相关论文: A hyper-reduced MAC scheme for the parametric Stok…

The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation…

We present a matrix-free flow solver for high-order finite element discretizations of the incompressible Navier-Stokes and Stokes equations with GPU acceleration. For high polynomial degrees, assembling the matrix for the linear systems…

Assessing IC manufacturing process fluctuations and their impacts on IC interconnect performance has become unavoidable for modern DSM designs. However, the construction of parametric interconnect models is often hampered by the rapid…

Reduced Order Modelling (ROM) has been widely used to create lower order, computationally inexpensive representations of higher-order dynamical systems. Using these representations, ROMs can efficiently model flow fields while using…

Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries…

We propose a two-fold approach to model reduction of fluid-structure interaction. The state equations for the fluid are solved with reduced basis methods. These are model reduction methods for parametric partial differential equations using…

In computational fluid dynamics, the demand for increasingly multidisciplinary reliable simulations, for both analysis and design optimization purposes, requires transformational advances in individual components of future solvers. At the…

We present an efficient deep learning technique for the model reduction of the Navier-Stokes equations for unsteady flow problems. The proposed technique relies on the Convolutional Neural Network (CNN) and the stochastic gradient descent…

This chapter provides an extended overview about Reduced Order Models (ROMs), with a focus on their features in terms of efficiency and accuracy. In particular, the aim is to browse the more common ROM frameworks, considering both intrusive…

Shallow flows are governed by the Navier-Stokes equations. They are commonly modelled using the shallow water equations, a great simplification of the Navier-Stokes equations, which often yields inaccurate results. For that reason, a model…

Topology optimization problems generally support multiple local minima, and real-world applications are typically three-dimensional. In previous work [I. P. A. Papadopoulos, P. E. Farrell, and T. M. Surowiec, Computing multiple solutions of…

This paper focuses on a new framework for reduced order modelling of non-intrusive data with application to 2D flows. To overcome the shortcomings of intrusive model order reduction usually derived by combining the POD and the Galerkin…

We propose an efficient residual minimization technique for the nonlinear model-order reduction of parameterized hyperbolic partial differential equations. Our nonlinear approximation space is a span of snapshots evaluated on a shifted…

In this work, we develop Non-Intrusive Reduced Order Models (NIROMs) that combine Proper Orthogonal Decomposition (POD) with a Radial Basis Function (RBF) interpolation method to construct efficient reduced order models for time-dependent…

First order semi-linear coupling of scalar hypoelliptic equations of second order leads to a natural class of incompressible Navier Stokes equation systems, which encompasses systems with variable viscosity and essentially Navier Stokes…

We present an abstract framework for a posteriori error estimation for approximations of scalar parabolic evolution equations, based on elliptic reconstruction techniques [10, 9, 3, 5]. In addition to its original application (to derive…

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…

This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional…

We consider the Navier-Stokes equations in a channel with a narrowing of varying height. The model is discretized with high-order spectral element ansatz functions, resulting in 6372 degrees of freedom. The steady-state snapshot solutions…

Projection-based reduced-order models (PROMs) have demonstrated accuracy, reliability, and robustness in approximating high-dimensional, differential equation-based computational models across many applications. For this reason, it has been…