Complex physical models depending on microstructures developing over
time often result in simulation schemes that are very demanding concerning
computational time. The two-scale model considered in the current
presentation describes a phase transition of a binary mixture with
the evolution of equiaxed dendritic microstructures. It consists
of a macroscopic heat equation and a family of microscopic cell problems
modeling the phase transition. Those phase transitions need to be
resolved by very fine computational meshes leading to the demanding
numerical complexity. The current study presents a reduced version
of this two-scale model. The reduction aims at accelerating the microscopic
model, which is parametrized by the macroscopic temperature, while
maintaining the accuracy of the detailed system. Parameter dependency,
non-linearity, time-dependency, coupled field-variables and high
solution complexity are challenging difficulties. They are addressed
by a combination of several approaches: Proper Orthogonal Decomposition
(POD), Empirical Interpolation Method (EIM) and a partitioning approach
generating sub-models for different solution regimes. A new partitioning
criterion based on feature extraction is applied. The applicability
of the reduction scheme is demonstrated experimentally: while the
accuracy is largely maintained, the dimensionality of the detailed
model and the computation time are reduced significantly.
%0 Journal Article
%1 redeker2015podeim
%A Redeker, Magnus
%A Haasdonk, Bernard
%D 2015
%I Springer US
%J Advances in Computational Mathematics
%K 78M34 Empirical Model Parametrized Proper decomposition; from:mhartmann ians interpolation; model; orthogonal reduction; two-scale vorlaeufig
%N 5
%P 987--1013
%R 10.1007/s10444-014-9367-y
%T A POD-EIM reduced two-scale model for crystal growth
%U http://dx.doi.org/10.1007/s10444-014-9367-y
%V 41
%X Complex physical models depending on microstructures developing over
time often result in simulation schemes that are very demanding concerning
computational time. The two-scale model considered in the current
presentation describes a phase transition of a binary mixture with
the evolution of equiaxed dendritic microstructures. It consists
of a macroscopic heat equation and a family of microscopic cell problems
modeling the phase transition. Those phase transitions need to be
resolved by very fine computational meshes leading to the demanding
numerical complexity. The current study presents a reduced version
of this two-scale model. The reduction aims at accelerating the microscopic
model, which is parametrized by the macroscopic temperature, while
maintaining the accuracy of the detailed system. Parameter dependency,
non-linearity, time-dependency, coupled field-variables and high
solution complexity are challenging difficulties. They are addressed
by a combination of several approaches: Proper Orthogonal Decomposition
(POD), Empirical Interpolation Method (EIM) and a partitioning approach
generating sub-models for different solution regimes. A new partitioning
criterion based on feature extraction is applied. The applicability
of the reduction scheme is demonstrated experimentally: while the
accuracy is largely maintained, the dimensionality of the detailed
model and the computation time are reduced significantly.
@article{redeker2015podeim,
abstract = {Complex physical models depending on microstructures developing over
time often result in simulation schemes that are very demanding concerning
computational time. The two-scale model considered in the current
presentation describes a phase transition of a binary mixture with
the evolution of equiaxed dendritic microstructures. It consists
of a macroscopic heat equation and a family of microscopic cell problems
modeling the phase transition. Those phase transitions need to be
resolved by very fine computational meshes leading to the demanding
numerical complexity. The current study presents a reduced version
of this two-scale model. The reduction aims at accelerating the microscopic
model, which is parametrized by the macroscopic temperature, while
maintaining the accuracy of the detailed system. Parameter dependency,
non-linearity, time-dependency, coupled field-variables and high
solution complexity are challenging difficulties. They are addressed
by a combination of several approaches: Proper Orthogonal Decomposition
(POD), Empirical Interpolation Method (EIM) and a partitioning approach
generating sub-models for different solution regimes. A new partitioning
criterion based on feature extraction is applied. The applicability
of the reduction scheme is demonstrated experimentally: while the
accuracy is largely maintained, the dimensionality of the detailed
model and the computation time are reduced significantly.},
added-at = {2018-07-20T10:54:46.000+0200},
author = {Redeker, Magnus and Haasdonk, Bernard},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/26c36981e661041cc94b573a0415660d4/mathematik},
doi = {10.1007/s10444-014-9367-y},
file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Redeker2014_www_preprint_POD_EIM_crystal_growth.pdf:PDF},
interhash = {281ab3f9ebcc66666b576054b40b68a1},
intrahash = {6c36981e661041cc94b573a0415660d4},
issn = {1019-7168},
journal = {Advances in Computational Mathematics},
keywords = {78M34 Empirical Model Parametrized Proper decomposition; from:mhartmann ians interpolation; model; orthogonal reduction; two-scale vorlaeufig},
language = {English},
number = 5,
owner = {redeker},
pages = {987--1013},
publisher = {Springer US},
timestamp = {2019-12-18T14:37:55.000+0100},
title = {A {POD-EIM} reduced two-scale model for crystal growth},
url = {http://dx.doi.org/10.1007/s10444-014-9367-y},
volume = 41,
year = 2015
}
