The superconsistent collocation method, which is based on a
collocation grid different from the one used to represent the
solution, has proven to be very accurate in the resolution of
various functional equations. Excellent results can be also
obtained for what concerns preconditioning. Some analysis and
numerous experiments, regarding the use of finite-differences
preconditioners, for matrices arising from pseudospectral
approximations of advection-diffusion boundary value problems, are
presented...
The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting...
In this paper we present a nonsingularity result which is a generalization of Nekrasov property by using two different permutations of the index set. The main motivation comes from the following observation: matrices that are Nekrasov matrices up to the same permutations of rows and columns, are nonsingular. But, testing all the permutations of the index set for the given matrix is too expensive. So, in some cases, our new nonsingularity criterion allows us to use the results already calculated...
The integration to steady state of many initial value ODEs and PDEs using the forward Euler method
can alternatively be considered as gradient descent for an associated minimization problem.
Greedy algorithms such as steepest descent for determining the step size are as
slow to reach steady state as is forward Euler integration with the best uniform step size.
But other, much faster methods using bolder step size selection exist.
Various alternatives are investigated from both theoretical and practical...
The purpose of our work is to develop an automatic shape optimization tool for runner wheel blades in reaction water turbines, especially in Kaplan turbines. The fluid flow is simulated using an in-house incompressible turbulent flow solver based on recently introduced isogeometric analysis (see e.g. J. A. Cotrell et al.: Isogeometric Analysis: Toward Integration of CAD and FEA, Wiley, 2009). The proposed automatic shape optimization approach is based on a so-called hybrid optimization which combines...