%0 Journal Article %1 Rao2018Stopping %A Rao, Kaustubh %A Malan, Paul %A Perot, J. Blair %D 2018 %J Journal of Computational Physics %K 26a18-iteration 47j25-nonlinear-operators-iterative-procedures 65f10-iterative-methods-for-linear-systems 65n55-pdes-bvps-multigrid-methods-domain-decomposition %P 265--284 %R 10.1016/j.jcp.2017.09.033 %T A Stopping Criterion for the Iterative Solution of Partial Differential Equations %U http://dx.doi.org/10.1016/j.jcp.2017.09.033 %V 352 %X A stopping criterion for iterative solution methods is presented that accurately estimates the solution error using low computational overhead. The proposed criterion uses information from prior solution changes to estimate the error. When the solution changes are noisy or stagnating it reverts to a less accurate but more robust, low-cost singular value estimate to approximate the error given the residual. This estimator can also be applied to iterative linear matrix solvers such as Krylov subspace or multigrid methods. Examples of the stopping criterion's ability to accurately estimate the non-linear and linear solution error are provided for a number of different test cases in incompressible fluid dynamics.

@article{Rao2018Stopping, abstract = {{A stopping criterion for iterative solution methods is presented that accurately estimates the solution error using low computational overhead. The proposed criterion uses information from prior solution changes to estimate the error. When the solution changes are noisy or stagnating it reverts to a less accurate but more robust, low-cost singular value estimate to approximate the error given the residual. This estimator can also be applied to iterative linear matrix solvers such as Krylov subspace or multigrid methods. Examples of the stopping criterion's ability to accurately estimate the non-linear and linear solution error are provided for a number of different test cases in incompressible fluid dynamics.}}, added-at = {2019-03-01T00:11:50.000+0100}, author = {Rao, Kaustubh and Malan, Paul and Perot, J. Blair}, biburl = {https://www.bibsonomy.org/bibtex/2c2e00b63e4985948fc625ac371fee52f/gdmcbain}, citeulike-article-id = {14475083}, citeulike-attachment-1 = {rao_18_stopping_1146541.pdf; /pdf/user/gdmcbain/article/14475083/1146541/rao_18_stopping_1146541.pdf; 86400291a4b28a99d44f191066faa00bdd19e8f4}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.jcp.2017.09.033}, doi = {10.1016/j.jcp.2017.09.033}, file = {rao_18_stopping_1146541.pdf}, interhash = {13e4eeddbf678419755b64e02f81e2c5}, intrahash = {c2e00b63e4985948fc625ac371fee52f}, issn = {00219991}, journal = {Journal of Computational Physics}, keywords = {26a18-iteration 47j25-nonlinear-operators-iterative-procedures 65f10-iterative-methods-for-linear-systems 65n55-pdes-bvps-multigrid-methods-domain-decomposition}, month = jan, pages = {265--284}, posted-at = {2018-10-22 04:09:45}, priority = {5}, timestamp = {2019-03-01T00:11:50.000+0100}, title = {{A Stopping Criterion for the Iterative Solution of Partial Differential Equations}}, url = {http://dx.doi.org/10.1016/j.jcp.2017.09.033}, volume = 352, year = 2018 }