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         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/26c36981e661041cc94b573a0415660d4/mhartmann",         
         "tags" : [
            "reduction;","Empirical","two-scale","decomposition;","Parametrized","78M34","Proper","orthogonal","interpolation;","Model","model;","vorlaeufig"
         ],
         
         "intraHash" : "6c36981e661041cc94b573a0415660d4",
         "interHash" : "281ab3f9ebcc66666b576054b40b68a1",
         "label" : "A POD-EIM reduced two-scale model for crystal growth",
         "user" : "mhartmann",
         "description" : "",
         "date" : "2018-07-20 10:54:15",
         "changeDate" : "2018-07-20 08:54:15",
         "count" : 8,
         "pub-type": "article",
         "journal": "Advances in Computational Mathematics","publisher":"Springer US",
         "year": "2015", 
         "url": "http://dx.doi.org/10.1007/s10444-014-9367-y", 
         
         "author": [ 
            "Magnus Redeker","Bernard Haasdonk"
         ],
         "authors": [
         	
            	{"first" : "Magnus",	"last" : "Redeker"},
            	{"first" : "Bernard",	"last" : "Haasdonk"}
         ],
         "volume": "41","number": "5","pages": "987--1013","abstract": "Complex physical models depending on microstructures developing over\n\ttime often result in simulation schemes that are very demanding concerning\n\tcomputational time. The two-scale model considered in the current\n\tpresentation describes a phase transition of a binary mixture with\n\tthe evolution of equiaxed dendritic microstructures. It consists\n\tof a macroscopic heat equation and a family of microscopic cell problems\n\tmodeling the phase transition. Those phase transitions need to be\n\tresolved by very fine computational meshes leading to the demanding\n\tnumerical complexity. The current study presents a reduced version\n\tof this two-scale model. The reduction aims at accelerating the microscopic\n\tmodel, which is parametrized by the macroscopic temperature, while\n\tmaintaining the accuracy of the detailed system. Parameter dependency,\n\tnon-linearity, time-dependency, coupled field-variables and high\n\tsolution complexity are challenging difficulties. They are addressed\n\tby a combination of several approaches: Proper Orthogonal Decomposition\n\t(POD), Empirical Interpolation Method (EIM) and a partitioning approach\n\tgenerating sub-models for different solution regimes. A new partitioning\n\tcriterion based on feature extraction is applied. The applicability\n\tof the reduction scheme is demonstrated experimentally: while the\n\taccuracy is largely maintained, the dimensionality of the detailed\n\tmodel and the computation time are reduced significantly.",
         "issn" : "1019-7168",
         
         "file" : ":http\\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/Redeker2014_www_preprint_POD_EIM_crystal_growth.pdf:PDF",
         
         "owner" : "redeker",
         
         "language" : "English",
         
         "doi" : "10.1007/s10444-014-9367-y",
         
         "bibtexKey": "redeker2015podeim"

      }
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         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/23dd6f86fc81e402da2863b42b274769f/mhartmann",         
         "tags" : [
            "phase","Phase","solutions","Two-scale","elasticity;","regularity","models;","with","Liquid","of","field","and","epitaxy","model;","vorlaeufig","Existence"
         ],
         
         "intraHash" : "3dd6f86fc81e402da2863b42b274769f",
         "interHash" : "6bd6b727acd4d159816a6108339ac0f4",
         "label" : "Well-Posedness of a Two Scale Model for Liquid Phase Epitaxy with\n\tElasticity",
         "user" : "mhartmann",
         "description" : "",
         "date" : "2018-07-20 10:54:15",
         "changeDate" : "2018-07-20 08:54:15",
         "count" : 2,
         "pub-type": "article",
         "journal": "Contin. Mech. Thermodyn.",
         "year": "2017", 
         "url": "http://dx.doi.org/10.1007/s00161-015-0462-1", 
         
         "author": [ 
            "Michael Kutter","Christian Rohde","Anna-Margarete Sändig"
         ],
         "authors": [
         	
            	{"first" : "Michael",	"last" : "Kutter"},
            	{"first" : "Christian",	"last" : "Rohde"},
            	{"first" : "Anna-Margarete",	"last" : "Sändig"}
         ],
         "volume": "29","number": "4","pages": "989-1016",
         "issn" : "0935-1175",
         
         "owner" : "seusdd",
         
         "doi" : "10.1007/s00161-015-0462-1",
         
         "bibtexKey": "kutter2017wellposedness"

      }
	  
   ]
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