Solving eigenvalue response matrix equations with nonlinear techniques

TL;DR: A new energy expansion technique based on the Karhunen–Loeve Transform (KLT) is developed for use in the eigenvalue response matrix method (ERMM), which links nodes using truncated expansions of boundary fluxes in each phase-space variable.

TL;DR: In this article, a stochastic-deterministic, response matrix method for transient analyses of nuclear systems is presented. But the method is based on the response matrix formalism, which describes a system by a set of response functions.

TL;DR: In this paper, the Karhunen-Loeve Transform (KLT) was used to produce basis sets appropriate for the energy variable based on "snapshots", which employed small, representative problems to provide input spectra with which the KLT produces an orthogonal basis for the application.

TL;DR: In this paper, a high-order transient transport method based on the response matrix formalism was developed for application to reactor kinetics problems, which combines recent advances in both static and dynamic transport.

TL;DR: The PETSc 2.0 package as discussed by the authors uses object-oriented programming to conceal the details of the message passing, without concealing the parallelism, in a high-quality set of numerical software libraries.

TL;DR: The aim of this paper is to present the reader with a perspective on how JFNK may be applicable to applications of interest and to provide sources of further practical information.

TL;DR: The Scalable Library for Eigenvalue Problem Computations (SLEPc) is a software library for computing a few eigenvalues and associated eigenvectors of a large sparse matrix or matrix pencil that has been developed on top of PETSc and enforces the same programming paradigm.