2013
DOI: 10.1137/120902690
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A Flexible Krylov Solver for Shifted Systems with Application to Oscillatory Hydraulic Tomography

Abstract: We discuss efficient solutions to systems of shifted linear systems arising in computations for oscillatory hydraulic tomography (OHT). The reconstruction of hydrogeological parameters such as hydraulic conductivity and specific storage using limited discrete measurements of pressure (head) obtained from sequential oscillatory pumping tests, leads to a nonlinear inverse problem. We tackle this using the quasi-linear geostatistical approach [15]. This method requires repeated solution of the forward (and adjoin… Show more

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Cited by 39 publications
(81 citation statements)
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“…We present a combination of inner FOM and outer GMRES in Algorithm 3. Therefore, the collinearity factor for the inner Krylov method (multishift FOM) is given by (20) without any further manipulations. When combining multishift IDR(s) and QMRIDR(s) as presented in Algorithm 4, a new variant of IDR(s) has been developed which leads to collinear residuals with collinearity factor given by (27), cf.…”
Section: Resultsmentioning
confidence: 99%
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“…We present a combination of inner FOM and outer GMRES in Algorithm 3. Therefore, the collinearity factor for the inner Krylov method (multishift FOM) is given by (20) without any further manipulations. When combining multishift IDR(s) and QMRIDR(s) as presented in Algorithm 4, a new variant of IDR(s) has been developed which leads to collinear residuals with collinearity factor given by (27), cf.…”
Section: Resultsmentioning
confidence: 99%
“…Most recently, multiple shift-and-invert preconditioners have been applied within a flexible GMRES iteration, cf. [10,20]. Since even the one-time application of a shift-and-invert preconditioner can be computationally costly, polynomial preconditioners have been developed for shifted problems in [1].…”
Section: Discussionmentioning
confidence: 99%
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