烦忧
发表于 2025-3-28 17:04:47
Introduction,es have gained an ever increasing importance. In several fields, from aerospace and mechanical engineering to life sciences, numerical simulations of partial differential equations (PDEs) currently provide a virtual platform ancillary to material/mechanics testing or . experiments. These are in turn
罗盘
发表于 2025-3-28 19:17:26
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charisma
发表于 2025-3-29 01:11:10
RB Methods: Basic Principles, Basic Properties,n projection onto an .-dimensional space . (the RB space) that approximates the high-fidelity (say, finite element) solution of the given PDE, for any choice of the parameter within a prescribed parameter set. We illustrate the main steps needed to set up such methods efficiently. We discuss in deta
TERRA
发表于 2025-3-29 05:54:18
On the Algebraic and Geometric Structure of RB Methods,s least-squares RB approximation) and the Galerkin high-fidelity approximation (3.11) are highlighted, for the purpose of illustrating, in a more fitting way and from a different perspective, the mathematical structure underpinning RB methods. The key role played by the transformation matrix in defi
Vasodilation
发表于 2025-3-29 08:26:03
The Theoretical Rationale Behind,anifold that are directly inherited from the parametrized differential operators. We define the Kolmogorov .-width to measure how well suited .-dimensional subspaces are to approximate the solution manifold. At the end we show that a wise selection of snapshots yields exponential convergence when ap
Left-Atrium
发表于 2025-3-29 11:48:30
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讽刺滑稽戏剧
发表于 2025-3-29 17:31:53
RB Methods in Action: Setting up the Problem, for this operation are given, and examples of parametrized PDEs are discussed that are inspired by the four problems of Chap. 2. The primary purpose is to highlight the different role played by physical and geometric parameters. A further critical issue addressed concerns the possible affine parame
moratorium
发表于 2025-3-29 23:40:44
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不确定
发表于 2025-3-30 03:20:44
Extension to Nonaffine Problems,fline/online decomposition relies on that assumption, in case of nonaffine problems we recover an approximate affine expansion by means of the so-called empirical interpolation method (EIM). We provide a detailed description of the EIM, focusing on linear problems for the sake of simplicity. A possi
Infuriate
发表于 2025-3-30 07:34:39
Extension to Nonlinear Problems,milinear equation. Both high-fidelity and RB approximations, as well as their interplay with Newton linearization, are analyzed, before considering in detail the case of Navier-Stokes equations. The underlying RB construction is essentially the same as for the previous linear PDEs, hence the focus i