相关论文: Towards an Efficient Shifted Cholesky QR for Appli…

We present a modified model order reduction (MOR) technique for the FFT-based simulation of composite microstructures. It utilizes the earlier introduced MOR technique (Kochmann et al. [2019]), which is based on solving the…

This paper presents a parametric Model Order Reduction (MOR) method for weakly coupled thermo-mechanical Finite Element (FE) models of machine tools and other similar mechatronic systems. This work proposes a reduction method, Krylov Modal…

Model order reduction (MOR) is an important step in the design process of integrated circuits. Specifically, the electromagnetic models extracted from modern complex designs result in a large number of passive elements that introduce…

The efficient and accurate QR decomposition for matrices with hierarchical low-rank structures, such as HODLR and hierarchical matrices, has been challenging. Existing structure-exploiting algorithms are prone to numerical instability as…

Model Order Reduction (MOR) based on Proper Orthogonal Decomposition (POD) and Smooth Particle Hydrodynamics (SPH) has proven effective in various applications. Most MOR methods utilizing POD are implemented within a pure Eulerian…

We provide an introduction to POD-MOR with focus on (nonlinear) parametric PDEs and (nonlinear) time-dependent PDEs, and PDE constrained optimization with POD surrogate models as application. We cover the relation of POD and SVD, POD from…

The numerical simulation of electromagnetic transients in fusion devices is essential for analyzing plasma stability and disruptive events. However, it remains computationally demanding due to the large-scale dense systems arising from…

Dynamical systems are pervasive in almost all engineering and scientific applications. Simulating such systems is computationally very intensive. Hence, Model Order Reduction (MOR) is used to reduce them to a lower dimension. Most of the…

We propose a data-driven model order reduction (MOR) technique for parametrized partial differential equations that exhibit parameter-dependent jump-discontinuities. Such problems have poor-approximability in a linear space and therefore,…

Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection bases, especially for problems with slowly decaying Kolmogorov n-widths. Additionally,…

We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…

This article deals with the efficient and certified numerical approximation of the smallest eigenvalue and the associated eigenspace of a large-scale parametric Hermitian matrix. For this aim, we rely on projection-based model order…

We discuss the recent developments of projection-based model order reduction (MOR) techniques targeting Hamiltonian problems. Hamilton's principle completely characterizes many high-dimensional models in mathematical physics, resulting in…

Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov $n$-width of the solution manifold, the resulting reduced-order model (ROM) can…

Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…

Model Order Reduction (MOR) methods enable the generation of real-time-capable digital twins, which can enable various novel value streams in industry. While traditional projection-based methods are robust and accurate for linear problems,…

This article proposes and analyzes several variants of the randomized Cholesky QR factorization of a matrix $X$. Instead of computing the R factor from $X^T X$, as is done by standard methods, we obtain it from a small, efficiently…

Model order reduction (MOR) has long been a mainstream strategy to accelerate large-scale transient circuit simulation. Dynamic Mode Decomposition (DMD) represents a novel data-driven characterization method, extracting dominant dynamical…

A quadratic approximation manifold is presented for performing nonlinear, projection-based, model order reduction (PMOR). It constitutes a departure from the traditional affine subspace approximation that is aimed at mitigating the…

Systems of differential-algebraic equations (DAEs) represent a widespread formalism in the modeling of constrained mechanical systems and electrical networks. Due to the automatic, object-oriented generation of the equations of motion and…