SCIENTIFIC COMPUTING AND IMAGING INSTITUTE
at the University of Utah

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

SCI Publications

2002


J.A. Weiss, J.C. Gardiner, C. Bonifasi-Lista. “Ligament Material Behavior is Nonlinear, Viscoelastic and Rate-Independent Under Shear Loading,” In Journal of Biomechanics, Vol. 35, pp. 943--950. 2002.


R.T. Whitaker, V. Elangovan. “A Direct Approach to Estimating Surfaces in Tomographic Data,” In J. Med. Img. Anal., Vol. 6, No. 3, pp. 235--249. 2002.


R.T. Whitaker, J. Gregor. “A Maximum Likelihood Surface Estimator for Dense Range Data,” In IEEE Trans. Pattern Anal. & Mach. Intel., pp. 1372--1387. 2002.


R.T. Whitaker, E. L. Valdes-Juarez. “On the Reconstruction of Height Functions and Terrain Maps from Dense Range Data,” In IEEE Trans. Imag. Proc., Vol. 11, No. 7, pp. 704--716. 2002.


D. Xiu, G.E. Karniadakis. “The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations,” In SIAM Journal on Scientific Computing, Vol. 24, No. 2, pp. 619--644. 2002.
DOI: 10.1137/S1064827501387826

ABSTRACT

We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error. Several continuous and discrete processes are treated, and numerical examples show substantial speed-up compared to Monte Carlo simulations for low dimensional stochastic inputs.

Keywords: polynomial chaos, Askey scheme, orthogonal polynomials, stochastic differential equations, spectral methods, Galerkin projection


D. Xiu, D. Lucor, C.-H. Su, G.E. Karniadakis. “Stochastic Modeling of Flow-Structure Interactions using Generalized Polynomial Chaos,” In Journal of Fluids Engineering, Vol. 124, No. 1, pp. 51--59. 2002.
DOI: 10.1115/1.1436089

ABSTRACT

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We present a generalized polynomial chaos algorithm to model the input uncertainty and its propagation in flow-structure interactions. The stochastic input is represented spectrally by employing orthogonal polynomial functionals from the Askey scheme as the trial basis in the random space. A standard Galerkin projection is applied in the random dimension to obtain the equations in the weak form. The resulting system of deterministic equations is then solved with standard methods to obtain the solution for each random mode. This approach is a generalization of the original polynomial chaos expansion, which was first introduced by N. Wiener (1938) and employs the Hermite polynomials (a subset of the Askey scheme) as the basis in random space. The algorithm is first applied to second-order oscillators to demonstrate convergence, and subsequently is coupled to incompressible Navier-Stokes equations. Error bars are obtained, similar to laboratory experiments, for the pressure distribution on the surface of a cylinder subject to vortex-induced vibrations.


D. Xiu, G.E. Karniadakis. “Modeling Uncertainty in Steady State Diffusion Problems via Generalized Polynomial Chaos,” In Computer Methods in Applied Mechanics and Engineering, Vol. 191, No. 43, pp. 4927--4948. 2002.

ABSTRACT

We present a generalized polynomial chaos algorithm for the solution of stochastic elliptic partial differential equations subject to uncertain inputs. In particular, we focus on the solution of the Poisson equation with random diffusivity, forcing and boundary conditions. The stochastic input and solution are represented spectrally by employing the orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener [Amer. J. Math. 60 (1938) 897]. A Galerkin projection in random space is applied to derive the equations in the weak form. The resulting set of deterministic equations for each random mode is solved iteratively by a block Gauss–Seidel iteration technique. Both discrete and continuous random distributions are considered, and convergence is verified in model problems and against Monte Carlo simulations.

Keywords: Uncertainty, Random diffusion, Polynomial chaos


J. Xu, D. Xiu, G.E. Karniadakis. “A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations,” In Journal of Scientific Computing, Vol. 17, No. 1-4, pp. 585--597. 2002.
DOI: 10.1023/A:1015122714039

ABSTRACT

We present a semi-Lagrangian method for integrating the three-dimensional incompressible Navier–Stokes equations. We develop stable schemes of secondorder accuracy in time and spectral accuracy in space. Specifically, we employ a spectral element (Jacobi) expansion in one direction and Fourier collocation in the other two directions. We demonstrate exponential convergence for this method, and investigate the non-monotonic behavior of the temporal error for an exact three-dimensional solution. We also present direct numerical simulations of a turbulent channel-flow, and demonstrate the stability of this approach even for marginal resolution unlike its Eulerian counterpart.

2001


I. Ahmad, M. Berzins. “MOL Solvers for Hyperbolic PDEs with Source Terms,” In Mathematics and Computers in Simulation, Vol. 56, pp. 1115--1125. 2001.


O. Alter, Y. Yamamoto. “Quantum Measurement of a Single System,” Wiley-Blackwell, May, 2001.
ISBN: 9780471283089
DOI: 10.1002/9783527617128


O. Alter, P.O. Brown, D. Botstein. “Processing and Modeling Genome-Wide Expression Data Using Singular Value Decomposition,” In Microarrays: Optical Technologies and Informatics, Vol. 4266, Edited by M.L. Bittner and Y. Chen and A.N. Dorsel and E.R. Dougherty (International Society for Optical Engineering Bellingham), pp. 171--186. 2001.


M. Bertram, D. Laney, M. Duchaineau, C.D. Hansen, B. Hamann, K. Joy. “Wavelet Representation of Contour Sets,” In Proceeding of IEEE Visualization 2001, pp. 303--310, 566. 2001.


M. Berzins, A.S. Tomlin, S. Ghorai, I. Ahmad J.Ware. “Unstructured Mesh Adaptive Mesh MOL Solvers for Atmospheric Reacting Flow Problems,” In The Adaptive Method of Lines, Note: invited chapter, Edited by A. Vande Wouwer and Ph. Saucez and W. Schiesser, CRC Press, Boca Raton, Florida, USA., pp. 317--351. 2001.
ISBN: 1-58488-231-X


M. Berzins, L. Durbeck. “Unstructured Mesh Solvers for Hyperbolic PDEs with Source Terms: Error Estimates and Mesh Quality,” In Godunonv Methods: Theory and Applications, Note: Proc. of Godunov Conf. October 18-22, Oxford UK, Edited by E. Toro et al., Kluwer Academic/Plenum, pp. 117--124. 2001.


M. Berzins. “Modified Mass Matrices and Positivity Preservation for Hyperbolic and Parabolic PDEs,” In Communications in Numerical Methods in Engineering, Vol. 17, pp. 659--666. 2001.


J.D. Brederson, M. Ikits, C.R. Johnson, C.D. Hansen. “A Prototype System For Synergistic Data Display,” In IEEE Virtual Reality 2001, 2001.


D. Breen, R.T. Whitaker. “A Level-Set Approach for the Metamorphosis of Solid Models,” In IEEE Trans. Vis & Comp. Graph., Vol. 7, No. 2, pp. 173--192. 2001.


C.R. Butson. “From Action Potentials to Surface Potentials,” In Multilevel Neuronal Modeling Workshop, Edinburgh, Scotland, May, 2001.


C.R. Butson, G.A. Clark. “Random Noise Confers a Paradoxical Improvement in the Ability of a Simulated Hermissenda Photoreceptor Network to Encode Light Intensity,” In Society for Neuroscience Conference, November, 2001.


N.M. Cordaro, J.A. Weiss, J.A. Szivek. “Strain Transfer Between a CPC Coated Strain Gauge and Cortical Bone During Bending,” In Journal of Biomedical Materials Research, Vol. 58, No. 2, pp. 147--155. 2001.