Related papers: Model order reduction with novel discrete empirica…
Reduced order models (ROM) can represent spatiotemporal processes in significantly fewer dimensions and can be solved many orders faster than their governing partial differential equations (PDEs). For example, using a proper orthogonal…
Spatiotemporally chaotic systems, such as the solutions of some nonlinear partial differential equations, are dynamical systems that evolve toward a lower dimensional manifold. This manifold has an intricate geometry with heterogeneous…
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…
This contribution explores the combined capabilities of reduced basis methods and IsoGeometric Analysis (IGA) in the context of parameterized partial differential equations. The introduction of IGA enables a unified simulation framework…
We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first…
Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
Galerkin and Petrov-Galerkin projection-based reduced-order models (ROMs) of transient partial differential equations are typically obtained by performing a dimension reduction and projection process that is defined at either the spatially…
We propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic…
In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties that originate from active forces generated from…
This work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply (Petrov-)Galerkin…
We introduce improved Reduced Order Models (ROM) for convection-dominated flows. These non-linear closure models are inspired from successful numerical stabilization techniques used in Large Eddy Simulations (LES), such as Local Projection…
Approximating solutions of non-linear parametrized physical problems by interpolation presents a major challenge in terms of accuracy. In fact, pointwise interpolation of such solutions is rarely efficient and leads generally to incorrect…
Accurate simulations are essential for engineering applications, and intricate continuum mechanical material models are constructed to achieve this goal. However, the increasing complexity of the material models and geometrical properties…
The numerical simulation of incompressible flows is challenging due to the tight coupling of velocity and pressure. Projection methods offer an effective solution by decoupling these variables, making them suitable for large-scale…
Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications…
In this paper, a type of novel projection-based, time-segmented reduced order model (ROM) is proposed for dynamic fluid-structure interaction (FSI) problems based upon the arbitrary Lagrangian--Eulerian (ALE)-finite element method (FEM) in…
In this work, Galerkin projection is used to build Reduced Order Models (ROM) for two-dimensional Rayleigh-B\'enard (RB) convection with no-slip walls. We compare an uncoupled projection approach that uses separate orthonormal bases for…
Linear reduced-order modeling (ROM) simplifies complex simulations by approximating the behavior of a system using a simplified kinematic representation. Typically, ROM is trained on input simulations created with a specific spatial…
Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…