Search

We examine the possibility of using the standard Newton's method for solving a class of nonlinear eigenvalue problems arising from electronic structure calculation. We show that the Jacobian matrix associated with this nonlinear system has a special structure that can be exploited to reduce the computational complexity of the Newton's method. Preliminary numerical experiments indicate that the Newton's method can be more efficient for small problems in which a few smallest eigenpairs are needed.

We describe an efficient implementation and present a performance study of an algebraic multilevel sub-structuring (AMLS) method for sparse eigenvalue problems. We assess the time and memory requirements associated with the key steps of the algorithm, and compare itwith the shift-and-invert Lanczos algorithm in computational cost. Our eigenvalue problems come from two very different application areas: the accelerator cavity design and the normal mode vibrational analysis of the polyethylene particles. We show that the AMLS method, when implemented carefully, is very competitive with the traditional method in broad application areas, especially when large numbers of eigenvalues are sought.

Sparse systems of linear equations and eigen-equations arise at the heart of many large-scale, vital simulations in DOE. Examples include the Accelerator Science and Technology SciDAC (Omega3P code, electromagnetic problem), the Center for Extended Magnetohydrodynamic Modeling SciDAC(NIMROD and M3D-C1 codes, fusion plasma simulation). The Terascale Optimal PDE Simulations (TOPS)is providing high-performance sparse direct solvers, which have had significant impacts on these applications. Over the past several years, we have been working closely with the other SciDAC teams to solve their large, sparse matrix problems arising from discretization of the partial differential equations. Most of these systems are very ill-conditioned, resulting in extremely poor convergenc deployed our direct methods techniques in these applications, which achieved significant scientific results as well as performance gains. These successes were made possible through the SciDAC model of computer scientists and application scientists working together totake full advantage of terascale computing systems and new algorithms research.

Algebraic sub-structuring refers to the process of applying matrix reordering and partitioning algorithms to divide a large sparse matrix into smaller submatrices from which a subset of spectral components are extracted and combined to form approximate solutions to the original problem. In this paper, we show that algebraic sub-structuring can be effectively used to solve generalized eigenvalue problems arising from the finite element analysis of an accelerator structure.

By applying the locally optimal rotation method to deal with the lowest eigenvalue of a Hessian matrix, we have efficiently incorporated the hyperdynamics method into the ab initio scheme. In the present method, we only need to calculate the first derivative of the potential and several more force calls in each molecular dynamics (MD) step, which makes hyperdynamics simulation applicable in ab initio MD simulations. With this implementation, we are able to simulate defect diffusion in silicon with boost factors up to 105. We utilized both direct MD and the hyperdynamics method to investigate diffusion of lithium atoms and silicon vacancies in silicon. We identified the complex diffusion process. The obtained diffusion coefficients of Li atoms and Si vacancies are in good agreement with the direct MD results. [ABSTRACT FROM AUTHOR]

For problems of complex and difficulty data processing of gas emission amount in gas geological statistics method, data source of gas emission amount was analyzed, and gas emission amount database was established. Gas emission amount data was screened by percentile method, so as to find out the data which could reflect real gas emission amount rule of mine. A gas emission amount screening module was established by use of C programming language and the second development tool of CAD and applied in No.12 Coal Mine of China Pingmei Shenma Group. The application result shows that the gas emission amount screening module improves data processing speed and preparation efficiency of gas geological map and saves a lot of manpower and material resources.