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In this work, we propose a new stochastic domain decomposition method for solving steady-state partial differential equations (PDEs) with random inputs. Based on the efficiency of the Variable-separation (VS) method in simulating stochastic…

Numerical Analysis · Mathematics 2025-02-06 Liang Chen , Yaru Chen , Qiuqi Li , Zhiwen Zhang

We extend the index-aware model-order reduction method to systems of nonlinear differential-algebraic equations with a special nonlinear term f(Ex), where E is a singular matrix. Such nonlinear differential-algebraic equations arise, for…

Numerical Analysis · Mathematics 2020-02-25 Nicodemus Banagaaya , Giuseppe Ali , Sara Grundel , Peter Benner

In this paper, we propose a model order reduction based adaptive parareal method for time-dependent partial differential equations. By using the data obtained by the fine propagator in each iteration of the plain parareal method together…

Numerical Analysis · Mathematics 2026-01-19 Xiaoying Dai , Miao Hu , Shuwei Shen

In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically, we consider a class of nonlinear dynamical systems whose nonlinear terms are polynomial…

Dynamical Systems · Mathematics 2023-01-24 Pawan Goyal , Igor Pontes Duff , Peter Benner

We extend a localized model order reduction method for the distributed finite element solution of elliptic boundary value problems in the cloud. We give a computationally efficient technique to compute the required inner product matrices…

Numerical Analysis · Mathematics 2025-04-01 Tom Gustafsson , Antti Hannukainen , Vili Kohonen

Frequency-based methods have been successfully employed in creating high fidelity data-driven reduced order models (DDROMs) for linear dynamical systems. These methods require access to values (and sometimes derivatives) of the…

Numerical Analysis · Mathematics 2024-01-04 Michael S. Ackermann , Serkan Gugercin

Time domain simulations are crucial for analyzing transient behavior and broadband responses in electromagnetic problems. However, conventional numerical methods such as finite element method in time domain (FEMTD) and finite difference…

Computational Physics · Physics 2025-02-19 Ruth Medeiros , Valentín de la Rubia

Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…

Numerical Analysis · Mathematics 2024-01-17 Francesco Andreuzzi , Nicola Demo , Gianluigi Rozza

We present domain decomposition finite element/finite difference method for the solution of hyperbolic equation. The domain decomposition is performed such that finite elements and finite differences are used in different subdomains of the…

Numerical Analysis · Mathematics 2016-03-23 L. Beilina

We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…

Numerical Analysis · Mathematics 2019-04-15 Roland Pulch

The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…

Numerical Analysis · Mathematics 2022-10-26 Petr N. Vabishchevich

Physical laws governing population dynamics are generally expressed as differential equations. Research in recent decades has incorporated fractional-order (non-integer) derivatives into differential models of natural phenomena, such as…

Numerical Analysis · Mathematics 2022-12-08 A. P. Harris , T. A. Biala , A. Q. M. Khaliq

In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…

Numerical Analysis · Mathematics 2024-08-29 Hendrik Kleikamp , Lukas Renelt

This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient…

Numerical Analysis · Mathematics 2025-10-14 Margarita Chasapi , Pablo Antolin , Annalisa Buffa

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…

Hardware Architecture · Computer Science 2011-11-09 Peng Li , Frank Liu , Xin Li , Lawrence T. Pileggi , Sani R. Nassif

We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…

Numerical Analysis · Mathematics 2019-12-25 Christopher Beattie , Serkan Gugercin , Zoran Tomljanovic

We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients based on model order reduction techniques and the Laplace…

Numerical Analysis · Mathematics 2026-01-06 Fernando Henríquez , Jan S. Hesthaven

Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…

Signal Processing · Electrical Eng. & Systems 2020-04-09 Mustaffa Alfatlawi , Vaibhav Srivastava

This work presents a purely data-driven, wavelet-based framework for modal identification and reduced-order modeling of mechanical systems with assumed linear dynamics characterized by closely spaced modes with classical or non-classical…

Signal Processing · Electrical Eng. & Systems 2025-10-28 Anargyros Michaloliakos , Benjamin J. Chang , Lawrence A. Bergman , Alexander F. Vakakis

In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to…

Numerical Analysis · Mathematics 2020-11-23 Fabrizio Garotta , Nicola Demo , Marco Tezzele , Massimo Carraturo , Alessandro Reali , Gianluigi Rozza