Related papers: An EIM-degradation free reduced basis method via o…
The Reduced Basis Method (RBM) is a model reduction technique used to solve parametric PDEs that relies upon a basis set of solutions to the PDE at specific parameter values. To generate this reduced basis, the set of a small number of…
The Reduced Basis Method (RBM) is a popular certified model reduction approach for solving parametrized partial differential equations. One critical stage of the \textit{offline} portion of the algorithm is a greedy algorithm, requiring…
The Reduced Basis (RB) method is a well established method for the model order reduction of problems formulated as parametrized partial differential equations. One crucial requirement for the application of RB schemes is the availability of…
This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient…
This paper introduces a generalization of the empirical interpolation method (EIM) and the reduced basis method (RBM) in order to allow their combination with data mining and data assimilation. The purpose is to be able to derive sound…
In this paper, we present the first reduced basis method well-suited for the collocation framework. Two fundamentally different algorithms are presented: the so-called Least Squares Reduced Collocation Method (LSRCM) and Empirical Reduced…
This contribution explores the combined capabilities of reduced basis methods and IsoGeometric Analysis (IGA) in the context of parameterized partial differential equations. The introduction of IGA enables a unified simulation framework…
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…
Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions --- computed for properly chosen parameters, using a full-order…
We present a model reduction approach that extends the original empirical interpolation method to enable accurate and efficient reduced basis approximation of parametrized nonlinear partial differential equations (PDEs). In the presence of…
The Poisson-Boltzmann equation (PBE) is a nonlinear elliptic PDE that arises in biomolecular modeling and is a fundamental tool for structural biology. It is used to calculate electrostatic potentials around an ensemble of fixed charges…
The radiative transfer equation (RTE) is a fundamental mathematical model to describe physical phenomena involving the propagation of radiation and its interactions with the host medium. Deterministic methods can produce accurate solutions…
The Reduced Basis Method can be exploited in an efficient way only if the so-called affine dependence assumption on the operator and right-hand side of the considered problem with respect to the parameters is satisfied. When it is not, the…
This contribution presents a model order reduction strategy for fast parametric modelling of problems with cracks formulated on spline discretizations. In the context of damage detection, parametric reduced order models (ROMs) are well…
A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems are presented. First, the Galerkin reduced basis (RB) formulation is presented which…
In gradient-based time domain topology optimization, design sensitivity analysis (DSA) of the dynamic response is essential, and requires high computational cost to directly differentiate, especially for high-order dynamic system. To…
Finite-sample bias is a pervasive challenge in the estimation of structural equation models (SEMs), especially when sample sizes are small or measurement reliability is low. A range of methods have been proposed to improve finite-sample…
Real-world systems are often characterized by high-dimensional nonlinear dynamics, making them challenging to control in real time. While reduced-order models (ROMs) are frequently employed in model-based control schemes, dimensionality…
We consider the elastic scattering problem by multiple disjoint arcs or \emph{cracks} in two spatial dimensions. A key aspect of our approach lies in the parametric description of each arc's shape, which is controlled by a potentially…
Scientific and engineering problems often involve parametric partial differential equations (PDEs), such as uncertainty quantification, optimizations, and inverse problems. However, solving these PDEs repeatedly can be prohibitively…