장호종 교수

We study the computation of sparse null bases of equilibrium matrices in the context of structural optimization and incompressible fluid flow. In our approach we emphasize the parallel computatin and examine the applications. New block decomposition and node ordering schemes are suggested, and numerical examples are considered.

We consider some numerical solution methods for equilibrium equations Af + E λ = r, Ef = s. Algebraic problems of this form evolve from many applications such as structural optimization, fluid flow, and circuits. An important approach, called the force method, to the solution to such problems involves dimension reduction nullspace computation for E. The purpose of this paper is to investigate the substructuring method for the solution step of the force method in the context of the incompressible

An ecient method for reanalysis of a damaged struc-tures is presented. Perturbation analysis for the equality constra-ined least squares problem is adapted to handle structural reanaly-sis, and related theoretical and numerical results are presented.

We describe aparallel implementation of a relaxed Hermitian and skew-Hermitian splitting preconditioner for the numerical solution of saddle point problems arising from the steady incompressible Navier-Stokesequations. The equations are linearized by the Picarditeration and discretized with the finite element and finite difference schemes on two-dimensional and three-dimensional domains. We report strong scalability results for up to 32 cores.

Recently iterative algorithms based on the optimization of the Rayleigh quotient have been developed, and a CG scheme for the optimization of the Rayleigh quotient has been proven to be a very attractive and promising technique for large sparse eigenproblems for interior eigenvalues. Ax = /spl lambda/Bx (1) The given matrices A, and B are assumed to be large and sparse, and symmetric and B is further assumed to be positive definite. Also, the method is very amenable to parallel computations. A p

In this study, we shall be concerned with computing in parallel a few of the smallest eigenvalues and their corresponding eigenvectors of the eigenvalue problem, Ax = λBx, where A is symmetric, and B is symmetric positive definite. Both A and B are large and sparse. Recently iterative algorithms based on the optimization of the Rayleigh quotient have been developed, and CG scheme for the optimization of the Rayleigh quotient has been proven a very attractive and promising technique for large spa