From 02e29e1537714a016a99304bcb8ab40e1ae825ff Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Sun, 24 May 2020 21:17:32 -0600 Subject: [PATCH] Use @cite style for references in step-70. --- doc/doxygen/references.bib | 89 +++++++++++++++++++++++++++++++--- examples/step-70/doc/intro.dox | 50 +++++++------------ 2 files changed, 98 insertions(+), 41 deletions(-) diff --git a/doc/doxygen/references.bib b/doc/doxygen/references.bib index 83841ad06a..5911337e85 100644 --- a/doc/doxygen/references.bib +++ b/doc/doxygen/references.bib @@ -673,6 +673,74 @@ year = {2008}, % Step 70 % ------------------------------------ + + +@InProceedings{Freund1995, + author = {Freund, J. and Stenberg, R.}, + title = {On weakly imposed boundary conditions for + second order problems}, + booktitle = {Proceedings of the Ninth International Conference on + Finite Elements in Fluids}, + year = 1995, + pages = {327--336}} + +@article{Angot1999, + doi = {10.1007/s002110050401}, + url = {https://doi.org/10.1007/s002110050401}, + year = {1999}, + month = feb, + publisher = {Springer Science and Business Media {LLC}}, + volume = {81}, + number = {4}, + pages = {497--520}, + author = {Philippe Angot and Charles-Henri Bruneau and Pierre Fabrie}, + title = {A penalization method to take into account obstacles in incompressible viscous flows}, + journal = {Numerische Mathematik} +} + + +@article{Glowinski1999, + doi = {10.1016/s0301-9322(98)00048-2}, + url = {https://doi.org/10.1016/s0301-9322(98)00048-2}, + year = {1999}, + month = aug, + publisher = {Elsevier {BV}}, + volume = {25}, + number = {5}, + pages = {755--794}, + author = {R. Glowinski and T.-W. Pan and T.I. Hesla and D.D. Joseph}, + title = {A distributed Lagrange multiplier/fictitious domain method for particulate flows}, + journal = {International Journal of Multiphase Flow} +} + +@article{Boffi2008, + doi = {10.1016/j.cma.2007.09.015}, + url = {https://doi.org/10.1016/j.cma.2007.09.015}, + year = {2008}, + month = apr, + publisher = {Elsevier {BV}}, + volume = {197}, + number = {25-28}, + pages = {2210--2231}, + author = {Daniele Boffi and Lucia Gastaldi and Luca Heltai and Charles S. Peskin}, + title = {On the hyper-elastic formulation of the immersed boundary method}, + journal = {Computer Methods in Applied Mechanics and Engineering} +} + + +@article{Heltai2012, + doi = {10.1016/j.cma.2012.04.001}, + url = {https://doi.org/10.1016/j.cma.2012.04.001}, + year = {2012}, + month = jul, + publisher = {Elsevier {BV}}, + volume = {229-232}, + pages = {110--127}, + author = {Luca Heltai and Francesco Costanzo}, + title = {Variational implementation of immersed finite element methods}, + journal = {Computer Methods in Applied Mechanics and Engineering} +} + @article{Riviere1999, doi = {10.1023/a:1011591328604}, url = {https://doi.org/10.1023/a:1011591328604}, @@ -682,7 +750,8 @@ year = {2008}, number = {3/4}, pages = {337--360}, author = {B{\'{e}}atrice Rivi{\`{e}}re and Mary F. Wheeler and Vivette Girault}, - journal = {Computational Geosciences} + journal = {Computational Geosciences}, + title = {Improved energy estimates for interior penalty, constrained and discontinuous {G}alerkin methods for elliptic problems. {P}art {I}}. } % ------------------------------------ @@ -714,13 +783,17 @@ year = {2008}, } @article{GLHPW2018, - title={Flexible and Scalable Particle-in-Cell Methods With Adaptive Mesh Refinement for Geodynamic Computations}, - author={Gassm{\"o}ller, Rene and Lokavarapu, Harsha and Heien, Eric and Puckett, Elbridge Gerry and Bangerth, Wolfgang}, - journal={Geochemistry, Geophysics, Geosystems}, - volume={19}, - number={9}, - pages={3596--3604}, - year={2018} + doi = {10.1029/2018gc007508}, + url = {https://doi.org/10.1029/2018gc007508}, + year = {2018}, + month = sep, + publisher = {American Geophysical Union ({AGU})}, + volume = {19}, + number = {9}, + pages = {3596--3604}, + author = {Rene Gassm\"{o}ller and Harsha Lokavarapu and Eric Heien and Elbridge Gerry Puckett and Wolfgang Bangerth}, + title = {Flexible and Scalable Particle-in-Cell Methods With Adaptive Mesh Refinement for Geodynamic Computations}, + journal = {Geochemistry, Geophysics, Geosystems} } @TechReport{Saad1991, diff --git a/examples/step-70/doc/intro.dox b/examples/step-70/doc/intro.dox index 48089972a1..1492e7d508 100644 --- a/examples/step-70/doc/intro.dox +++ b/examples/step-70/doc/intro.dox @@ -84,7 +84,7 @@ to as $\mathcal{L}^2$ penalization whereas if the penalization depends on both the velocity and its gradient, it is an $\mathcal{H}^1$ penalization. The case of the $\mathcal{L}^2$ penalization is very similar to a Darcy-type approach. Both $\mathcal{L}^2$ and $\mathcal{H}^1$ penalizations have been -analyzed extensively (see, for example, Angot 1999). +analyzed extensively (see, for example, @cite Angot1999). - The embedded domain $\Gamma$ has an intrinsic dimension `dim` which is smaller than that of $\Omega$ (`spacedim`), thus its spacedim-dimensional measure is @@ -93,8 +93,9 @@ surface embedded in a three-dimensional domain. This is of course physically impossible, but one may consider very thin sheets of metal moving in a fluid as essentially lower-dimensional if the thickness of the sheet is negligible. In this case, the boundary -condition is imposed weakly on $\Gamma$ by applying the Nitsche method (see -Freund, 1995). +condition is imposed weakly on $\Gamma$ by applying the +Nitsche method (see +@cite Freund1995). Both approaches have very similar requirements and result in highly similar formulations. Thus, we treat them almost in the same way. @@ -199,8 +200,8 @@ on the fluid domain, where no strong conditions on the test functions on $\Gamma + \beta (\textbf{v},\textbf{g})_{\Gamma}. @f} -The integrals over $\Gamma$ are lower-dimensional integrals. It can be shown (see Freund, -1995) that there exists a positive constant +The integrals over $\Gamma$ are lower-dimensional integrals. It can be shown (see +@cite Freund1995) that there exists a positive constant $C_1$ so that if $\beta > C_1$, the weak imposition of the boundary will be consistent and stable. The first two additional integrals on $\Gamma$ (the second line in the equation above) appear naturally after integrating by parts, @@ -461,8 +462,8 @@ attached to the solid material, they can be idealized as a set of disconnected infinitesimally small "particles", which carry the required `JxW` information with the movement of the solid. deal.II has the ability to distribute and store such a set of particles in large-scale parallel computations in the form of -the ParticleHandler class (for details on the implementation see Gassmöller et -al., 2018), and we will make use of this functionality in this tutorial. +the ParticleHandler class (for details on the implementation see @cite GLHPW2018), +and we will make use of this functionality in this tutorial. Thus, the approach taken in this step is as follows: - Create a parallel::distributed::Triangulation for the domain $\Gamma$; @@ -521,31 +522,14 @@ case, this is illustrated by inserting a circle of passive tracer particles that are advected by the fluid and which return to their original position, thus demonstrating the time-reversibility of the flow. -

References

- +This tutorial program uses a number of techniques on imposing velocity +conditions on non-matching interfaces in the interior of the fluid. +For more background material, you may want to look up the following references: +@cite Freund1995, +@cite Angot1999, +@cite Glowinski1999, +@cite Boffi2008, +@cite Heltai2012. -- 2.39.5