Related papers: Localized Reduced Basis Additive Schwarz Methods
In this paper, we propose a new approach to model reduction of parameterized partial differential equations (PDEs) based on the concept of adaptive reduced bases. The presented approach is particularly suited for large-scale nonlinear…
A local approach to the time integration of PDEs by exponential methods is proposed, motivated by theoretical estimates by A.Iserles on the decay of off-diagonal terms in the exponentials of sparse matrices. An overlapping domain…
In this paper we revisit the Restricted Additive Schwarz method for solving discretized Helmholtz problems, using impedance boundary conditions on subdomains (sometimes called ORAS). We present this method in its variational form and show…
Parameter space reduction has been proved to be a crucial tool to speed-up the execution of many numerical tasks such as optimization, inverse problems, sensitivity analysis, and surrogate models' design, especially when in presence of…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…
Fractional Laplace equations are becoming important tools for mathematical modeling and prediction. Recent years have shown much progress in developing accurate and robust algorithms to numerically solve such problems, yet most solvers for…
We consider the computation of averaged coefficients for the homogenization of elliptic partial differential equations. In this problem, like in many multiscale problems, a large number of similar computations parametrized by the…
We consider parameter identification problems in parametrized partial differential equations (PDE). This leads to nonlinear ill-posed inverse problems. One way to solve them are iterative regularization methods, which typically require…
Random sampling has been used to find low-rank structure and to build fast direct solvers for multiscale partial differential equations of various types. In this work, we design an accelerated Schwarz method for radiative transfer equations…
In this research, an online basis enrichment strategy for the constraint energy minimizing generalized multiscale finite element method in mixed formulation is proposed. The online approach is based on the technique of oversampling. One…
Dimension reduction is often needed in the area of data mining. The goal of these methods is to map the given high-dimensional data into a low-dimensional space preserving certain properties of the initial data. There are two kinds of…
We present a class of reduced basis (RB) methods for the iterative solution of parametrized symmetric positive-definite (SPD) linear systems. The essential ingredients are a Galerkin projection of the underlying parametrized system onto a…
In this paper, a methodology for fine scale modeling of large scale structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse…
We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…
We are interested in the approximation of partial differential equations with a data-driven approach based on the reduced basis method and machine learning. We suppose that the phenomenon of interest can be modeled by a parametrized partial…
In this work, we propose a novel model order reduction approach for two-phase flow in porous media by introducing a formulation in which the mobility, which realizes the coupling between phase saturations and phase pressures, is regarded as…
The paper presents a novel methodology to build surrogate models of complicated functions by an active learning-based sequential decomposition of the input random space and construction of localized polynomial chaos expansions, referred to…
In this paper, we propose a certified reduced basis (RB) method for quasilinear elliptic problems together with its application to nonlinear magnetostatics equations, where the later model permanent magnet synchronous motors (PMSM). The…
A two-level overlapping Schwarz method is developed for second order elliptic problems with highly oscillatory and high contrast coefficients, for which it is known that the standard coarse problem fails to give a robust preconditioner. In…