Browsing by Author "Palma, J.M.L.M."
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- Inexact subspace iteration for the consecutive solution of linear systems with changing right-hand sidesPublication . Balsa, Carlos; Daydé, Michel; Palma, J.M.L.M.; Ruiz, DanielWe propose a two-phase acceleration technique for the solution of Symmetric and Positive Definite linear systems with multiple right-hand sides. In the first phase we compute some partial spectral information related to the ill conditioned part of the given coefficient matrix and, in the second phase, we use this information to improve the convergence of the Conjugate Gradient algorithm. This approach is adequate for large scale problems, like the simulation of time dependent differential equations, where it is necessary to solve consecutively several linear systems with the same coefficient matrix (or with matrices that present very close spectral properties) but with changing right-hand sides. To compute the spectral information, in the first phase, we combine the block Conjugate Gradient algorithm with the Inexact Subspace Iteration to build a purely iterative algorithm, that we call BlockCGSI. We proceed to an inner-outer convergence analysis and we show that it is possible to determine when to stop the inner iteration in order to achieve the targeted invariance in the outer iteration. The spectral information is used in a second phase to remove the effect of the smallest eigenvalues in two different ways: either by building a Spectral Low Rank Update preconditioner, or by performing a deflation of the initial residual in order to remove part of the solution corresponding to the smallest eigenvalues.
- Linear and nonlinear models in wind resource assessment and wind turbine micro-siting in complex terrainPublication . Palma, J.M.L.M.; Castro, Fernando A.; Ribeiro, Luís Frölén; Rodrigues, Álvaro H.; Pinto, A.P.The current trend of increasing the electricity production from wind energy has led to the installation of wind farms in areas of greater orographic complexity, raising doubts on the use of simple, linear, mathematical models of the fluid flow equations, so common in the wind energy engineering. The present study shows how conventional techniques, linear models and cup anemometers, can be combined with flow simulation by computational fluid dynamics techniques (nonlinear models) and measurements by sonic anemometers, and discuss their relative merits in the characterisation of the wind over a coastal region—a cliff over the sea. The computational fluid dynamic techniques were particularly useful, providing a global view of the wind flow over the cliff and enabling the identification of separated flow regions, clearly unsuitable for installation of wind turbines. These locations display a pulsating flow, with periods between 1 and 7min, in agreement with sonic anemometer measurements, and both a turbulence intensity and a gust factor well above the wind turbine design conditions.