English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The reduced basis method (RBM) empowers repeated and rapid evaluation ofparametrized partial differential equations through an offline-onlinedecomposition, a.k.a. a learning-execution process. A key feature of the methodis a greedy algorithm repeatedly scanning the training set, a finediscretization of the parameter domain, to identify the next dimension of theparameter-induced solution manifold along which we expand the surrogatesolution space. Although successfully applied to problems with fairly highparametric dimensions, the challenge is that this scanning cost dominates theoffline cost due to it being proportional to the cardinality of the trainingset which is exponential with respect to the parameter dimension. In this work,we review three recent attempts in effectively delaying this curse ofdimensionality, and propose two new hybrid strategies through successiverefinement and multilevel maximization of the error estimate over the trainingset. All five offline-enhanced methods and the original greedy algorithm aretested and compared on {two types of problems: the thermal block problem andthe geometrically parameterized Helmholtz problem.

Adaptive greedy algorithms based on parameter-domain decomposition and reconstruction for the reduced basis method