diff --git a/paper.bib b/paper.bib index 16887cf..4172da6 100644 --- a/paper.bib +++ b/paper.bib @@ -69,7 +69,7 @@ @article{conde2017implicit @inproceedings{2018_wso, - Author = {Ketcheson, David and Seibold, Benjamin and Shirokoff, David and Zhou, Dong}, + Author = {Ketcheson, David I. and Seibold, Benjamin and Shirokoff, David and Zhou, Dong}, Booktitle = {Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018}, Editor = {Sherwin, Spencer et. al.w}, Title = {DIRK Schemes with High Weak Stage Order}, @@ -209,3 +209,25 @@ @article{conde2018embedded journal={arXiv preprint arXiv:1806.08693}, year={2018} } + +@article{vermeire2019optimal, + title={Optimal {R}unge--{K}utta schemes for pseudo time-stepping with + high-order unstructured methods}, + author={Vermeire, Brian C and Loppi, Niki A and Vincent, Peter E}, + journal={Journal of Computational Physics}, + volume={383}, + pages={55--71}, + year={2019}, + publisher={Elsevier}, + doi={10.1016/j.jcp.2019.01.003} +} + +@article{vermeire2020optimal, + title={Optimal embedded pair {R}unge--{K}utta schemes for pseudo-time stepping}, + author={Vermeire, Brian C and Loppi, Niki A and Vincent, Peter E}, + journal={Journal of Computational Physics}, + pages={109499}, + year={2020}, + publisher={Elsevier}, + doi={10.1016/j.jcp.2020.109499} +} diff --git a/paper.md b/paper.md index 370a5aa..fe70b69 100644 --- a/paper.md +++ b/paper.md @@ -44,7 +44,7 @@ The original (and still primary) focus of the package is on the design of Runge-Kutta methods, but some routines for designing other classes of methods are also included. -# Statement of need +# Statement of need Over the last several decades, a great deal of work has gone into the design of numerical ODE solvers. Initially this work was aimed at developing general @@ -129,14 +129,14 @@ enabling its efficient solution for methods with many steps. # Related research and software -`RK-Opt` development has proceeded in close connection to the `NodePy` package. -Whereas `RK-Opt` is focused on the design of numerical methods, `NodePy` is focused +`RK-Opt` development has proceeded in close connection to the `NodePy` package (https://github.com/ketch/NodePy). +Whereas `RK-Opt` is focused on the design of numerical methods, `NodePy` is focused more on their analysis. A common workflow involves generating new methods with `RK-Opt` and then studying their properties in more detail using `NodePy`. Some of the research projects that have made use of `RK-Opt` include development of: - - SSP Runge-Kutta methods + - SSP Runge-Kutta methods [@2008_explicit_ssp;@2009_implicit_ssp;@gottlieb2015optimal] - SSP linear multistep methods [@2009_monotonicity] - SSP general linear methods [@2011_tsrk;@2017_msrk] @@ -145,10 +145,11 @@ Some of the research projects that have made use of `RK-Opt` include development - Optimal Runge-Kutta stability polynomials [@2012_optimal_stability_polynomials] - Additive and downwind SSP Runge-Kutta methods [@2011_dwssp;@2018_perturbations] - Optimal Runge-Kutta methods for specific PDE semi-discretizations [@parsani-eccomas;@Parsani_finnish;@2013_sd_erk;@2014_ssp_rkdg] + - Optimal Runge-Kutta methods for pseudo-time stepping [@vermeire2019optimal;@vermeire2020optimal] - Embedded pairs for Runge-Kutta methods [@conde2018embedded] - Runge-Kutta methods with high weak stage order [@2018_wso] - SSP multistage, multiderivative methods [@christlieb2016explicit;@grant2019strong;@reynoso2017strong] - + As can be seen from this list, applications have mostly stemmed from the work of the main developer's research group, but have since expanded beyond that.