Related papers: The Frequency Reduced-Basis method: Reduced order …
In this work, we present an approach for the efficient treatment of parametrized geometries in the context of POD-Galerkin reduced order methods based on Finite Volume full order approximations. On the contrary to what is normally done in…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
In this work, we address parametric non-stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the optimisation-based domain decomposition approach, we derive an optimal…
This article presents an innovative approach for developing an efficient reduced-order model to study the dispersion of urban air pollutants. The need for real-time air quality monitoring has become increasingly important, given the rise in…
In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the…
In this paper we present algorithms for an efficient implementation of the Localized Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical simulation of partial differential equations with a continuum of…
Transport-dominated phenomena provide a challenge for common mode-based model reduction approaches. We present a model reduction method, which is suited for these kind of systems. It extends the proper orthogonal decomposition (POD) by…
We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…
In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We…
In this paper, we present a new nonintrusive reduced basis method when a cheap low-fidelity model and expensive high-fidelity model are available. The method relies on proper orthogonal decomposition (POD) to generate the high-fidelity…
The use of model-based numerical simulation of wave propagation in rooms for engineering applications requires that acoustic conditions for multiple parameters are evaluated iteratively and this is computationally expensive. We present a…
This paper focuses on the numerical solution of a dual-phase-lag heat conduction equation on a space unbounded domain. First, based on the Laplace transform and the Pad\'e approximation, a high-order local artificial boundary condition is…
The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is…
This paper presents a novel method that allows to generalise the use of the Adam-Bashforth to Partial Differential Equations with local and non local operator. The Method derives a two step Adam-Bashforth numerical scheme in Laplace space…
We propose a multiscale method for mixed-dimensional elliptic problems with highly heterogeneous coefficients arising, for example, in the modeling of fractured porous media. The method is based on the Localized Orthogonal Decomposition…
Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…
We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…
Time domain simulations of electromagnetic problems are highly valuable in engineering applications, as they allow for the analysis of transient behavior and broadband responses. These simulations utilize time stepping schemes, where each…
In the context of simulation-based methods, multiple challenges arise, two of which are considered in this work. As a first challenge, problems including time-dependent phenomena with complex domain deformations, potentially even with…