Look-Ahead Procedures For Lanczos-Type Product Methods Based On Three-Term Lanczos Recurrences

Lanczos-type product methods for the solution of large sparse non-Hermitian linear systems either square the Lanczos process or combine it with a local minimization of the residual. They inherit from the underlying Lanczos process the danger of breakdown. For various Lanczostype product methods that are based on the Lanczos three-term recurrence, look-ahead versions are presented, which avoid such breakdowns or near breakdowns at the cost of a small computational overhead. Different look-ahead strategies are discussed and their efficiency is demonstrated by several numerical examples

A Boundary Functional for the Least-Squares Finite-Element Solution of Neutron Transport Problems

The least-squares finite-element framework for the neutron transport equation is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. This approach is extended by incorporating the boundary conditions into the least-squares functional. The proof of the V-ellipticity and continuity of the new functional leads to bounds of the discretization error for different regimes. For a P 1 approximation of the angular dependence the resulting system of partial differential equations for the moments is explicitly derived. In the diffusion limit this system is essentially a Poisson equation for the zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. The use of these bounds is demonstrated in numerical examples for a spatial discretization using trilinear finite elements on a uniform tessellation into cubes

A Boundary Functional For The Least-Squares Finite Element Solution Of Neutron Transport Problems

. The least-squares finite-element framework for the neutron transport equation is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. This approach is extended by incorporating the boundary conditions into the leastsquares functional. The proof of the V-ellipticity and continuity of the new functional leads to bounds of the discretization error for different regimes. For a P 1 and a P 2 approximation of the angular dependence the resulting system of partial differential equations for the moments is explicitly derived. In the diffusion limit this system is essentially a Poisson equation for the zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. The use of these bounds is demonstrated in numerical examples for a spatial discretization using trilinear finite elements on a uniform tessellation into ..