SCIENTIFIC COMPUTING AND IMAGING INSTITUTE
at the University of Utah

An internationally recognized leader in visualization, scientific computing, and image analysis

SCI Publications

2005


D. Xiu, J.S. Hesthaven. “High Order Collocation Methods for Differential Equations with Random Inputs,” In SIAM Journal on Scientific Computing, Vol. 27, No. 3, pp. 1118--1139. 2005.
DOI: 10.1137/040615201

ABSTRACT

Recently there has been a growing interest in designing efficient methods for the solution of ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin methods appear to be superior to other nonsampling methods and, in many cases, to several sampling methods. However, when the governing equations take complicated forms, numerical implementations of stochastic Galerkin methods can become nontrivial and care is needed to design robust and efficient solvers for the resulting equations. On the other hand, the traditional sampling methods, e.g., Monte Carlo methods, are straightforward to implement, but they do not offer convergence as fast as stochastic Galerkin methods. In this paper, a high-order stochastic collocation approach is proposed. Similar to stochastic Galerkin methods, the collocation methods take advantage of an assumption of smoothness of the solution in random space to achieve fast convergence. However, the numerical implementation of stochastic collocation is trivial, as it requires only repetitive runs of an existing deterministic solver, similar to Monte Carlo methods. The computational cost of the collocation methods depends on the choice of the collocation points, and we present several feasible constructions. One particular choice, basedon sparse grids, depends weakly on the dimensionality of the random space and is more suitable for highly accurate computations of practical applications with large dimensional random inputs. Numerical examples are presented to demonstrate the accuracy and efficiency of the stochastic collocation methods.

Keywords: collocation methods, stochastic inputs, differential equations, uncertainty quantification


D. Xiu, R. Ghanem, I.G. Kevrekidis. “An Equation-free, Multiscale Approach to Uncertainty Quantification,” In IEEE Computing in Science and Engineering Journal (CiSE), Vol. 7, No. 3, pp. 16--23. 2005.
DOI: 10.1109/MCSE.2005.46

ABSTRACT

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The authors' equation- and Galerkin-free computational approach to uncertainty quantification for dynamical systems conducts UQ computations using short bursts of appropriately initialized ensembles of simulations. Their basic procedure estimates the quantities arising in stochastic Galerkin computations.

Keywords: Analytical models, Computational modeling, Context modeling, Microscopy, Nonlinear equations, Partial differential equations, Performance analysis, Sampling methods, Stochastic processes, Uncertainty


B. Yilmaz, R.S. MacLeod, B.B. Punske, B. Taccardi, D.H. Brooks. “Training Set Selection for Statistical Estimation of Epicardial Activation Mapping from Intravenous Multielectrode Catheters,” In IEEE Trans Biomed. Eng., pp. (in press). 2005.


B. Yilmaz, R.S. MacLeod, B.B. Punske, B. Taccardi, D.H. Brooks. “Venous Catheter Based Mapping of Ectopic Epicardial Activation: Training Data Set Selection for Statistical Estimation,” In IEEE Trans Biomed Eng, Vol. 52, No. 11, pp. 1823--1831. November, 2005.


S.-E. Yoon, P. Lindstrom, V. Pascucci, D. Manocha. “Cache-Oblivious Mesh Layouts,” In ACM Transactions on Graphics: ACM SIGGRAPH 2005 Papers, Vol. 24, No. 3, pp. 886--893. August, 2005.


S.-E. Yoon, P. Lindstrom, V. Pascucci, D. Manocha. “Cache-Oblivious Layouts of Polygonal Meshes,” In Proceedings of Massive 2005 (workshop on Massive Geometric Data Sets), pp. 29--33. 2005.


Z. Yosibash, R.M. Kirby. “Dynamic Response of Various Von-Karman Non-Linear Plate Models and their 3-D Counterparts,” In International Journal of Solids and Structures, Vol. 42, pp. 2517--2531. 2005.


S. Zhang, D.H. Laidlaw, G. Kindlmann. “Diffusion Tensor MRI Visualization,” In The Visualization Handbook, Edited by C.D. Hansen and C.R. Johnson, Elsevier, pp. 327--340. 2005.
ISBN: 0-12-387582-X

2004


O. Alter, G.H. Golub. “Integrative Analysis of Genome-Scale Data by Using Pseudoinverse Projection Predicts Novel Correlation Between DNA Replication and RNA Transcription,” In Proceedings of the National Academy of Sciences, Vol. 101, No. 47, Proceedings of the National Academy of Sciences, pp. 16577--16582. November, 2004.
DOI: 10.1073/pnas.0406767101


O. Alter, G.H. Golub, P.O. Brown, D. Botstein. “Novel Genome-Scale Correlation Between DNA Replication and RNA Transcription During the Cell Cycle in Yeast is Predicted by Data-Driven Models,” In Proceedings of the Miami Nature Biotechnology Winter Symposium on the Cell Cycle, Chromosomes and Cancer, Vol. 15, Edited by M.P. Deutscher and S. Black and P.E. Boehmer and G. D'Urso and T. Fletcher and F. Huijing and A. Marshall and B. Pulverer and B. Renault and J.D. Rosenblatt and J.M. Slingerland and W.J. Whelan, 2004.


S. Amer-Yahia, F. Du, J. Freire. “A Comprehensive Solution to the XML-to-Relational Mapping Problem,” In Proceedings of the 6th Annual ACM International Workshop on Web Information and Data Management, Washington DC, USA, pp. 31--38. 2004.
ISBN: 1-58113-978-0


A.E. Anderson, C.L. Peters, B.D. Tuttle, J.A. Weiss. “Development and Validation of a Subject-Specific Finite Element Model of the Pelvis: Assessment of Model Sensitivity,” In Proceedings of The 6th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering, pp. (6 pages). 2004.


A.E. Anderson, C.L. Peters, B.D. Tuttle, J.A. Weiss. “A Subject-Specific Finite Element Model of the Pelvis Accurately Predicts Cortical Strains Under Acetabular Loading,” In Proceedings of 50th Annual Meeting of the Orthopaedic Research Society, San Francisco, CA, Vol. 29, pp. 1334. March, 2004.


D. Barbosa, J. Freire, A. Mendelzon. “Information Preservation in XML-to-Relational Mappings,” In Database and XML Technologies, Lecture Notes in Computer Science (LNCS), Vol. 3186/2004, pp. 66--81. 2004.
ISBN: 978-3-540-22969-8


F.F. Bernardon, C.A. Pagot, J.L.D. Comba, C.T. Silva. “GPU-based Tiled Ray Casting using Depth Peeling,” SCI Institute Technical Report, No. UUSCI-2004-006, University of Utah, 2004.


M. Berzins. “Variable Order Finite Elements and Positivity Preservation for Hyperbolic PDEs,” In Applied Numerical Mathematics, Vol. 48, No. 3-4, pp. 253--439. March, 2004.


R. Borgo, V. Pascucci, R. Scopigno. “Massive Data Pre-Processing with a Cluster Based Approach,” In Proceedings of the 2004 Eurographics Symposium on Parallel Graphics and Visualization (EG-PGV-04), Note: UCRL-PROC-208678, Eurographics Association, Aire-la-Ville, Switzerland pp. 67--74. June, 2004.


P.-T. Bremer, H. Edelsbrunner, B. Hamann, V. Pascucci. “A Topological Hierarchy for Functions on Triangulated Surfaces,” In IEEE Transactions on Visualization and Computer Graphics, Vol. 10, No. 4, Note: UCRL-JRNL-208700, pp. 385-396. July/August, 2004.


P.-T. Bremer, V. Pascucci, B. Hamann. “Maximizing adaptivity in hierarchical topological models,” In Trends in Software, Note: UCRL-BOOK-200013, Edited by T. Moeller and B. Hamann and B. Russell, Springer, pp. 121--130. January, 2004.


D.H. Brooks, A. Ghodrati, Y. Zhang, G. Tadmor, R.S. MacLeod. “Inverse Electrocardiography in the Framework of Dynamic Imaging Problems,” In Proceedings of the IEEE Engineering in Medicine and Biology Society 26th Annual International Conference, San Francisco, CA, pp. 3565--3568. September, 2004.