Related papers: A Reduced Order Modeling Method with Variable-Sepa…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
Partitioned methods allow one to build a simulation capability for coupled problems by reusing existing single-component codes. In so doing, partitioned methods can shorten code development and validation times for multiphysics and…
This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…
This paper is concerned with the numerical solution of compressible fluid flow in a fractured porous medium. The fracture represents a fast pathway (i.e., with high permeability) and is modeled as a hypersurface embedded in the porous…
This work recasts time-dependent optimal control problems governed by partial differential equations in a Dynamic Mode Decomposition with control framework. Indeed, since the numerical solution of such problems requires a lot of…
A comprehensive approach for real-time computations using a database of parameterized linear reduced-order models (ROMs) is proposed. The method proceeds by sampling offline ROMs for specific values of the parameters and interpolating…
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…
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…
In recent years, large-scale numerical simulations played an essential role in estimating the effects of explosion events in urban environments, for the purpose of ensuring the security and safety of cities. Such simulations are…
Nonlinear and nonaffine terms in parametric partial differential equations can potentially lead to a computational cost of a reduced order model (ROM) that is comparable to the cost of the original full order model (FOM). To address this,…
We propose a novel numerical algorithm utilizing model reduction for computing solutions to stationary partial differential equations involving the spectral fractional Laplacian. Our approach utilizes a known characterization of the…
A parallelizable iterative procedure based on domain decomposition is presented and analyzed for weak Galerkin finite element methods for second order elliptic equations. The convergence analysis is established for the decomposition of the…
In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, our goal is a contribution towards the development of…
A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…
In this contribution, a finite element scheme to impose mixed boundary conditions without introducing Lagrange multipliers is presented for hyperbolic systems described as port-Hamiltonian systems. The strategy relies on finite element…
A hydraulic fracturing system with super-hydrophobic proppants is characterized by a transient triple-porosity Navier-Stokes model. For this complex multiphysics system, particularly in the context of three-dimensional space, a local…
We focus on the numerical modelling of water waves by means of depth averaged models. We consider in particular PDE systems which consist in a nonlinear hyperbolic model plus a linear dispersive perturbation involving an elliptic operator.…
We propose an efficient algorithm that combines overlapping domain decomposition and proper generalized decomposition (PGD) to construct surrogate models of linear elliptic parametric problems. The technique is composed of an offline and an…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…
We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected…