Space-time proper generalized decompositions for the resolution of transient elastodynamic models

DOI10.1016/j.cma.2012.11.003zbMath1297.74016OpenAlexW2045519343MaRDI QIDQ465872

J. Herrera, D. Rodríguez-Gómez

Publication date: 24 October 2014

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2012.11.003

zbMATH Keywords

model reductionelastodynamicsingular value decomposition (SVD)proper generalized decomposition (PGD)multi-field proper generalized decomposition (MF-PGD)tensorial formalism

Mathematics Subject Classification ID

Related Items (12)

Exploring space separation techniques for 3D elastic waves simulations ⋮ Adaptive isogeometric analysis for transient dynamics: space-time refinement based on hierarchical a-posteriori error estimations ⋮ Toward an optimal a priori reduced basis strategy for frictional contact problems with LATIN solver ⋮ Non-incremental response evaluation in geometrically nonlinear structural dynamics using a space-time stiffness operator ⋮ A multiscale large time increment/FAS algorithm with time-space model reduction for frictional contact problems ⋮ Real-time direct integration of reduced solid dynamics equations ⋮ Heterogeneous asynchronous time integrators for computational structural dynamics ⋮ PGD reduced-order modeling for structural dynamics applications ⋮ Multi-temporal decomposition for elastoplastic ratcheting solids ⋮ Ideal minimal residual-based proper generalized decomposition for non-symmetric multi-field models -- application to transient elastodynamics in space-time domain ⋮ Proper generalized decomposition with time adaptive space separation for transient wave propagation problems in separable domains ⋮ A Newmark space-time formulation in structural dynamics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Proper generalized decomposition for multiscale and~multiphysics problems
• Proper generalized decompositions and separated representations for the numerical solution of high dimensional stochastic problems
• A first step towards the use of proper general decomposition method for structural optimization
• On the convergence of a greedy rank-one update algorithm for a class of linear systems
• Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity
• An overview of the proper generalized decomposition with applications in computational rheology
• A monolithic approach to fluid-structure interaction
• On the deterministic solution of multidimensional parametric models using the proper generalized decomposition
• A global model reduction approach for 3D fatigue crack growth with confined plasticity
• The LATIN multiscale computational method and the proper generalized decomposition
• On the verification of model reduction methods based on the proper generalized decomposition
• 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
• Projection-based reduction of fluid-structure interaction systems using monolithic space-time modes
• A priori hyperreduction method: an adaptive approach
• A monolithic approach to fluid-structure interaction using space-time finite elements
• A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids. II: Transient simulation using space-time separated representations
• Alleviating mesh constraints: model reduction, parallel time integration and high resolution homogenization
• Results and questions on a nonlinear approximation approach for solving high-dimensional partial differential equations
• A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids
• A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations
• Space-time finite element methods for second-order hyperbolic equations
• The ubiquitous Kronecker product
• A space-time discontinuous Galerkin method for linearized elastodynamics with element-wise momentum balance
• The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview
• Formulation and analysis of variational methods for time integration of linear elastodynamics
• Generalized spectral decomposition method for solving stochastic finite element equations: invariant subspace problem and dedicated algorithms
• PHYSICAL INTERPRETATION OF THE PROPER ORTHOGONAL MODES USING THE SINGULAR VALUE DECOMPOSITION
• Recent advances on the use of separated representations
• A computational strategy for thermo-poroelastic structures with a time-space interface coupling
• Time finite element methods for structural dynamics
• On the Early History of the Singular Value Decomposition
• A LATIN computational strategy for multiphysics problems: application to poroelasticity
• A continuous space-time finite element method for the wave equation
• Algorithms for Numerical Analysis in High Dimensions
• Partitioned analysis of coupled mechanical systems

This page was built for publication: Space-time proper generalized decompositions for the resolution of transient elastodynamic models