Omar M. Knio

Bio: Omar M. Knio is an academic researcher from King Abdullah University of Science and Technology. The author has contributed to research in topics: Polynomial chaos & Vortex. The author has an hindex of 51, co-authored 322 publications receiving 10779 citations. Previous affiliations of Omar M. Knio include Johns Hopkins University & Durham University.

Spectral methods for uncertainty quantification : with applications to computational fluid dynamics

Abstract: Introduction: Uncertainty Quantification and Propagation.- Basic Formulations.- Spectral Expansions.- Non-intrusive Methods.- Galerkin Methods.- Detailed Elementary Applications.- Application to Navier-Stokes Equations.- Advanced topics.- Solvers for Stochastic Galerkin Problems.- Wavelet and Multiresolution Analysis Schemes.- Adaptive Methods.- Epilogue.

Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes

Abstract: This paper gives an overview of the use of polynomial chaos (PC) expansions to represent stochastic processes in numerical simulations. Several methods are presented for performing arithmetic on, as well as for evaluating polynomial and nonpolynomial functions of variables represented by PC expansions. These methods include {Taylor} series, a newly developed integration method, as well as a sampling-based spectral projection method for nonpolynomial function evaluations. A detailed analysis of the accuracy of the PC representations, and of the different methods for nonpolynomial function evaluations, is performed. It is found that the integration method offers a robust and accurate approach for evaluating nonpolynomial functions, even when very high-order information is present in the PC expansions.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Fast parallel algorithms for short-range molecular dynamics

Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model [presentation]

Abstract: Abstract A two-dimensional version of the Pennsylvania State University mesoscale model has been applied to Winter Monsoon Experiment data in order to simulate the diurnally occurring convection observed over the South China Sea. The domain includes a representation of part of Borneo as well as the sea so that the model can simulate the initiation of convection. Also included in the model are parameterizations of mesoscale ice phase and moisture processes and longwave and shortwave radiation with a diurnal cycle. This allows use of the model to test the relative importance of various heating mechanisms to the stratiform cloud deck, which typically occupies several hundred kilometers of the domain. Frank and Cohen's cumulus parameterization scheme is employed to represent vital unresolved vertical transports in the convective area. The major conclusions are: Ice phase processes are important in determining the level of maximum large-scale heating and vertical motion because there is a strong anvil componen...

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Abstract: The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.