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We describe an efficient implementation of an algorithm for computing selected elements of a general sparse symmetric matrix <i>A</i> that can be decomposed as <i>A</i> = <i>LDLT</i>, where <i>L</i> is lower triangular and <i>D</i> is diagonal. Our implementation, which is called <i>SelInv</i>, is built on top of an efficient supernodal left-looking(More)
An important a r e a of research in computational biochemistry is the design of molecules for speciic applications. The design of these molecules, which depends on the accurate determination of their three-dimensional structure, can beformulated as a global optimization problem. In this study, we present results from the application of a new conformation(More)
The self-consistent field (SCF) iteration, widely used for computing the ground state energy and the corresponding single particle wave functions associated with a many-electron atomistic system, is viewed in this paper as an optimization procedure that minimizes the Kohn– Sham (KS) total energy indirectly by minimizing a sequence of quadratic surrogate(More)
We investigate the convergence of the self-consistent field (SCF) iteration used to solve a class of nonlinear eigenvalue problems. We show that for the class of problem considered, the SCF iteration produces a sequence of approximate solutions that contain two convergent subsequences. These subsequences may converge to two different limit points, neither(More)
A new direct constrained optimization algorithm for minimizing the Kohn-Sham (KS) total energy functional is presented in this paper. The key ingredients of this algorithm involve projecting the total energy functional into a sequences of sub-spaces of small dimensions and seeking the minimizer of total energy functional within each subspace. The minimizer(More)
A m ultigrid preconditioned conjugate gradient algorithm is introduced into a semiconductor device modeling code, DANCIR. This code simulates a wide variety of semiconductor devices by n umericallysolving the drift-diiusion equations. The most time consuming aspect of the simulation is the solution of three linear systems within each iteration of the Gummel(More)
A new tool for optimal heat transfer design has been constructed by coupling the OPT++ optimization library to the TACO2D nite element heat transfer code. The optimization heat transfer code can beused to quickly and eeciently nd optimal operating parameters required for target design criteria. This tool has been applied to the heat transfer design of a(More)
We describe the design and implementation of KSSOLV, a MATLAB toolbox for solving a class of nonlinear eigenvalue problems known as the <i>Kohn-Sham equations</i>. These types of problems arise in electronic structure calculations, which are nowadays essential for studying the microscopic quantum mechanical properties of molecules, solids, and other(More)
Object-oriented programming is a relatively new tool in the development of optimization software. The code extensibility and the rapid algorithm prototyping capability enabled by this programming paradigm promise to enhance the reliability, utility, and ease of use of optimization software. While the use of object-oriented programming is growing, there are(More)