf¨ urth

Reference 56

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This paper cites Efficient r-adaptive isogeometric anal- ysis with Winslow’s mapping and monitor function approach.

Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization Efficient r-adaptive isogeometric anal- ysis with Winslow’s mapping and monitor function approach

Reference 57

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