Publication

On the asymptotic optimality of spectral coarse spaces

Publications associées (30)

A hierarchical preconditioner for wave problems in quasilinear complexity

The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit the property th ...

2022

Isogeometric analysis with C1 hierarchical functions on planar two-patch geometries

Rafael Vazquez Hernandez

Adaptive isogeometric methods for the solution of partial diifferential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to apply the multi-level construction of hierarchical spline ...

2020

Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis

Annalisa Buffa, Rafael Vazquez Hernandez

We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t. the surface differential operators. Using these result ...

Springer2020

Random extrapolation for primal-dual coordinate descent

Volkan Cevher, Ahmet Alacaoglu

We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with sparse data, an ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2020

Multi space reduced basis preconditioners for parametrized Stokes equations

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

We introduce a two-level preconditioner for the efficient solution of large scale saddle point linear systems arising from the finite element (FE) discretization of parametrized Stokes equations. This preconditioner extends the Multi Space Reduced Basis (M ...

PERGAMON-ELSEVIER SCIENCE LTD2019

Homogenization of Multiscale Eddy Current Problem by Localized Orthogonal Decomposition Method

Xiaotao Ren

A homogenization approach for the solution of multiscale eddy current problem is proposed. The method is based on the subspace decomposition and it involves a coarse space and a nested fine space. The homogenized problem is posed in the coarse space with t ...

Institute of Electrical and Electronics Engineers2019

Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings

Masato Mimura

The objective of this series is to study metric geometric properties of disjoint unions of Cayley graphs of amenable groups by group properties of the Cayley accumulation points in the space of marked groups. In this Part II, we prove that a disjoint union ...

2019

Multi space reduced basis preconditioners for parametrized partial differential equations

Niccolò Dal Santo

The multiquery solution of parametric partial differential equations (PDEs), that is, PDEs depending on a vector of parameters, is computationally challenging and appears in several engineering contexts, such as PDE-constrained optimization, uncertainty qu ...

EPFL2018

Efficient preconditioning of hp-FEM matrices arising from time-varying problems: an application to topology optimization

Jan Sickmann Hesthaven, Paolo Gatto

We previously introduced a preconditioner that has proven effective for hp-FEM dis- cretizations of various challenging elliptic and hyperbolic problems. The construc- tion is inspired by standard nested dissection, and relies on the assumption that the Sc ...

Elsevier2017

Efficient Preconditioning of hp-FEM Matrices by Hierarchical Low-Rank Approximations

Jan Sickmann Hesthaven, Paolo Gatto

We introduce a preconditioner based on a hierarchical low-rank compression scheme of Schur complements. The construction is inspired by standard nested dissection, and relies on the assumption that the Schur complements can be approximated, to high precisi ...

Springer Verlag2017