Sixth Bay Area Scientific Computing Day

University of San Francisco
San Francisco, California
March 5, 2005

Abstracts of the Talks

Quantum Monte Carlo Study of Photoprotection via Carotenoids in Photosynthetic Centers

Alan Aspuru-Guzik
University of California at Berkeley

Quantum Monte Carlo (QMC) methods are a powerful approach for the study of the electronic structure of atoms, molecules and solids. In this talk, we describe the application of QMC methods in the study of photoprotection in photosynthetic centers. The biological problem will be discussed, as well as the role of computation in prediction and description of the processes involved. We emphasize the scientific computing aspects of the project. In particular, we describe a novel approach for linear-scaling QMC calculations, as well as the features of the Zori QMC code. Our study is the result of an INCITE Award (Innovative and Novel Computational Impact on Theory and Experiment) from the U.S. Department of Energy's Office of Science.

ITALIQS:Iterative Linear Algebra for Large Interacting Quantum Simulations

Wenbin Chen
University of California at Davis

Simulation of interacting quantum systems are an increasingly powerful tool in investigating many of the most fundamental properties of materials, such as magnetic, optical response and conductivity. However, current simulations are limited to a few hundred particles. One of the primary bottlenecks turns out to be the solution of multi-scale p-cyclic linear systems. In this talk, we will focus on the develpment of robust and effective methods for solving such linear systems.

Krylov Subspace-Based Dimension Reduction of Higher-Order Linear Dynamical Systems

Roland Freund
University of California at Davis

A standard approach to reduced-order modeling of higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for reduced-order modeling of first-order systems. While this approach results in reduced-order models that are optimal in a Pade sense, in general, these models do not preserve the form of the original higher-order system.

In this talk, we present a new approach to reduced-order modeling of higher-order systems based on projections onto suitably partitioned Krylov basis matrices that are obtained by applying Krylov-subspace techniques to an equivalent first-order system. We show that the resulting reduced-order models preserve the form of the original higher-order system. Moreover, possible additional properties such as passivity or reciprocity are also preserved. While the resulting reduced-order models are no longer optimal in the Pade sense, we show that they still satisfy a Pade-type approximation property. We also discuss some implementation details and present some numerical examples.

Adaptive Mesh Refinement in Accelerator Cavity Design
Lixin Ge
Stanford Linear Accelerator Center

SLAC and RPI are collaborating on adaptive mesh refinement (AMR) for improving electromagnetic calculations in accelerator cavity design. This new capability is being developed under the DOE SciDAC Accelerator Simulation Project, specifically targeted for SLAC's frequency domain codes, Omega3P and S3P that are based on unstructured grids. Simulation results showing faster rate of convergence to desired accuracy in frequency and wall loss determinations while using significantly less degrees of freedom will be presented.

Error Bounds on Extra Precise Iterative Refinement

Yozo Hida
University of California at Berkeley

We present the design and testing of an algorithm for iterative refinement of the solution of linear equations, where the residual is computed with extra precision. This algorithm was originally proposed in the 1960s as a means to compute very accurate solutions to all but the most ill-conditioned linear systems of equations. However two obstacles have until now prevented its adoption in standard subroutine libraries like LAPACK: (1) There was no standard way to access the higher precision arithmetic needed to compute residuals, and (2) it was unclear how to compute a reliable error bound for the computed solution. The completion of the new BLAS Technical Forum Standard has recently removed the first obstacle. To overcome the second obstacle, we show how a single application of iterative refinement can be used to compute an error bound at small cost, and use this to compute both an error bound in the usual infinity norm, and a componentwise relative error bound.

We report extensive test results on over 6.2 million matrices of dimension 5, 10, 100, and 1000. As long as a normwise (resp. componentwise) condition number computed by the algorithm is less than 1/[max(10, sqrt(n))*eps], the computed normwise (resp. componentwise) error bound is at most 1/[max(10, sqrt(n))*eps] and indeed bounds the true error. Here, n is the matrix dimension and eps is the single precision roundoff error. For worse conditioned problems, we get similarly small correct error bounds in over 89% of cases.

Two Methods for Discretization and Preconditioning of Electromagnetic Problems

Tzanio Kolev
Lawrence Livermore National Laboratory

The numerical solution of electromagnetic problems is of critical importance in a number of practical applications and production codes. Many of the current discretization methods for these problems are based on the complicated edge elements introduced by Nedelec and result in a linear system that is difficult to precondition. In this talk I will discuss my experience with two different approximtion techniques for models related to Maxwell's equations -- one suggesting a new discretization scheme and a second one addressing the preconditioning of a Nedelec discretization.

In the first approach, the original problem is reformulated to one involving simple, piecewise-polynomial, finite elements and standard preconditioners for second order elliptic problems. This method belongs to the recently proposed family of negative-norm least-squares algorithms for electromagnetic problems, as well as the Maxwell eigenvalue problem. An interesting feature of the scheme is that the theory and implementation for general hexahedral meshes is straightforward from that on tetrahedra. More importantly, the resulting discrete linear system is well-conditioned and symmetric. Finally, the overall numerical algorithm can be efficiently implemented and has an optimal convergence rate, even for solutions with low regularity. This work is based on my dissertation under the supervision of J. Bramble and J. Pasciak (Texas A and M University).

The second method is an algebraic multigrid (AMG) preconditioner for the definite Maxwell equations discretized with lowest order edge elements. This approach combines the element agglomeration AMGe with the recently introduced adaptive AMG in order to efficiently eliminate the nullspace on coarse levels. It is based on a set of topological tables, e.g. the fine-grid discrete gradient operator describing the edges in terms of the vertices of the mesh. An important property of the scheme is that it can handle the discontinuity in the coefficients, which occur naturally on the interfaces between different materials. This is a joint work with P. Vassilevski (LLNL).

Correlation Effects in Screened-Exchange Density Functional Theory
Byounghak Lee
Lawrence Berkeley National Laboratory

Understanding electronic structure of nano-systems is the foundation of nanoscience. Present simulation methods are either too expensive (e.g., GW method) for nanostructures or limited to ground states of the systems (e.g., local density approximation of density functional theory). In this talk, we discuss a promising approach called Screened-Exchange Density Functional Theory(sX-DFT), which can be applied to larger systems and can predict excited state properties. It has been demonstrated that this method improves the bandgap of semiconductors such as Si, GaAs, Ge, etc., but the underlying physics is not always clear. We compare the self-energy term in the sX-DFT formalism with the one in the GW approximation and the exchange-correlation hole with the one of variational Monte Carlo simulations to shed a light on the origin of the good agreement with experiments and nature of the screening. We also discuss possible ways improving the performance of the simulation and the formalism.

Nonlinear Eigenvalue Problems from Modeling Accelerator Cavities with External Coupling

Lie-Quan Lee
Stanford Linear Accelerator Center

Damping higher-order-modes in accelerating cavities is of great importance for beam stability considerations. Such modes when subject to external coupling can be found as solutions to a nonlinear eigenvalue problem when Maxwell's equations are formulated in the frequency domain with outgoing wave conditions imposed at the coupler ports. We will discuss the parallel Second Order Arnoldi (for a special case) and other methods in the recent accelerator cavity design and modeling.

This is a joint work with Lixin Ge, Zenghai Li, Cho Ng, and Kwok Ko at SLAC, Zhaojun Bai at UC Davis, Weiguo Gao, Parry Husbands, Xiaoye Li, Chao Yang, and Esmond Ng at LBL.

Calculating Transport Properties of Nanodevices

Song Li
Stanford University

The Non Equilibrium Green's Function (NEGF) method is a powerful technique to compute quantum transport properties of nanoscale electronic devices. It is applicable to a wide range of devices, ranging from nano transistors, molecular switches, nano wires, etc. Accurately simulating such devices often requires a 2D or a full 3D model. This leads to a large computational expense. We review existing methods for the fast computation of the density of charge using the Schrodinger-Poisson equation, and propose a new algorithm which has a significantly lower computational cost and is exact (in the absence of computer roundoff errors). The algorithm is applicable in the presence of various boundary conditions for the source, drain and gate regions, and for devices of arbitrary geometry.

Statistical Analysis of Subcellular Proteins in Fluorescence Microscopy Imagery

Raquel Romano
Lawrence Berkeley National Laboratory

Due to the increasing ease of acquiring, viewing, and storing large amounts of microscopy imagery, there is a present need for analysis tools that extract useful quantitative information from large sets of image data. With this increasing volume and variety of data, the range of biological questions which may be posed expands, thus demanding analysis methods that generalize to a variety of tasks, rather than narrow tools specifically hand-designed to satisfy the criteria of individual experiments. We propose that statistical approaches such as independent components analysis (ICA) can subsume and generalize more traditional image processing approaches for automatically detecting subcellular protein signals. By applying ICA to current studies in radiation biology that examine the levels of DNA repair proteins in irradiated cells, we show how local features may be directly learned from subsets of image data and used to build data-driven models for feature extraction and image classification.

This is joint work with Bahram Parvin in the Imaging and Informatics Group at LBNL

A Meta-Partitioner for Faster Supercomputer Simulations

Johan Steensland
Sandia National Laboratories

Structured adaptive mesh refinement (SAMR) methods are being widely used for computer simulations of various physical phenomena. Parallel implementations potentially offer realistic simulations of complex, three-dimensional applications. But achieving good scalability for large-scale applications is non-trivial. Performance is limited by the partitioners ability to efficiently use the underlying computer's resources. The goal of our research project is to improve scalability for general SAMR applications executing on general parallel computers. We engineer the dynamically adaptive meta-partitioner, able to select and configure the most appropriate partitioning method at run-time, based on system and application state. This presentation gives an overview of our project, reports on recent achievements, and discusses the project's significance in a wider scientific context.

A Comparison of Condition Numbers of the Full Rank Least Squares Problem

Joab Winkler
University of Sheffield

Abstract



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