Tensor train based isogeometric analysis for PDE approximation on parameter dependent geometries
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Publication:2096827
DOI10.1016/j.cma.2022.115593OpenAlexW4296535119MaRDI QIDQ2096827
Herbert De Gersem, Ion Gabriel Ion, Dimitrios Loukrezis
Publication date: 11 November 2022
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2204.02843
partial differential equationstensor decompositionisogeometric analysisparametric approximationtensor traingeometry deformation
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Cites Work
- Tensor Decompositions and Applications
- Tensor-Train Decomposition
- TT-cross approximation for multidimensional arrays
- High-performance computing of wind turbine aerodynamics using isogeometric analysis
- Realization of an integrated structural design process: analysis-suitable geometric modelling and isogeometric analysis
- Isogeometric analysis of free-surface flow
- Isogeometric analysis in electromagnetics: B-splines approximation
- Adaptive cross approximation of multivariate functions
- \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling
- NURBS-based isogeometric analysis for the computation of flows about rotating components
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- Sparse second moment analysis for elliptic problems in stochastic domains
- Isogeometric analysis of structural vibrations
- Approximation of boundary element matrices
- The ubiquitous Kronecker product
- Large deformation shape uncertainty quantification in acoustic scattering
- Modeling of a hydraulic arresting gear using fluid-structure interaction and isogeometric analysis
- Higher order B-spline collocation at the Greville abscissae
- Integration by interpolation and look-up for Galerkin-based isogeometric analysis
- Patient-specific isogeometric structural analysis of aortic valve closure
- Efficient matrix computation for tensor-product isogeometric analysis: the use of sum factorization
- Fundamental aspects of shape optimization in the context of isogeometric analysis
- Partial tensor decomposition for decoupling isogeometric Galerkin discretizations
- Uncertainty quantification for Maxwell's eigenproblem based on isogeometric analysis and mode tracking
- Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations
- A hybrid collocation-perturbation approach for PDEs with random domains
- Refined isogeometric analysis for fluid mechanics and electromagnetics
- Isogeometric analysis: an overview and computer implementation aspects
- IsoGeometric approximations for electromagnetic problems in axisymmetric domains
- Low rank tensor methods in Galerkin-based isogeometric analysis
- A black-box low-rank approximation algorithm for fast matrix assembly in isogeometric analysis
- Low-rank space-time decoupled isogeometric analysis for parabolic problems with varying coefficients
- Low rank interpolation of boundary spline curves
- Quantics-TT collocation approximation of parameter-dependent and stochastic elliptic PDEs
- The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
- Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions
- Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition
- Tensor Spaces and Numerical Tensor Calculus
- Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
- Isogeometric Analysis
- Mathematical analysis of variational isogeometric methods
- Finite Element Methods for Maxwell's Equations
- Solution of Linear Systems and Matrix Inversion in the TT-Format
- TT-GMRES: solution to a linear system in the structured tensor format
- An Adaptive Stochastic Galerkin Tensor Train Discretization for Randomly Perturbed Domains
- Blessing of dimensionality: mathematical foundations of the statistical physics of data
- Isogeometric Mortar Coupling for Electromagnetic Problems
- A Low-Rank Tensor Method for PDE-Constrained Optimization with Isogeometric Analysis
- A Hybrid Alternating Least Squares--TT-Cross Algorithm for Parametric PDEs
- Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples
- A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
