Related papers: Model-Order Reduction For Hyperbolic Relaxation Sy…
There is a tendency to write the equations of general relativity as a first order symmetric system of time dependent partial differential equations. However, for numerical reasons, it might be advantageous to use a second order formulation…
Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic convergence of Newton's method. Using first-order derivatives of…
In this paper we consider different model reduction techniques for systems with moving loads. Due to the time-dependency of the input and output matrices, the application of time-varying projection matrices for the reduction offers new…
We consider the numerical solution of large-scale symmetric differential matrix Riccati equations. Under certain hypotheses on the data, reduced order methods have recently arisen as a promising class of solution strategies, by forming…
We present a methodology that extends invariant manifold theory to a class of autonomous piecewise linear systems with nonsmoothness at the equilibrium, providing a framework for model order reduction in mechanical structures with compliant…
We consider the development of high order space and time numerical methods based on Implicit-Explicit (IMEX) multistep time integrators for hyperbolic systems with relaxation. More specifically, we consider hyperbolic balance laws in which…
In this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization,…
In this article a framework for the generation of a computationally fast surrogate model for district heating networks is presented. An appropriate model results in an index-1 hyperbolic, differential algebraic equation quadratic in state,…
In this paper, we discuss reduced order modelling approaches to bifurcating systems arising from continuum mechanics benchmarks. The investigation of the beam's deflection is a relevant topic of investigation with fundamental implications…
Direct numerical simulation of dynamical systems is of fundamental importance in studying a wide range of complex physical phenomena. However, the ever-increasing need for accuracy leads to extremely large-scale dynamical systems whose…
A novel numerical scheme to solve coupled systems of conservation laws is introduced. The scheme is derived based on a relaxation approach and does not require information on the Lax curves of the coupled systems, which simplifies the…
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…
The relaxation in the calculus of variation motivates the numerical analysis of a class of degenerate convex minimization problems with non-strictly convex energy densities with some convexity control and two-sided $p$-growth. The…
A reduced-order model based on Proper Orthogonal Decomposition (POD) is proposed for the bidomain equations of cardiac electrophysiology. Its accuracy is assessed through electrocardiograms in various configurations, including myocardium…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…
This paper introduces an interpolation framework for the weighted-H2 model reduction problem. We obtain a new representation of the weighted-H2 norm of SISO systems that provides new interpolatory first order necessary conditions for an…
Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and…
In this paper, we present a new approach to obtain so-called damping estimates for self-similar solutions to general hyperbolic relaxation systems applying the method of characteristics. Such damping estimates are an important part of the…
For a time-limited version of the H$_2$ norm defined over a fixed time interval, we obtain a closed form expression of the gradients. After that, we use the gradients to propose a time-limited model order reduction method. The method…
We consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions…