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In this paper we develop a systematic reduction procedure for determining intermediate integrals of second order hyperbolic equations so that exact solutions of the second order PDEs under interest can be obtained by solving first order…

Mathematical Physics · Physics 2024-05-07 Natale Manganaro , Alessandra Rizzo

By a further study of the mechanism of the hyperbolic regularization of the moment system for Boltzmann equation proposed in [Z. Cai, Y. Fan, R. Li, Comm. Math. Sci. 11(2): 547-571, 2013], we point out that the key point is treating the…

Mathematical Physics · Physics 2016-02-17 Yuwei Fan , Julian Koellermeier , Jun Li , Ruo Li , Manuel Torrilhon

In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in…

Numerical Analysis · Mathematics 2017-07-10 Michele Botti , Daniele Di Pietro , Pierre Sochala

The renormalization method which is a type of perturbation method is extended to a tool to study weakly nonlinear time-delay systems. For systems with order-one delay, we show that the renormalization method leads to reduced systems without…

Pattern Formation and Solitons · Physics 2009-11-13 Shin-itiro Goto

In this work, we focus on reduced order modeling (ROM) techniques for hyperbolic conservation laws with application in uncertainty quantification (UQ) and in conjunction with the well-known Monte Carlo sampling method. Because we are…

Numerical Analysis · Mathematics 2018-08-13 R. Crisovan , D. Torlo , R. Abgrall , S. Tokareva

It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…

Computational Physics · Physics 2007-05-23 J. M. Aguirregabiria

We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online…

Numerical Analysis · Mathematics 2016-03-09 Remi Abgrall , David Amsallem , Roxana Crisonovan

Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques…

Numerical Analysis · Mathematics 2024-07-17 Julian Koellermeier , Philipp Krah , Jonas Kusch

This paper presents a novel model order reduction technique tailored for power systems with a large share of inverter-based energy resources. Such systems exhibit an increased level of dynamic stiffness compared to traditional power…

Systems and Control · Electrical Eng. & Systems 2024-07-08 Simon Muntwiler , Ognjen Stanojev , Andrea Zanelli , Gabriela Hug , Melanie N. Zeilinger

We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of…

Numerical Analysis · Mathematics 2018-07-24 Giacomo Albi , Michael Herty , Lorenzo Pareschi

Suppressing vibrations in mechanical systems, usually described by second-order dynamical models, is a challenging task in mechanical engineering in terms of computational resources even nowadays. One remedy is structure-preserving model…

Optimization and Control · Mathematics 2023-09-25 Rebekka S. Beddig , Peter Benner , Ines Dorschky , Timo Reis , Paul Schwerdtner , Matthias Voigt , Steffen W. R. Werner

Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…

Dynamical Systems · Mathematics 2026-05-14 Dan Wilson

In this paper we present a new first-order hyperbolic reformulation of the Cahn-Hilliard equation. The model is obtained from the combination of augmented Lagrangian techniques proposed earlier by the authors of this paper, with a classical…

Numerical Analysis · Mathematics 2024-08-08 Firas Dhaouadi , Michael Dumbser , Sergey Gavrilyuk

In this paper we propose a reduction procedure for determining generalized travelling waves for first order quasilinear hyperbolic nonhomogeneous systems. The basic idea is to look for solutions of the governing model which satisfy a…

Mathematical Physics · Physics 2025-07-23 N. Manganaro , A. Rizzo

We propose a model reduction technique for parametrized partial differential equations arising from scalar hyperbolic conservation laws. The key idea of the technique is to construct basis functions that are local in parameter and time…

Numerical Analysis · Mathematics 2018-05-16 Donsub Rim , Kyle T. Mandli

We provide an analytical framework for balanced realization model order reduction of linear control systems which depend on an unknown parameter. Besides recovering known results for the first order corrections, we obtain explicit novel…

Systems and Control · Computer Science 2016-06-24 Carles Batlle , Nestor Roqueiro

We show how the basic idea of parabolic Jacobi relaxation can be modified to obtain a new class of hyperbolic relaxation schemes that are suitable for the solution of elliptic equations. Some of the analytic and numerical properties of…

General Relativity and Quantum Cosmology · Physics 2018-10-31 Hannes R. Rüter , David Hilditch , Marcus Bugner , Bernd Brügmann

A framework is developed for applying accelerated methods to general hyperbolic programming, including linear, second-order cone, and semidefinite programming as special cases. The approach replaces a hyperbolic program with a convex…

Optimization and Control · Mathematics 2017-05-30 James Renegar

In [1] is proposed a simplified DeC method, that, when combined with the residual distribution (RD) framework, allows to construct a high order, explicit FE scheme with continuous approximation avoiding the inversion of the mass matrix for…

Numerical Analysis · Mathematics 2022-11-17 Rémi Abgrall , Elise Le Mélédo , Philipp Öffner , Davide Torlo

For hyperbolic first-order systems of linear partial differential equations (master equations), appearing in description of kinetic processes in physics, biology and chemistry we propose a new procedure to obtain their complete closed-form…

Analysis of PDEs · Mathematics 2007-05-23 E. I. Ganzha , V. M. Loginov , S. P. Tsarev