Dynamical iteration schemes for coupled simulation in nanoelectronics

A Class of Nested Iteration Schemes for Generalized Coupled Sylvester Matrix Equation

Global Krylov subspace methods are the most efficient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose the nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as an inner iteration to approximate each outer iterate, while each...

Partitioned but Strongly Coupled Iteration Schemes for Nonlinear Fluid-Structure Interaction

We look at the computational procedure of computing the response of a coupled fluid-structure interaction problem. We use the so called strong fluid-structure coupling — a totally implicit formulation. At each time step in an implicit formulation, new values for the solution variables have to be computed by solving a nonlinear system of equations, where we assume that we have solvers for the su...

Iteration schemes for the divide - and - conquereigenvalue

We propose globally convergent iteration schemes for updating the eigenvalues of a symmetric matrix after a rank-1 modiication. Such calculations are the core of the divide-and-conquer technique for the symmetric tridiagonal eigenvalue problem. We prove the superlinear convergence right from the start of our schemes which allows us to improve the complexity bounds of 3]. The eeec-tiveness of ou...

Higher Order Iteration Schemes for Unconstrained Optimization

Using a predictor-corrector tactic, this paper derives new iteration schemes for unconstrained optimization. It yields a point (predictor) by some line search from the current point; then with the two points it constructs a quadratic interpolation curve to approximate some ODE trajectory; it finally determines a new point (corrector) by searching along the quadratic curve. In particular, this p...

Continuous iteration of dynamical maps