Indefinite Ruhe’s Variant of the Block Lanczos Method for Solving the Systems of Linear Equations

In this paper, we equip Cn with an indefinite scalar product with a specific Hermitian matrix, and our aim is to develop some block Krylov methods to indefinite mode. In fact, by considering the block Arnoldi, block FOM, and block Lanczos methods, we design the indefinite structures of these block Krylov methods; along with some obtained results, we offer the application of this methods in solving linear systems, and as the testifiers, we design numerical examples.

An Out-of-Core Eigen-Solver with OpenMP Parallel Scheme for Large Spare Damped System

An out-of-core block Lanczos method with the OpenMP parallel scheme was developed to solve large spare damped eigenproblems. The symmetric generalized eigenproblem is first solved using the block Lanczos method with the preconditioned conjugate gradient (PCG) method, and the condensed damped eigenproblem is then solved to obtain the complex eigenvalues. Since the PCG solvers and out-of-core schemes are used, a large-scale eigenproblem can be solved using minimal computer memory. The out-of-core arrays only need to be read once in each Lanczos iteration, so the proposed method requires little extra CPU time. In addition, the second-level OpenMP parallel computation in the PCG solver is suggested to avoid using a large block size that often increases the number of iterations needed to achieve convergence.

The Effects of Fluid Structure Interactions on the Dynamic Characteristics of the Reactor Internals Structure of SMART

The Korea Atomic Energy Research Institutes has been developing the SMART (System integrated Modular Advanced ReacTor), an environment-friendly nuclear reactor, for the generation of electricity, and to perform desalination. SMART reactors can be exposed to various external and internal loads caused by seismic and coolant flows. Reactor structures need to be maintained for the reactor’s safety and integrity against these loads during the operational time of the SMART. This paper presents two FE-models, 3-D solid models of the reactor internals in the air and in the coolant, and then compares the results of the dynamic characteristic for the two FE-models using a commercial Finite Element tool, ANSYS V12. A solver was selected by the Block Lanczos method. These FE-models are looking forward to being executed in various researches concerning the SMART in further studies.