{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T00:22:10Z","timestamp":1740097330983,"version":"3.37.3"},"publisher-location":"Cham","reference-count":29,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319405261"},{"type":"electronic","value":"9783319405285"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-40528-5_23","type":"book-chapter","created":{"date-parts":[[2016,9,14]],"date-time":"2016-09-14T02:50:15Z","timestamp":1473821415000},"page":"507-523","source":"Crossref","is-referenced-by-count":2,"title":["Space and Time Parallel Multigrid for Optimization and Uncertainty Quantification in PDE Simulations"],"prefix":"10.1007","author":[{"given":"Lars","family":"Grasedyck","sequence":"first","affiliation":[]},{"given":"Christian","family":"L\u00f6bbert","sequence":"additional","affiliation":[]},{"given":"Gabriel","family":"Wittum","sequence":"additional","affiliation":[]},{"given":"Arne","family":"N\u00e4gel","sequence":"additional","affiliation":[]},{"given":"Volker","family":"Schulz","sequence":"additional","affiliation":[]},{"given":"Martin","family":"Siebenborn","sequence":"additional","affiliation":[]},{"given":"Rolf","family":"Krause","sequence":"additional","affiliation":[]},{"given":"Pietro","family":"Benedusi","sequence":"additional","affiliation":[]},{"given":"Uwe","family":"K\u00fcster","sequence":"additional","affiliation":[]},{"given":"Bj\u00f6rn","family":"Dick","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,9,15]]},"reference":[{"issue":"1","key":"23_CR1","doi-asserted-by":"crossref","first-page":"852","DOI":"10.1137\/140960980","volume":"3","author":"J. Ballani","year":"2015","unstructured":"Ballani, J., Grasedyck, L.: Hierarchical tensor approximation of output quantities of parameter-dependent PDEs. SIAM\/ASA J. Uncertain. Quantif. 3 (1), 852\u2013872 (2015)","journal-title":"SIAM\/ASA J. Uncertain. Quantif."},{"key":"23_CR2","volume-title":"Multigrid Methods IV","author":"P. Bastian","year":"1994","unstructured":"Bastian, P., Wittum, G.: Robustness and adaptivity: the UG concept. In: Hemker, P., Wesseling, P. (eds.) Multigrid Methods IV, Proceedings of the Fourth European Multigrid Conference. Birkh\u00e4user, Basel (1994)"},{"key":"23_CR3","volume-title":"Numerical Mathematics and Advanced Applications \u2013 ENUMATH 2015","author":"P. Benedusi","year":"2016","unstructured":"Benedusi, P., Hupp, D., Arbenz, P., Krause, R.: A parallel multigrid solver for time-periodic incompressible Navier\u2013Stokes equations in 3d. In: Karas\u00f6zen, B., Manguoglu, M., Tezer-Sezgin, M., G\u00f6ktepe, S., Ugur, \u00d6. (eds.) Numerical Mathematics and Advanced Applications \u2013 ENUMATH 2015. Springer, Ankara (2016)"},{"key":"23_CR4","unstructured":"Corporation, I.: Enhanced Intel\u00ae; SpeedStep\u00ae; Technology for the Intel\u00ae; Pentium\u00ae; M Processor. White Paper (2004). http:\/\/download.intel.com\/design\/network\/papers\/30117401.pdf"},{"key":"23_CR5","doi-asserted-by":"crossref","unstructured":"Dahmen, W., DeVore, R., Grasedyck, L., S\u00fcli, E.: Tensor-sparsity of solutions to high-dimensional elliptic partial differential equations. Found. Comput. Math. 1\u201362 (2015). http:\/\/dx.doi.org\/10.1007\/s10208-015-9265-9","DOI":"10.1007\/s10208-015-9265-9"},{"issue":"2","key":"23_CR6","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/s00791-015-0251-1","volume":"17","author":"B. Dick","year":"2015","unstructured":"Dick, B., Vogel, A., Khabi, D., Rupp, M., K\u00fcster, U., Wittum, G.: Utilization of empirically determined energy-optimal CPU-frequencies in a numerical simulation code. Comput. Vis. Sci. 17 (2), 89\u201397 (2015). http:\/\/dx.doi.org\/10.1007\/s00791-015-0251-1","journal-title":"Comput. Vis. Sci."},{"key":"23_CR7","doi-asserted-by":"crossref","first-page":"105","DOI":"10.2140\/camcos.2012.7.105","volume":"7","author":"M. Emmett","year":"2012","unstructured":"Emmett, M., Minion, M.L.: Toward an efficient parallel in time method for partial differential equations. Commun. Appl. Math. Comput. Sci. 7, 105\u2013132 (2012)","journal-title":"Commun. Appl. Math. Comput. Sci."},{"key":"23_CR8","doi-asserted-by":"crossref","first-page":"2029","DOI":"10.1137\/090764189","volume":"31","author":"L. Grasedyck","year":"2010","unstructured":"Grasedyck, L.: Hierarchical singular value decomposition of tensors. SIAM J. Matrix Anal. Appl. 31, 2029\u20132054 (2010)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"5","key":"23_CR9","doi-asserted-by":"crossref","first-page":"A2424","DOI":"10.1137\/130942401","volume":"37","author":"L. Grasedyck","year":"2015","unstructured":"Grasedyck, L., Kluge, M., Kr\u00e4mer, S.: Variants of alternating least squares tensor completion in the tensor train format. SIAM J. Sci. Comput. 37 (5), A2424\u2013A2450 (2015)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"23_CR10","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s00791-015-0247-x","volume":"17","author":"L. Grasedyck","year":"2015","unstructured":"Grasedyck, L., Kriemann, R., L\u00f6bbert, C., N\u00e4gel, A., Wittum, G., Xylouris, K.: Parallel tensor sampling in the hierarchical tucker format. Comput. Vis. Sci. 17 (2), 67\u201378 (2015)","journal-title":"Comput. Vis. Sci."},{"issue":"5","key":"23_CR11","doi-asserted-by":"crossref","first-page":"706","DOI":"10.1007\/s00041-009-9094-9","volume":"15","author":"W. Hackbusch","year":"2009","unstructured":"Hackbusch, W., K\u00fchn, S.: A new scheme for the tensor representation. J. Fourier Anal. Appl. 15 (5), 706\u2013722 (2009)","journal-title":"J. Fourier Anal. Appl."},{"issue":"3","key":"23_CR12","first-page":"421","volume":"13","author":"M. Heisig","year":"1996","unstructured":"Heisig, M., Lieckfeldt, R., Wittum, G., Mazurkevich, G., Lee, G.: Non steady-state descriptions of drug permeation through stratum corneum. I. The biphasic brick-and-mortar model. Pharm. Res. 13 (3), 421\u2013426 (1996)","journal-title":"I. The biphasic brick-and-mortar model. Pharm. Res."},{"issue":"4","key":"23_CR13","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s00791-014-0230-y","volume":"16","author":"M. Hoffer","year":"2013","unstructured":"Hoffer, M., Poliwoda, C., Wittum, G.: Visual reflection library: a framework for declarative gui programming on the java platform. Comput. Vis. Sci. 16 (4), 181\u2013192 (2013)","journal-title":"Comput. Vis. Sci."},{"issue":"3\u20134","key":"23_CR14","first-page":"187","volume":"29","author":"A. Mazouz","year":"2014","unstructured":"Mazouz, A., Laurent, A., Beno\u00eet, P., Jalby, W.: Evaluation of CPU frequency transition latency. Comput. Sci. 29 (3\u20134), 187\u2013195 (2014). http:\/\/dx.doi.org\/10.1007\/s00450-013-0240-x","journal-title":"Comput. Sci."},{"key":"23_CR15","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/978-3-662-05105-4_2","volume-title":"Visualization and Mathematics III","author":"M. Meyer","year":"2003","unstructured":"Meyer, M., Desbrun, M., Schr\u00f6der, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. In: Hege, H.C., Polthier, K. (eds.) Visualization and Mathematics III, pp. 35\u201357. Springer, Berlin (2003)"},{"key":"23_CR16","doi-asserted-by":"crossref","first-page":"S244","DOI":"10.1137\/14097536X","volume":"37","author":"M.L. Minion","year":"2015","unstructured":"Minion, M.L., Speck, R., Bolten, M., Emmett, M., Ruprecht, D.: Interweaving PFASST and parallel multigrid. SIAM J. Sci. Comput. 37, S244\u2013S263 (2015)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"23_CR17","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.ijpharm.2011.02.023","volume":"418","author":"S. Mitragotri","year":"2011","unstructured":"Mitragotri, S., Anissimov, Y.G., Bunge, A.L., Frasch, H.F., Guy, R.H., Hadgraft, J., Kasting, G.B., Lane, M.E., Roberts, M.S.: Mathematical models of skin permeability: an overview. Int. J. Pharm. 418 (1), 115\u2013129 (2011)","journal-title":"Int. J. Pharm."},{"key":"23_CR18","doi-asserted-by":"crossref","unstructured":"Naegel, A., Heisig, M., Wittum, G.: Detailed modeling of skin penetration \u2013 an overview. Adv. Drug Delivery Rev. 65 (2), 191\u2013207 (2013). http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0169409X12003559 . Modeling the human skin barrier \u2013 towards a better understanding of dermal absorption","DOI":"10.1016\/j.addr.2012.10.009"},{"issue":"2","key":"23_CR19","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s00791-015-0248-9","volume":"17","author":"A. N\u00e4gel","year":"2015","unstructured":"N\u00e4gel, A., Schulz, V., Siebenborn, M., Wittum, G.: Scalable shape optimization methods for structured inverse modeling in 3D diffusive processes. Comput. Vis. Sci. 17 (2), 79\u201388 (2015)","journal-title":"Comput. Vis. Sci."},{"issue":"2","key":"23_CR20","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1016\/j.ejpb.2008.11.009","volume":"72","author":"A. N\u00e4gel","year":"2009","unstructured":"N\u00e4gel, A., Heisig, M., Wittum, G.: A comparison of two- and three-dimensional models for the simulation of the permeability of human stratum corneum. Eur. J. Pharm. Biopharm. 72 (2), 332\u2013338 (2009)","journal-title":"Eur. J. Pharm. Biopharm."},{"issue":"4","key":"23_CR21","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/s00791-014-0231-x","volume":"16","author":"S. Reiter","year":"2013","unstructured":"Reiter, S., Vogel, A., Heppner, I., Rupp, M., Wittum, G.: A massively parallel geometric multigrid solver on hierarchically distributed grids. Comput. Vis. Sci. 16 (4), 151\u2013164 (2013). http:\/\/dx.doi.org\/10.1007\/s00791-014-0231-x","journal-title":"Comput. Vis. Sci."},{"key":"23_CR22","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/s10208-014-9200-5","volume":"14","author":"V. Schulz","year":"2014","unstructured":"Schulz, V.: A Riemannian view on shape optimization. Found. Comput. Math. 14, 483\u2013501 (2014)","journal-title":"Found. Comput. Math."},{"key":"23_CR23","unstructured":"Schulz, V., Siebenborn, M.: Computational comparison of surface metrics for PDE constrained shape optimization. Comput. Methods Appl. Math. (submitted) (2015). arxiv.org\/abs\/1509.08601"},{"key":"23_CR24","unstructured":"Schulz, V., Siebenborn, M., Welker, K.: A novel Steklov-Poincar\u00e9 type metric for efficient PDE constrained optimization in shape spaces. SIAM J. Optim. (submitted) (2015). arxiv.org\/abs\/1506.02244"},{"key":"23_CR25","doi-asserted-by":"crossref","unstructured":"Schulz, V., Siebenborn, M., Welker, K.: Structured inverse modeling in parabolic diffusion problems. SIAM J. Control Optim. 53 (6), 3319\u20133338 (2015). arXiv.org\/abs\/1409.3464","DOI":"10.1137\/140985883"},{"key":"23_CR26","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1007\/s10543-014-0517-x","volume":"55","author":"R. Speck","year":"2015","unstructured":"Speck, R., Ruprecht, D., Emmett, M., Minion, M.L., Bolten, M., Krause, R.: A multi-level spectral deferred correction method. BIT Numer. Math. 55, 843\u2013867 (2015)","journal-title":"BIT Numer. Math."},{"key":"23_CR27","doi-asserted-by":"crossref","unstructured":"Speck, R., Ruprecht, D., Minion, M., Emmett, M., Krause, R.: Inexact spectral deferred corrections. In: Domain Decomposition Methods in Science and Engineering XXII. Lecture Notes in Computational Science and Engineering, vol. 104, pp. 127\u2013133. Springer, Cham (2015)","DOI":"10.1007\/978-3-319-18827-0_39"},{"issue":"4","key":"23_CR28","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/s00791-014-0232-9","volume":"16","author":"A. Vogel","year":"2013","unstructured":"Vogel, A., Reiter, S., Rupp, M., N\u00e4gel, A., Wittum, G.: UG4: a novel flexible software system for simulating PDE based models on high performance computers. Comput. Vis. Sci. 16 (4), 165\u2013179 (2013). http:\/\/dx.doi.org\/10.1007\/s00791-014-0232-9","journal-title":"Comput. Vis. Sci."},{"issue":"2","key":"23_CR29","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s00791-015-0250-2","volume":"17","author":"G. Wittum","year":"2015","unstructured":"Wittum, G.: Editorial: algorithmic requirements for HPC. Comput. Vis. Sci. 17 (2), 65\u201366 (2015)","journal-title":"Comput. Vis. Sci."}],"container-title":["Lecture Notes in Computational Science and Engineering","Software for Exascale Computing - SPPEXA 2013-2015"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-40528-5_23","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,13]],"date-time":"2019-09-13T09:13:11Z","timestamp":1568365991000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-40528-5_23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319405261","9783319405285"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-40528-5_23","relation":{},"ISSN":["1439-7358","2197-7100"],"issn-type":[{"type":"print","value":"1439-7358"},{"type":"electronic","value":"2197-7100"}],"subject":[],"published":{"date-parts":[[2016]]}}}