{ "types" : { "Bookmark" : { "pluralLabel" : "Bookmarks" }, "Publication" : { "pluralLabel" : "Publications" }, "GoldStandardPublication" : { "pluralLabel" : "GoldStandardPublications" }, "GoldStandardBookmark" : { "pluralLabel" : "GoldStandardBookmarks" }, "Tag" : { "pluralLabel" : "Tags" }, "User" : { "pluralLabel" : "Users" }, "Group" : { "pluralLabel" : "Groups" }, "Sphere" : { "pluralLabel" : "Spheres" } }, "properties" : { "count" : { "valueType" : "number" }, "date" : { "valueType" : "date" }, "changeDate" : { "valueType" : "date" }, "url" : { "valueType" : "url" }, "id" : { "valueType" : "url" }, "tags" : { "valueType" : "item" }, "user" : { "valueType" : "item" } }, "items" : [ { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/231349ea93435c3ff57fe0a82903585ad/mhartmann", "tags" : [ "Clarifier-thickener","model","vorlaeufig" ], "intraHash" : "31349ea93435c3ff57fe0a82903585ad", "interHash" : "30f48a0a2ba2fcd4d880f12e258508a3", "label" : "Computational uncertainty quantification for a clarifier-thickener\n\tmodel with several random perturbations: A hybrid stochastic Galerkin\n\tapproach", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "count" : 1, "pub-type": "article", "journal": "Computers & Chemical Engineering", "year": "2016", "url": "http://www.sciencedirect.com/science/article/pii/S0098135416300503", "author": [ "Andrea Barth","Raimund B�rger","Ilja Kröker","Christian Rohde" ], "authors": [ {"first" : "Andrea", "last" : "Barth"}, {"first" : "Raimund", "last" : "B�rger"}, {"first" : "Ilja", "last" : "Kröker"}, {"first" : "Christian", "last" : "Rohde"} ], "volume": "89","pages": "11 -- 26", "issn" : "0098-1354", "owner" : "seusdd", "doi" : "http://dx.doi.org/10.1016/j.compchemeng.2016.02.016", "bibtexKey": "barth2016computational" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2699c9caf6155e0598d9c980105b8118d/mhartmann", "tags" : [ "a-posteriori","decomposition,","dynamical","error","estimates,","kernel","methods,","model","nonlinear","offline/online","projection","reduction,","subspace","systems,","vorlaeufig" ], "intraHash" : "699c9caf6155e0598d9c980105b8118d", "interHash" : "e80ae72fe2c1f9f79f4f7f8f5ce00735", "label" : "Efficient a-posteriori error estimation for nonlinear kernel-based\n\treduced systems", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "count" : 11, "pub-type": "article", "journal": "Systems and Control Letters", "year": "2012", "url": "http://www.sciencedirect.com/science/article/pii/S0167691111002672", "author": [ "D. Wirtz","B. Haasdonk" ], "authors": [ {"first" : "D.", "last" : "Wirtz"}, {"first" : "B.", "last" : "Haasdonk"} ], "volume": "61","number": "1","pages": "203 - 211","abstract": "In this paper, we consider the topic of model reduction for nonlinear\n\tdynamical systems based on kernel expansions. Our approach allows\n\tfor a full offline/online decomposition and efficient online computation\n\tof the reduced model. In particular, we derive an a-posteriori state-space\n\terror estimator for the reduction error. A key ingredient is a local\n\tLipschitz constant estimation that enables rigorous a-posteriori\n\terror estimation. The computation of the error estimator is realized\n\tby solving an auxiliary differential equation during online simulations.\n\tEstimation iterations can be performed that allow a balancing between\n\testimation sharpness and computation time. Numerical experiments\n\tdemonstrate the estimation improvement over different estimator versions\n\tand the rigor and effectiveness of the error bounds.", "file" : ":/home/dwirtz/dwirtzwww/WH10_preprint.pdf:PDF", "doi" : "10.1016/j.sysconle.2011.10.012", "bibtexKey": "wirtz2012efficient" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/26c36981e661041cc94b573a0415660d4/mhartmann", "tags" : [ "78M34","Empirical","Model","Parametrized","Proper","decomposition;","interpolation;","model;","orthogonal","reduction;","two-scale","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" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2c9ff784e6a0440b80b45055fa2c9df7e/mhartmann", "tags" : [ "a-posteriori","decomposition,","dynamical","error","estimates,","kernel","methods,","model","nonlinear","offline/online","parameterized","projection","reduction,","subspace","systems,","vorlaeufig" ], "intraHash" : "c9ff784e6a0440b80b45055fa2c9df7e", "interHash" : "e6dce191069323c30bda8a87cce2913a", "label" : "A-posteriori error estimation for parameterized kernel-based systems", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "count" : 8, "pub-type": "inproceedings", "booktitle": "Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical\n\tModelling", "year": "2012", "url": "http://www.ifac-papersonline.net/", "author": [ "Daniel Wirtz","Bernard Haasdonk" ], "authors": [ {"first" : "Daniel", "last" : "Wirtz"}, {"first" : "Bernard", "last" : "Haasdonk"} ], "abstract": "This work is concerned with derivation of fully offine/online decomposable\n\teffcient aposteriori error estimators for reduced parameterized nonlinear\n\tkernel-based systems. The dynamical systems under consideration consist\n\tof a nonlinear, time- and parameter-dependent kernel expansion representing\n\tthe system's inner dynamics as well as time- and parameter-affne\n\tinputs, initial conditions and outputs. The estimators are established\n\tfor a reduction technique originally proposed in [7] and are an extension\n\tof the estimators derived in [11] to the fully time-dependent, parameterized\n\tsetting. Key features for the effcient error estimation are to use\n\tlocal Lipschitz constants provided by a certain class of kernels\n\tand an iterative scheme to balance computation cost against estimation\n\tsharpness. Together with the affnely time/parameter-dependent system\n\tcomponents a full offine/online decomposition for both the reduction\n\tprocess and the error estimators is possible. Some experimental results\n\tfor synthetic systems illustrate the effcient evaluation of the derived\n\terror estimators for different parameters.", "owner" : "haasdonk", "bibtexKey": "wirtz2012aposteriori" } ] }