Established methods for calculating residual stresses from the strains measured when using the slitting method give results for the stresses that exist within the depth range of the slit. Practical considerations typically limit this range to about 90-95% of the specimen thickness. Force and moment equilibrium can provide additional information that may be used to estimate the residual stresses...

This paper deals with the combination of two solution methods: multigrid and GMRES [SIAM J. Sci. Comput., 14 (1993), pp. 856–869]. The generality and parallelizability of this combination are established by applying it to systems of nonlinear PDEs. As the “preconditioner” for a nonlinear Krylov subspace method, we use the full approximation storage (FAS) scheme [Math. Comp., 31 (1977), pp. 333–...

In this work we consider the design of robust and eecient nite element approximation methods for solving advection-diiusion equations. Speciically, we consider the stabilisation of discrete approximations using uniform grids which do not resolve boundary layers, as might arise using a multi-level (or multigrid) iteration strategy to solve the discrete problem. Our analysis shows that when using...

There has been much recent research on preconditioning discretisations of the Helmholtz operator ∆+ k (subject to suitable boundary conditions) using a discrete version of the so-called “shifted Laplacian” ∆+(k+iε) for some ε > 0. This is motivated by the fact that, as ε increases, the shifted problem becomes easier to solve iteratively. Despite many numerical investigations, there has been no ...

In this research, a novel method to decrease micro-residual stresses of fibrous composites by adding carbon nanotubes (CNTs) is proposed in detail. The negative coefficient of thermal expansion and the high young’s modulus of CNTs can be utilized to counterbalance the process induced residual stresses in composites. To this end, first, the effects of adding CNTs to the matrix of fibrous composi...

The Conjugate Gradient (CG) method is often used to solve a positive definite linear system Ax = b. This paper analyzes two hard cases for CG or any Krylov subspace type methods by either analytically finding the residual formulas or tightly bound the residuals from above and below, in contrast to existing results which only bound residuals from above. The analysis is based on a general framewo...

In this work, a two-layer coupled fluid-structure-structure interaction model is considered, which incorporates an anisotropic structure model into the fluid-structure interaction problems. We propose two domain decomposition solvers for such a class of coupled problems: a Robin-Robin preconditioned GMRES solver combined with an inner Dirichlet-Neumann iterative solver, and a Robin-Robin precon...

Residual tumor cells remain beyond the margins of every glioblastoma (GBM) resection. Their resistance to postsurgical therapy is considered a major driving force of mortality, but their biology remains largely uncharacterized. In this study, residual tumor cells were derived via experimental biopsy of the resection margin after standard neurosurgery for direct comparison with samples from the ...