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z;~16<9_)W)&A;XGz)*~#Y*PpO_9JR}BSMC&eg3-+9c((dN-$y8{M$HJ?m%nF#a`Mw zh8C6(C#KU?wU9UlrIZkQwlIgwGhVKcZ%#gm`U$*l%0Rj&t%Nk=%qoF9Sh# z`Wa3>p)?{>Eagd&a3jx$;o(*AXhwG$1pZC^!tndypLL_J1;&JbCqEP` z4w#8HjD8)iC7oCUE<-3j$L_l3sQ&GMY!_d!fOs!D-==_9`AV`MKmSbY#RiM)d^eXV zWed#@3!SEJH)S>XB5`#E#|f`bFE9zVFiF|oqqP`*D_#14w%8FV$olw2xKN=XbHpQa t**ccbZF4-!ET@Z{GXLJIf&Yn-C~sgXPaq@+Tse42jNrlrC2eJb{{yr!IDY^D literal 0 HcmV?d00001 From 32aea0f58a26d6817030f689856f99d6b481bdc2 Mon Sep 17 00:00:00 2001 From: The Open Journals editorial robot <89919391+editorialbot@users.noreply.github.com> Date: Mon, 11 Dec 2023 16:31:47 +0000 Subject: [PATCH 2/7] Creating 10.21105.joss.05979.crossref.xml --- joss.05979/10.21105.joss.05979.crossref.xml | 172 ++++++++++++++++++++ 1 file changed, 172 insertions(+) create mode 100644 joss.05979/10.21105.joss.05979.crossref.xml diff --git a/joss.05979/10.21105.joss.05979.crossref.xml b/joss.05979/10.21105.joss.05979.crossref.xml new file mode 100644 index 0000000000..cb1dc5e3db --- /dev/null +++ b/joss.05979/10.21105.joss.05979.crossref.xml @@ -0,0 +1,172 @@ + + + + 20231211T163126-524309b25d53e003319613c3ba9b5cbfe680c7f0 + 20231211163126 + + JOSS Admin + admin@theoj.org + + The Open Journal + + + + + Journal of Open Source Software + JOSS + 2475-9066 + + 10.21105/joss + https://joss.theoj.org + + + + + 12 + 2023 + + + 8 + + 92 + + + + GECo: A collection of solvers for the self-gravitating +Vlasov equations + + + + Ellery + Ames + https://orcid.org/0000-0001-9444-585X + + + Anders + Logg + https://orcid.org/0000-0002-1547-4773 + + + + 12 + 11 + 2023 + + + 5979 + + + 10.21105/joss.05979 + + + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + + + + Software archive + 10.5281/zenodo.10351519 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/5979 + + + + 10.21105/joss.05979 + https://joss.theoj.org/papers/10.21105/joss.05979 + + + https://joss.theoj.org/papers/10.21105/joss.05979.pdf + + + + + + Automated Solution of Differential Equations +by the Finite Element Method + 84 + 10.1007/978-3-642-23099-8 + 978-3-642-23099-8 + 2012 + Logg, A., Mardal, K.-A., & Wells, +G. (Eds.). (2012). Automated Solution of Differential Equations by the +Finite Element Method (Vol. 84). Springer Berlin Heidelberg. +https://doi.org/10.1007/978-3-642-23099-8 + + + On axisymmetric and stationary solutions of +the self-gravitating Vlasov system + Ames + Class. Quantum Grav. + 15 + 33 + 10.1088/0264-9381/33/15/155008 + 2016 + Ames, E., Andréasson, H., & Logg, +A. (2016). On axisymmetric and stationary solutions of the +self-gravitating Vlasov system. Class. Quantum Grav., 33(15), 155008. +https://doi.org/10.1088/0264-9381/33/15/155008 + + + The Einstein-Vlasov System/Kinetic +Theory + Andréasson + Living Reviews in Relativity + 14 + 10.12942/lrr-2011-4 + 2011 + Andréasson, H. (2011). The +Einstein-Vlasov System/Kinetic Theory. Living Reviews in Relativity, 14. +https://doi.org/10.12942/lrr-2011-4 + + + Cosmic string and black hole limits of +toroidal Vlasov bodies in general relativity + Ames + Physical review D + 2 + 99 + 10.1103/PhysRevD.77.124044 + 2019 + Ames, E., Andréasson, H., & Logg, +A. (2019). Cosmic string and black hole limits of toroidal Vlasov bodies +in general relativity. Physical Review D, 99(2), 024012. +https://doi.org/10.1103/PhysRevD.77.124044 + + + Galactic Dynamics: Second +Edition + Binney + 0691130264 + 2008 + Binney, J., & Tremaine, S. +(2008). Galactic Dynamics: Second Edition. Princeton University Press. +ISBN: 0691130264 + + + Anderson acceleration for fixed-point +iterations + Walker + SIAM Journal of Numerical +Analysis + 49 + 10.1137/10078356X + 2011 + Walker, H. F., & Ni, P. (2011). +Anderson acceleration for fixed-point iterations. SIAM Journal of +Numerical Analysis, 49, 1715. +https://doi.org/10.1137/10078356X + + + + + + From d0ad19dfee4ab0b378601e781b2e3b9e0d877f82 Mon Sep 17 00:00:00 2001 From: The Open Journals editorial robot <89919391+editorialbot@users.noreply.github.com> Date: Mon, 11 Dec 2023 16:31:47 +0000 Subject: [PATCH 3/7] Creating 10.21105.joss.05979.jats --- joss.05979/10.21105.joss.05979.jats | 356 ++++++++++++++++++++++++++++ 1 file changed, 356 insertions(+) create mode 100644 joss.05979/10.21105.joss.05979.jats diff --git a/joss.05979/10.21105.joss.05979.jats b/joss.05979/10.21105.joss.05979.jats new file mode 100644 index 0000000000..979f998a55 --- /dev/null +++ b/joss.05979/10.21105.joss.05979.jats @@ -0,0 +1,356 @@ + + +
+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +5979 +10.21105/joss.05979 + +GECo: A collection of solvers for the self-gravitating +Vlasov equations + + + +https://orcid.org/0000-0001-9444-585X + +Ames +Ellery + + + + +https://orcid.org/0000-0002-1547-4773 + +Logg +Anders + + + + + +Flax and Teal + + + + +Chalmers University of Technology + + + + +20 +9 +2023 + +8 +92 +5979 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +Einstein-Vlasov + + + + + + Summary +

Gothenburgh Einstein solver Collection (GECo) is a collection of + solvers for stationary self-gravitating collisionless kinetic (Vlasov) + matter. The gravitational interaction may be taken to be either + Newtonian or general relativistic. GECo is focused on the solutions + which are axisymmetric, meaning that the gravitational and matter + fields have a rotational symmetry. In this setting stationary + solutions may be generated with the choice of a particular ansatz + function for the Vlasov distribution function. GECo allows users to + easily introduce new ansatz functions and explore the properties of + the resulting stationary solutions.

+
+ + Statement of need +

In understanding a physical model one usually starts with a + simplified setting, such as by imposing symmetry assumptions. In the + case of self-gravitating kinetic matter, stationary solutions in the + spherically symmetric setting are well understood + (Andréasson, + 2011; + Binney + & Tremaine, 2008). However, many of the physical systems of + interest such as accretion disks, galaxies, galaxy clusters and so on, + require models beyond spherical symmetry. When going beyond spherical + symmetry, the coupled and nonlinear PDE systems in high dimensions – + such as the self-gravitating Vlasov equations – are difficult to + investigate analytically, and numerical approaches are essential to + understand behavior of solutions and to answer questions of physical + and mathematical interest. The GECo code started with the desire to + understand properties of stationary and axisymmetric solutions of the + Einstein-Vlasov system.

+
+ + Method and implementation +

To construct stationary solutions, the code relies on a reduction + method in which the distribution function for the matter is assumed to + depend on the position and momentum phase-space coordinates solely + through conserved quantities, such as the particle energy and angular + momentum about the axis of symmetry. With this ansatz the + Einstein–Vlasov or Vlasov–Poisson system (depending on the + gravitational model used) forms a semi-linear integro-differential + system of equations. In GECo, the form of the ansatz is called a + MaterialModel and several different choices are + implemented as subclasses of the FEniCS/DOLFIN Expression class. The + semi-linear integro-differential system is solved via a + mass-preserving fixed point scheme using Anderson acceleration + (Walker + & Ni, 2011). At each step of the fixed point method, the + linear system of equations is solved using finite elements implemented + with the FEniCS toolkit + (Logg + et al., 2012). The computational domain is taken to be the + half-meridional plane + 0, z>0 \}]]> + {(r,z):r>0,z>0} + in cylindrical coordinates, with a semi-circular outer boundary; see + [fig:Solution]. + Details of the mathematical formulation and implementation can be + found in + (Ames + et al., 2016)

+
+ + Functionality +

The entrypoint for GECo is a run script written in Python. In this + file, the user selects the solver class + (EinsteinVlasovSolver or + VlasovPoisson) that specifies the model for the + gravitational interaction, a MaterialModel to + specify the particular form of the reduction ansatz, and several + parameters related to the model and discretization. Calling the + solve method within the script invokes the + solver to construct a stationary solution via the fixed point scheme + mentioned above, which runs until convergence within a specified + tolerance. Gravitational fields and matter quantities are saved in + XMDF and XML format that can be consumed by visualization software + like Paraview and VisIT, as well as postprocessing scripts. + Multi-component solutions may be constructed from multiple + MaterialModels by combining models in a + weighted sum.

+

GECo includes several postprocessing routines that:

+ + +

generate additional scalar data not computed during the fixed + point iteration;

+
+ +

represent the matter density as well as an ergoregion (if + present) in + + 2 + (i.e. reflected about the reflection plane and symmetry axis), as + shown in + [fig:2Ddensity];

+
+ +

represent the matter density as well as an ergoregion (if + present) as a volume in + + 3, + facilitating visualization of contours, as shown in + [fig:3Ddensity];

+
+ +

represent the density as a three-dimensional point cloud, as + shown in + [fig:PointCloud];

+
+ +

compute the Kretschmann curvature scalar.

+
+
+ +

Computed spatial density of torus solution on the + quarter plane computational domain. +

+ +
+ +

Computed spatial density of torus solution extended to + + + xy-plane. +

+ +
+ +

Computed spatial density of torus solution visualized as + iso surfaces in 3D. +

+ +
+ +

Computed spatial density of torus solution visualized as + a point cloud. +

+ +
+
+ + Documentation +

The documentation for GECo is published on the + GECo + GitHub pages.

+
+ + Limitations and future work +

We briefly list a few directions of interest for future work.

+ + +

GECo currently uses a uniform mesh. However, in axisymmetry + (unlike spherical symmetry) the solution is not uniquely defined + outside the support of the matter, and asymptotically flat + boundary conditions must be applied sufficiently far from the + matter. An adaptive mesh refinement algorithm was developed and + used in + (Ames + et al., 2019) to investigate properties of extreme rotating + toroidal solutions. It remains however to integrate such an + adaptive mesh refinement scheme into the core of GECo.

+
+ +

Currently the particles only interact via the gravitational + field generated by the particle distribution. An exciting area at + the frontier of astrophysics currently is the study of accretion + disks, where both central black holes and electromagnetic fields + play important roles. To lay groundwork for this area in + fundamental relativity, it is thus highly desirable to extend GECo + to the Einstein-Vlasov-Maxwell system and allow the inclusion of + central black holes.

+
+ +

While multi-species solutions can be generated in which the + different species follow different distribution ansatzes, the + particle properties are otherwise taken to be the same. + Astrophysical systems however often consist of particle-like + entities with very different properties (such as stars and dust). + We thus propose to allow different particle species to have + different particle properties such as mass and charge.

+
+
+
+ + + + + + Automated Solution of Differential Equations by the Finite Element Method + + LoggAnders + MardalKent-Andre + WellsGarth + + Springer Berlin Heidelberg + Berlin, Heidelberg + 2012 + 84 + 978-3-642-23099-8 + 10.1007/978-3-642-23099-8 + + + + + + AmesEllery + AndréassonHåkan + LoggAnders + + On axisymmetric and stationary solutions of the self-gravitating Vlasov system + Class. Quantum Grav. + IOP Publishing + 201607 + 33 + 15 + 10.1088/0264-9381/33/15/155008 + 155008 + + + + + + + AndréassonHåkan + + The Einstein-Vlasov System/Kinetic Theory + Living Reviews in Relativity + 2011 + 14 + 10.12942/lrr-2011-4 + + + + + + AmesEllery + AndréassonHåkan + LoggAnders + + Cosmic string and black hole limits of toroidal Vlasov bodies in general relativity + Physical review D + 201901 + 99 + 2 + 10.1103/PhysRevD.77.124044 + 024012 + + + + + + + BinneyJames + TremaineScott + + Galactic Dynamics: Second Edition + Princeton University Press + 2008 + 0691130264 + + + + + + WalkerHomer F. + NiPeng + + Anderson acceleration for fixed-point iterations + SIAM Journal of Numerical Analysis + 2011 + 49 + 10.1137/10078356X + 1715 + + + + + +
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