Related papers: An introduction to POD-Greedy-Galerkin reduced bas…
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…
In this paper, we propose a certified reduced basis (RB) method for quasilinear parabolic problems. The method is based on a space-time variational formulation. We provide a residual-based a-posteriori error bound on a space-time level and…
Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and…
At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But the computation of the high order derivatives of neural networks is costly,…
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…
A reduced-order model algorithm, based on approximations of Lax pairs, is proposed to solve nonlinear evolution partial differential equations. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the space where…
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…
In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes…
In this chapter we examine reduced order techniques for geometrical parametrized heat exchange systems, Poisson, and flows based on Stokes, steady and unsteady incompressible Navier-Stokes and Cahn-Hilliard problems. The full order finite…
We investigate reduced-order models for acoustic and electromagnetic wave problems in parametrically defined domains. The parameter-to-solution maps are approximated following the so-called Galerkin POD-NN method, which combines the…
In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties that originate from active forces generated from…
In this work we present a Reduced Order Model which is specifically designed to deal with turbulent flows in a finite volume setting. The method used to build the reduced order model is based on the idea of merging/combining…
In this paper, we study numerically the linear damped second-order hyperbolic partial differential equation (PDE) with affine parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The…
Reduced Order Models (ROMs) have gained a great attention by the scientific community in the last years thanks to their capabilities of significantly reducing the computational cost of the numerical simulations, which is a crucial objective…
We propose in this paper an adaptive reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus…
The quantification of multivariate uncertainties in partial differential equations can easily exceed any computing capacity unless proper measures are taken to reduce the complexity of the model. In this work, we propose a multidimensional…
In the present work, we investigate a cut finite element method for the parameterized system of second-order equations stemming from the splitting approach of a fourth order nonlinear geometrical PDE, namely the Cahn-Hilliard system. We…
We propose in this paper a Proper Generalized Decomposition (PGD) approach for the solution of problems in linear elastodynamics. The novelty of the work lies in the development of weak formulations of the PGD problems based on the…
We consider linear dynamical systems of ordinary differential equations or differential algebraic equations. Physical parameters are substituted by random variables for an uncertainty quantification. We expand the state variables as well as…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…