Related papers: Model Reduction for Large Scale Systems
In this paper, we consider model order reduction (MOR) methods for problems with slowly decaying Kolmogorov $n$-widths as, e.g., certain wave-like or transport-dominated problems. To overcome this Kolmogorov barrier within MOR, nonlinear…
In this research, we propose an online basis enrichment strategy within the framework of a recently developed constraint energy minimizing generalized multiscale discontinuous Galerkin method (CEM-GMsDGM). Combining the technique of…
This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed…
Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…
To efficiently tackle parametrized multi and/or large scale problems, we propose an adaptive localized model order reduction framework combining both local offline training and local online enrichment with localized error control. For the…
In the present paper non-convex multi-objective parameter optimization problems are considered which are governed by elliptic parametrized partial differential equations (PDEs). To solve these problems numerically the Pascoletti-Serafini…
We propose a procedure for the numerical approximation of invariance equations arising in the moment matching technique associated with reduced-order modeling of high-dimensional dynamical systems. The Galerkin residual method is employed…
In this contribution we device and analyze improved variants of the non-conforming dual approach for trust-region reduced basis (TR-RB) approximation of PDE-constrained parameter optimization that has recently been introduced in [Keil et…
We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized {nonlinear} elliptic partial differential equations (PDEs). CB-pMOR is designed to deal with large-scale problems for which full-order…
Variational formulations of time-dependent PDEs in space and time yield $(d+1)$-dimensional problems to be solved numerically. This increases the number of unknowns as well as the storage amount. On the other hand, this approach enables…
Model order reduction (MOR) techniques have always struggled in compressing information for advection dominated problems. Their linear nature does not allow to accelerate the slow decay of the Kolmogorov $N$--width of these problems. In the…
This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of…
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…
Topology Optimization (TO) provides a systematic approach for obtaining structure design with optimum performance of interest. However, the process requires numerical evaluation of objective function and constraints at each iteration, which…
Finite element based simulation of phenomena governed by partial differential equations is a standard tool in many engineering workflows today. However, the simulation of complex geometries is computationally expensive. Many engineering…
State estimation aims at approximately reconstructing the solution $u$ to a parametrized partial differential equation from $m$ linear measurements, when the parameter vector $y$ is unknown. Fast numerical recovery methods have been…
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,…
Model-reduction techniques aim to reduce the computational complexity of simulating dynamical systems by applying a (Petrov-)Galerkin projection process that enforces the dynamics to evolve in a low-dimensional subspace of the original…
Projection-based Reduced Order Models minimize the discrete residual of a "full order model" (FOM) while constraining the unknowns to a reduced dimension space. For problems with symmetric positive definite (SPD) Jacobians, this is…
In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…