Projection-based model-order reduction via graph autoencoders suited for unstructured meshes
Data-Centric EngineeringThis paper presents the development of a graph autoencoder architecture capable of performing projection-based model-order reduction (PMOR) using a nonlinear manifold least-squares Petrov–Galerkin (LSPG) projection scheme.
Liam Magargal +4 more
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An algorithm to create conservative Galerkin projection between meshes
, 2021 We present in this paper an algorithm to solve pure-convection problems with a conservative Lagrange-Galerkin formulation in the framework of the finite element method. The integrals obtained from the Lagrange-Galerkin formulation will be computed with an algorithm which leads to conservation of mass up to machine accuracy, when we transfer information
Gómez Molina, P. +2 more
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Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity
Results in Applied MathematicsThis paper explores an iterative approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order models.
Francesco Ballarin +2 more
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Uma nova técnica de aproximação para o método de Galerkin aplicado às equações integrais de contorno / [PDF]
, 2000 Tese (Doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico.No presente trabalho é apresentada uma nova estratégia de adaptatividade p para a aproximação de Galerkin das equações integrais de contorno.
Nicolazzi, Lauro Cesar
core
A Projection-Free Sparse Model Order Reduction Method for Thermomechanical Multibody Dynamics
MathematicsThermomechanical coupling effects significantly influence the dynamic response of flexible multibody systems operating in thermal environments. Accurate simulation using conventional projection-based reduced-order models remains challenging due to strong
Guiming Liang +5 more
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A local projection stabilization/continuous Galerkin–Petrov method for incompressible flow problems
, 2018 A local projection stabilization (LPS) method in space is considered to approximate the evolutionary Oseen equations. Optimal error bounds with constants independent of the viscosity parameter are obtained in the continuous-in-time case for both the ...
Novo, Julia +7 more
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Electronic Journal of Differential Equations, 2014 The operational block-pulse functions, a well-known method for solving functional equations, is employed to solve a system of nonlinear Volterra integro-differential equations.
Ali Ebadian, Amir Ahmad Khajehnasiri
doaj
Stochastic PDE projection on manifolds:Assumed-density and Galerkin filters
, 2016 We review the manifold projection method for stochastic nonlinear filtering in a more general setting than in our previous paper in Geometric Science of Information 2013. We still use a Hilbert space structure on a space of probability densities to project the infinite dimensional stochastic partial differential equation for the optimal filter onto a ...
Armstrong, John; id_orcid 0000-0002-4232-9555 +1 more
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Galerkin Projection Methods for Solving Multiple Linear Systems
, 2007 In this paper, we consider using conjugate gradient (CG) methods for solving multiple linear systems A(i) x(i) = b(i) , for 1 ≤ i ≤ s, where the coefficient matrices A(i) and the right-hand sides b( i) are different in general. In particular, we focus on the seed projection method which generates a Krylov subspace from a set of direction vectors ...
Ng, MKP, Chan, TF
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Weak Galerkin finite element method for second order problems on curvilinear polytopal meshes with Lipschitz continuous edges or faces. [PDF]
Comput Math Appl, 2023 Guan Q, Queisser G, Zhao W.
europepmc +1 more source