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This paper provides an overview of the new features of the finite element library deal.II, version 9.6. 

This work studies three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening (both h -multigrid), and polynomial global coarsening (a variant of p -multigrid). We have integrated the algorithms into the same framework—the open source finite-element library deal.II —, which allows us to make fair comparisons regarding their implementation complexity, computational efficiency, and parallel scalability as well as to compare the measurements with theoretically derived performance metrics. Serial simulations and parallel weak and strong scaling on up to 147,456 CPU cores on 3,072 compute nodes are presented. The results obtained indicate that global-coarsening algorithms show a better parallel behavior for comparable smoothers due to the better load balance, particularly on the expensive fine levels. In the serial case, the costs of applying hanging-node constraints might be significant, leading to advantages of local smoothing, even though the number of solver iterations needed is slightly higher. When using p - and h -multigrid in sequence ( hp -multigrid), the results indicate that it makes sense to decrease the degree of the elements first from a performance point of view due to the cheaper transfer. 

Abstract. Due to the increasing availability of high-performance computing over the past few decades, numerical models have become an important tool for research in geodynamics.Several generations of mantle convection software have been developed, but due to their differing methods and increasing complexity it is important to evaluate the accuracy of each new model generation to ensure published geodynamic research is reliable and reproducible.Here we explore the accuracy of the open-source, finite-element codes ASPECT and CitcomS as a function of mesh spacing using low to moderate-Rayleigh-number models in steady-state thermal convection.ASPECT (Advanced Solver for Problems in Earth's ConvecTion) is a new-generation mantle convection code that enables modeling global mantle convection with realistic parameters and complicated physical processes using adaptive mesh refinement (Kronbichler et al., 2012; Heister et al., 2017).We compare the ASPECT results with calculations from the finite-element code CitcomS (Zhong et al., 2000; Tan et al., 2006; Zhong et al., 2008), which has a long history of use in the geodynamics community.We find that the globally averaged quantities, i.e., root-mean-square (rms) velocity, mean temperature, and Nusselt number at the top and bottom of the shell, agree to within 1 % (and often much better) for calculations with sufficient mesh resolution.We also show that there is excellent agreement of the time evolution of both the rms velocity and the Nusselt numbers between the two codes for otherwise identical parameters.Based on our results, we are optimistic that similar agreement would be achieved for calculations performed at the convective vigor expected for Earth, Venus, and Mars. 

We are pleased to announce the release of ASPECT 2.5.0. ASPECT is the Advanced Solver for Problems in Earth's ConvecTion. It uses modern numerical methods such as adaptive mesh refinement, multigrid solvers, and a modular software design to provide a fast, flexible, and extensible mantle convection solver. ASPECT is available from https://aspect.geodynamics.org/ and the release is available from https://geodynamics.org/resources/aspect and https://github.com/geodynamics/aspect/releases/tag/v2.5.0 Among others this release includes the following significant changes: ASPECT now includes version 0.5.0 of the Geodynamic World Builder. (Menno Fraters and other contributors) ASPECT's manual has been converted from LaTeX to Markdown to be hosted as a website at https://aspect-documentation.readthedocs.io. (Chris Mills, Mack Gregory, Timo Heister, Wolfgang Bangerth, Rene Gassmoeller, and many others) New: ASPECT now requires deal.II 9.4 or newer. (Rene Gassmoeller, Timo Heister) ASPECT now supports a DebugRelease build type that creates a debug build and a release build of ASPECT at the same time. It can be enabled by setting the CMake option CMAKE_BUILD_TYPE to DebugRelease or by typing "make debugrelease". (Timo Heister) ASPECT now has a CMake option ASPECT_INSTALL_EXAMPLES that allows building and install all cookbooks and benchmarks. ASPECT now additionally installs the data/ directory. Both changes are helpful for installations that are used for teaching and tutorials. (Rene Gassmoeller) Changed: ASPECT now releases the memory used for storing initial conditions and the Geodynamic World Builder after model initialization unless an owning pointer to these objects is kept. This reduces the memory footprint for models initialized from large data files. (Wolfgang Bangerth) Added: Various helper functions to distinguish phase transitions for different compositions and compositional fields of different types. (Bob Myhill) Added: The 'adiabatic' initial temperature plugin can now use a spatially variable top boundary layer thickness read from a data file or specified as a function in the input file. Additionally, the boundary layer temperature can now also be computed following the plate cooling model instead of the half-space cooling model. (Daniel Douglas, John Naliboff, Juliane Dannberg, Rene Gassmoeller) New: ASPECT now supports tangential velocity boundary conditions with GMG for more geometries, such as 2D and 3D chunks. (Timo Heister, Haoyuan Li, Jiaqi Zhang) New: Phase transitions can now be deactivated outside a given temperature range specified by upper and lower temperature limits for each phase transition. This allows implementing complex phase diagrams with transitions that intersect in pressure-temperature space. (Haoyuan Li) New: There is now a postprocessor that outputs the total volume of the computational domain. This can be helpful for models using mesh deformation. (Anne Glerum) New: Added a particle property 'grain size' that tracks grain size evolution on particles using the 'grain size' material model. (Juliane Dannberg, Rene Gassmoeller) Fixed: Many bugs, see link below for a complete list. (Many authors. Thank you!). A complete list of all changes and their authors can be found at https://aspect.geodynamics.org/doc/doxygen/changes_between_2_84_80_and_2_85_80.html Wolfgang Bangerth, Juliane Dannberg, Menno Fraters, Rene Gassmoeller, Anne Glerum, Timo Heister, Bob Myhill, John Naliboff, and many other contributors. 

Abstract This paper provides an overview of the new features of the finite element library deal.II, version 9.4. 

Abstract This paper provides an overview of the new features of the finite element library deal.II , version 9.5.