SCI Publications

2004


X. Wan, D. Xiu, G.E. Karniadakis. “Stochastic Solutions for the Two-dimensional Advection-Diffusion Equation,” In SIAM Journal on Scientific Computing, Vol. 26, No. 2, pp. 578--590. 2004.
DOI: 10.1137/S106482750342684X

ABSTRACT

In this paper, we solve the two-dimensional advection-diffusion equation with random transport velocity. The generalized polynomial chaos expansion is employed to discretize the equation in random space while the spectral hp element method is used for spatial discretization. Numerical results which demonstrate the convergence of generalized polynomial chaos are presented. Specifically, it appears that the fast convergence rate in the variance is the same as that of the mean solution in the Jacobi-chaos unlike the Hermite-chaos. To this end, a new model to represent compact Gaussian distributions is also proposed.

Keywords: generalized polynomial chaos, advection-diffusion, stochastic modeling


C.H. Wolters, L. Grasedyck, A. Anwander, H. Hackbusch. “Efficient Computation of Lead Field Bases and Influence Matrix for the FEM-Based EEG and MEG Inverse Problem,” In Proceedings of The 14th International Conference on Biomagnetism, Boston, MA, pp. 104--107. August, 2004.


C.H. Wolters, L. Grasedyck, W. Hackbusch. “Efficient Computation of Lead Field Bases and Influence Matrix for the FEM-Based EEG and MEG Inverse Problem,” In Inverse Problems, Vol. 20, No. 4, pp. 1099--1116. 2004.


C.H. Wolters, A. Anwander, B. Maess, R.S. MacLeod, A.D. Friederici. “The Influence of Volume Conduction Effects on the EEG/MEG Reconstruction of the Sources of the Early Left Anterior Negativity,” In Proceedings of the IEEE Engineering in Medicine and Biology Society 26th Annual International Conference, San Francisco, CA, Vol. 5, pp. 3569--3572. September, 2004.


C.H. Wolters, A. Anwander, S. Reitzinger, G. Haase. “Algebraic Multigrid with Multiple Right-Hand-Side Treatment for an Efficient Computation of EEG and MEG Lead Field Bases,” In Proceedings of The 14th International Conference on Biomagnetism, Boston, MA, pp. 465--466. August, 2004.


C.H. Wolters, A. Anwander, S. Reitzinger, G. Haase. “Avoiding the Problem of FE Meshing: A Parallel Algebraic Multigrid with Multiple Right-Hand Side Treatment for an Efficient and Memory-Economical Computation of High Resolution EEG and MEG Lead Field Bases,” In Proceedings of the IEEE Engineering in Medicine and Biology Society 26th Annual International Conference, San Francisco, CA, Note: poster, September, 2004.


D. Xiu, G.E. Karniadakis. “Supersensitivity Due to Uncertain Boundary Conditions,” In International Journal for Numerical Methods in Engineering, Vol. 61, No. 12, pp. 2114--2138. 2004.
DOI: 10.1002/nme.1152

ABSTRACT

We study the viscous Burgers' equation subject to perturbations on the boundary conditions. Two kinds of perturbations are considered: deterministic and random. For deterministic perturbations, we show that small perturbations can result in O(1) changes in the location of the transition layer. For random perturbations, we solve the stochastic Burgers' equation using different approaches. First, we employ the Jacobi-polynomial-chaos, which is a subset of the generalized polynomial chaos for stochastic modeling. Converged numerical results are reported (up to seven significant digits), and we observe similar 'stochastic supersensitivity' for the mean location of the transition layer. Subsequently, we employ up to fourth-order perturbation expansions. We show that even with small random inputs, the resolution of the perturbation method is relatively poor due to the larger stochastic responses in the output. Two types of distributions are considered: uniform distribution and a 'truncated' Gaussian distribution with no tails. Various solution statistics, including the spatial evolution of probability density function at steady state, are studied.

Keywords: generalized polynomial chaos, stochastic Burgers' equation, supersensitivity, random boundary conditions


D. Xiu, D.M. Tartakovsky. “A Two-scale Non-perturbative Approach to Uncertainty Analysis of Diffusion in Random Composites,” In SIAM Journal on Multiscale Modeling and Simulation, Vol. 2, No. 4, pp. 662--674. 2004.
DOI: 10.1137/03060268X

ABSTRACT

Many physical systems, such as natural porous media, are highly heterogeneous and characterized by parameters that are uncertain due to the lack of sufficient data. This uncertainty (randomness) occurs on a multiplicity of scales. We focus on random composites with the two dominant scales of uncertainty: large-scale uncertainty in the spatial arrangement of materials and small-scale uncertainty in the parameters within each material. We propose an approach that combines random domain decompositions and polynomial chaos expansions to account for the large and small scales of uncertainty, respectively. We present a general framework and use one-dimensional diffusion to demonstrate that our combined approach provides robust, nonperturbative approximations for the statistics of system states.

Keywords: random fields, moment equations, random domain decomposition, polynomial chaos


Z. Yosibash, R.M. Kirby, D. Gottlieb. “Collocation Methods for the Solution of Von-Karman Dynamic Non-Linear Plate Systems,” In Journal of Computational Physics, Vol. 200, No. 2, pp. 432--461. 2004.


Y. Zhang, J.E. Guilkey, J.B. Hoying, J.A. Weiss. “Mechanical Simulation of Multicellular Structures with the Material Point Method,” In Proceedings of The 6th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering, pp. (6 pages). March, 2004.


K. Zhang, K. Damevski, V. Venkatachalapathy, S.G. Parker. “SCIRun2: A CCA Framework for High Performance Computing,” In Proceedings of The 9th International Workshop on High-Level Parallel Programming Models and Supportive Environments, April, 2004.

2003


M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, C.T. Silva, D. Levin. “Computing and Rendering Point Set Surfaces,” In IEEE Transactions on Visualization and Computer Graphics, Vol. 9, No. 1, pp. 3--15. 2003.
ISSN: 1077-2626


O. Alter, P.O. Brown, D. Botstein. “Generalized Singular Value Decomposition for Comparative Analysis of Genome-Scale Expression Datasets of Two Different Organisms,” In Proceedings of the National Academy of Sciences, Vol. 100, No. 6, Proceedings of the National Academy of Sciences, pp. 3351--3356. March, 2003.
DOI: 10.1073/pnas.0530258100


A. Baptista, T. Leen, Y. Zhang, A. Chawla, D. Maier, Wu-chang Feng, Wu-chi Feng, J. Walpole, C.T. Silva, J. Freire. “Environmental Observation and Forecasting Systems: Vision, Challenges and Successes of a Prototype,” In Proceedings of the International Society for Environmental Information Sciences Annual Conference (ISEIS '2003) on Systems Science and Information Technology for Environmental Applications, Regina, Sask, Canada, July, 2003.


M. Benedikt, C.Y. Chan, W. Fan, J. Freire, R. Rastogi. “Capturing Both Types and Constraints in Data Integration,” In Proceedings of the 2003 ACM SIGMOD International Conference on Management of Data, pp. 277--288. 2003.
ISBN: 1-58113-634-X


M. Berzins, A.G. Wilson. “Spatial Interaction Models and Fisher Information Theory A New Calibration Model,” In Environment and Planning, Vol. 35, pp. 2161--2176. 2003.


M. Bertram, X. Tricoche, H. Hagen. “Adaptive Smooth Scattered Data Approximation for Largescale Terrain Visualization,” In Proceedings of the Joint Eurographics-IEEE TCVG Symposium on Visualization: Data Visualization 2003, pp. 177--184. 2003.


P. Bohannon, J. Freire, J. Haritsa, M. Ramanath, P. Roy, J. Simeon. “Bridging the XML-Relational Divide with LegoDB: A Demonstration,” In International Conference on Data Engineering, pp. 759. 2003.
ISSN: 1063-6382


R. Borgo, R. Scopigno, P. Cignoni, V. Pascucci. “A Progressive Subdivision Paradigm (PSP),” In Proceedings of the Conference on Vision, Modeling and Visualization 2003 (VMV-03), Note: UCRL-PROC-208557, Edited by T. Ertl and B. Girod and G. Greiner and H. Niemann and H.-P. Seidel and E. Steinbach and R. Westermann, Aka GmbH, Berlin, Germany pp. 441--450. Nov, 2003.


P.-T. Bremer, H. Edelsbrunner, B. Hamann, V. Pascucci. “A Multi-resolution Data Structure for Two-dimensional Morse Functions,” In Proceedings of IEEE Conference on Visualization (VIS-03), Note: UCRL-JC-154014, pp. 139--146. October, 2003.