Certified real-time shape optimization using isogeometric analysis, PGD model reduction, and a posteriori error estimation

Basic methods in fluid mechanics (76Mxx) Numerical and other methods in solid mechanics (74Sxx) Numerical methods for partial differential equations, boundary value problems (65Nxx)

Cites Work

Integration of PGD-virtual charts into an engineering design process
Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models
A first step towards the use of proper general decomposition method for structural optimization
Isogeometric shape design optimization: exact geometry and enhanced sensitivity
Isogeometric simulation of turbine blades for aircraft engines
Isogeometric shape optimization of shells using semi-analytical sensitivity analysis and sensitivity weighting
Separated representations and PGD-based model reduction. Fundamentals and applications. Papers based on the presentations at the course
A multiscale method with patch for the solution of stochastic partial differential equations with localized uncertainties
Verifying calculations -- forty years on. An overview of classical verification techniques for FEM simulations.
PGD-based \textit{computational vademecum} for efficient design, optimization and control
Isogeometric analysis and proper orthogonal decomposition for parabolic problems
Isogeometric shell analysis: the Reissner-Mindlin shell
Parameterization of computational domain in isogeometric analysis: methods and comparison
On the verification of model reduction methods based on the proper generalized decomposition
Parametric free-form shape design with PDE models and reduced basis method
A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations
An error estimator for separated representations of highly multidimensional models
Full analytical sensitivities in NURBS based isogeometric shape optimization
Fictitious domain method and separated representations for the solution of boundary value problems on uncertain parameterized domains
Parametric solutions involving geometry: a step towards efficient shape optimization
Isogeometric fluid-structure interaction: Theory, algorithms, and computations
Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
A multiscale reduced-basis method for parametrized elliptic partial differential equations with multiple scales
Isogeometric analysis of structural vibrations
Structural shape optimization - A survey
A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations
A unified approach to a posteriori error estimation using element residual methods
Reduced basis isogeometric methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils
Fundamental aspects of shape optimization in the context of isogeometric analysis
Constitutive relation error estimators for (visco)plastic finite element analysis with softening
On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors
Numerical methods in sensitivity analysis and shape optimization. With CD-ROM
An interactive geometry modeling and parametric design platform for isogeometric analysis
\textit{A posteriori} error estimation and adaptive strategy for PGD model reduction applied to parametrized linear parabolic problems
Isogeometric shape optimization on triangulations
Multi-objective robust airfoil optimization based on non-uniform rational B-spline (NURBS) representation
Isogeometric design of anisotropic shells: optimal form and material distribution
A fictitious domain approach to the numerical solution of PDEs in stochastic domains
Subdomain-based flux-free a posteriori error estimators
The proper generalized decomposition for advanced numerical simulations. A primer
\(\overline {\text B}\) and \(\overline {\text F}\) projection methods for nearly incompressible linear and nonlinear elasticity and plasticity using higher-order NURBS elements
Isogeometric structural shape optimization
Robust control of PGD-based numerical simulations
On the techniques for constructing admissible stress fields in model verification: Performances on engineering examples
New bounding techniques for goal-oriented error estimation applied to linear problems
A basis for bounding the errors of proper generalised decomposition solutions in solid mechanics
An isogeometric locking-free NURBS-based solid-shell element for geometrically nonlinear analysis
Proper generalized decomposition of a geometrically parametrized heat problem with geophysical applications
Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
An optimal control approach to a posteriori error estimation in finite element methods
Reduced-Basis Approach for Homogenization beyond the Periodic Setting
Recovery of equilibrium on star patches using a partition of unity technique
Isogeometric Analysis
A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities
Introduction to Shape Optimization
Shape optimization for viscous flows by reduced basis methods and free‐form deformation
Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries
S<scp>HAPE</scp> O<scp>PTIMIZATION IN</scp> F<scp>LUID</scp> M<scp>ECHANICS</scp>
A survey on level set methods for inverse problems and optimal design
A practical guide to splines.

This page was built for publication: Certified real-time shape optimization using isogeometric analysis, PGD model reduction, and a posteriori error estimation