Generalized multiscale discontinuous Galerkin method for solving the heat problem with phase change

Stepanov, Sergei; Vasilyeva, Maria; Васильев, В. И.

doi:10.1016/j.cam.2017.12.004

Cited by 19 publications

(3 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the context of multiscale problems (cf. Example 6.2), the generalized multiscale discontinuous Galerkin method has been proposed in [29,30] and used for solving the heat problem with phase change in [107]. We will present the LRBMS method in Section 6.3.2.2.…”

Section: Nonconforming Approachmentioning

confidence: 99%

6 Localized model reduction for parameterized problems

Buhr

Iapichino

Ohlberger

et al. 2020

Snapshot-Based Methods and Algorithms

View full text Add to dashboard Cite

Section: Nonconforming Approachmentioning

confidence: 99%

6 Localized model reduction for parameterized problems

Buhr

Iapichino

Ohlberger

et al. 2020

Snapshot-Based Methods and Algorithms

View full text Add to dashboard Cite

“…In the context of multiscale problems (cf. Example 2.2), the generalized multiscale discontinuous Galerkin method has been proposed in [CEL17a,CEL18b] and used for solving the heat problem with phase change in [SVV18]. In this chapter we are going to present the localized reduced basis method (LRBMS) in Subsection 3.2.2 below.…”

Section: }mentioning

confidence: 99%

Localized model reduction for parameterized problems

Buhr¹,

Iapichino²,

Ohlberger³

et al. 2019

Preprint

View full text Add to dashboard Cite

In this contribution we present a survey of concepts in localized model order reduction methods for parameterized partial differential equations.The key concept of localized model order reduction is to construct local reduced spaces that have only support on part of the domain and compute a global approximation by a suitable coupling of the local spaces. In detail, we show how optimal local approximation spaces can be constructed and approximated by random sampling. An overview of possible conforming and non-conforming couplings of the local spaces is provided and corresponding localized a posteriori error estimates are derived. We introduce concepts of local basis enrichment, which includes a discussion of adaptivity. Implementational aspects of localized model reduction methods are addressed. Finally, we illustrate the presented concepts for multiscale, linear elasticity and fluid-flow problems, providing several numerical experiments. This work has been accepted as a chapter in P.

show abstract

“…Several feasibility restrictions limit their experimental investigation such as their cost and the availability of suitable facilities. Therefore, it is an application that requires the development of sophisticated and representative numerical models, among others, for the phase change problem, for the liquid film and for aerodynamics [5,6,7]. To what concerns anti-ice IPS, very limited experimental measurements are publicly available in the open literature.…”

mentioning

confidence: 99%