Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localized model reduction for nonlinear elliptic partial differential
  equations: localized training, partition of unity, and adaptive enrichment   We propose a component-based (CB) parametric model order reduction (pMOR)
formulation for parameterized {nonlinear} elliptic partial differential
equations (PDEs). CB-pMOR is designed to deal with large-scale problems for
which full-order solves are not affordable in a reasonable time frame or
parameters' variations induce topology changes that prevent the application of
monolithic pMOR techniques. We rely on the partition-of-unity method (PUM) to
devise global approximation spaces from local reduced spaces, and on Galerkin
projection to compute the global state estimate. We propose a randomized data
compression algorithm based on oversampling for the construction of the
components' reduced spaces: the approach exploits random boundary conditions of
controlled smoothness on the oversampling boundary. We further propose an
adaptive residual-based enrichment algorithm that exploits global reduced-order
solves on representative systems to update the local reduced spaces. We prove
exponential convergence of the enrichment procedure for linear coercive
problems; we further present numerical results for a two-dimensional nonlinear
diffusion problem to illustrate the many features of our proposal and
demonstrate its effectiveness.

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The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph