Journal ArticleDOI
Proper Generalized Decomposition with time adaptive space separation for transient wave propagation problems in separable domains
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TLDR
This work proposes a space separation with a time adaptive number of modes to efficiently capture transient wave propagation in separable domains and shows that the PGD solution approximates its standard finite element solution counterpart with acceptable accuracy, while reducing the storage needs and the computation time.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2021-07-01. It has received 6 citations till now. The article focuses on the topics: CPU time & Wave propagation.read more
Citations
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Journal ArticleDOI
Convolution Hierarchical Deep-Learning Neural Network Tensor Decomposition (C-HiDeNN-TD) for high-resolution topology optimization
Hengyang Li,Stefan Knapik,Yangfan Li,Chanwook Park,Jiachen Guo,Satyajit Mojumder,Ye Lu,Wei Chen,Daniel W. Apley,Wing Kam Liu +9 more
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Exploring space separation techniques for 3D elastic waves simulations
TL;DR: In this article , the 3D elastic wave simulations are decomposed into a sequence of lower dimensional problems with the Proper Generalized Decomposition (PGD) and the spatial discretization is performed with the Spectral Element Method (SEM) to provide more compact separated representations compared to the ones obtained with a finite element discretisation.
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Development of POD-based Reduced Order Models applied to shallow water equations using augmented Riemann solvers
TL;DR: In this article , a Roe-based reduced-order model based on the proper orthogonal decomposition was proposed to solve the shallow water equations in presence of source terms more efficiently.
Journal ArticleDOI
Proper Generalized Decomposition using Taylor expansion for non-linear diffusion equations
TL;DR: In this paper , the Proper Generalized Decomposition (PGD) method was used to solve non-linear diffusion equations and produce parametric solutions, which is a suitable alternative strategy to compute the solution of the equation.
References
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Journal ArticleDOI
A spectral element method for fluid dynamics: Laminar flow in a channel expansion
TL;DR: In this article, a spectral element method was proposed for numerical solution of the Navier-Stokes equations, where the computational domain is broken into a series of elements, and the velocity in each element is represented as a highorder Lagrangian interpolant through Chebyshev collocation points.
Journal Article
An introduction to the proper orthogonal decomposition
TL;DR: A tutorial is presented on the Proper Orthogonal Decomposition (POD), which finds applications in computationally processing large amounts of high-dimensio nal data with the aim of obtaining low-dimensional descriptions that capture much of the phenomena of interest.
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Recent Advances and New Challenges in the Use of the Proper Generalized Decomposition for Solving Multidimensional Models
TL;DR: This paper revisits a powerful discretization technique, the Proper Generalized Decomposition—PGD, illustrating its ability for solving highly multidimensional models.
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Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions
TL;DR: In this paper, a method to measure the dispersion on any numerical method related to the classical Galerkin FEM is presented, which does not require to compute the numerical solution and is extremely fast.