The deal.II finite element library: design, features, and insights

Abstract

deal.II is a state-of-the-art finite element library focused on generality, dimension-independent programming, parallelism, and extensibility. Herein, we outline its primary design considerations and its sophisticated features such as distributed meshes, $hp$-adaptivity, support for complex geometries, and matrix-free algorithms. But deal.II is more than just a software library: It is also a diverse and worldwide community of developers and users, as well as an educational platform. We therefore also discuss some of the technical and social challenges and lessons learned in running a large community software project over the course of two decades.

36 pages, 3 figures

References in corpus (4)

• DFT-FE -- A massively parallel adaptive finite-element code for large-scale density functional theory calculations
• Fast matrix-free evaluation of discontinuous Galerkin finite element operators
• OCCA: A unified approach to multi-threading languages
• A performance comparison of continuous and discontinuous Galerkin methods with fast multigrid solvers

Cited by in corpus (48)

• preCICE v2: A Sustainable and User-Friendly Coupling Library
• lifex: a flexible, high performance library for the numerical solution of complex finite element problems
• An electromechanics-driven fluid dynamics model for the simulation of the whole human heart
• Linking ghost penalty and aggregated unfitted methods
• A Flexible, Parallel, Adaptive Geometric Multigrid method for FEM
• A barrier method for frictional contact on embedded interfaces
• On the implementation of a robust and efficient finite element-based parallel solver for the compressible Navier-Stokes equations
• A phase-field model for quasi-dynamic nucleation, growth, and propagation of rate-and-state faults
• Effective continuum models for the buckling of non-periodic architected sheets that display quasi-mechanism behaviors
• MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs
• GALÆXI: Solving complex compressible flows with high-order discontinuous Galerkin methods on accelerator-based systems
• Propagating geometry information to finite element computations
• A stable loosely-coupled scheme for cardiac electro-fluid-structure interaction
• High-order arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for the incompressible Navier-Stokes equations
• Crack opening calculation in phase-field modeling of fluid-filled fracture: A robust and efficient strain-based method
• Space-time formulation, discretization, and computational performance studies for phase-field fracture optimal control problems
• A Deep Learning algorithm to accelerate Algebraic Multigrid methods in Finite Element solvers of 3D elliptic PDEs
• Biaxial characterization of soft elastomers: experiments and data-adaptive configurational forces for fracture
• Multiscale modeling of fiber reinforced materials via non-matching immersed methods
• Calibration and Validation of a Phase-Field Model of Brittle Fracture within the Damage Mechanics Challenge
• A modified combined active-set Newton method for solving phase-field fracture into the monolithic limit
• A Posteriori Single- and Multi-Goal Error Control and Adaptivity for Partial Differential Equations
• Exploiting high-contrast Stokes preconditioners to efficiently solve incompressible fluid-structure interaction problems
• Global existence of classical solutions and numerical simulations of a cancer invasion model
• A posteriori estimator for the adaptive solution of a quasi-static fracture phase-field model with irreversibility constraints
• Structure-preserving finite-element schemes for the Euler-Poisson equations
• Algorithms for Parallel Generic $hp$-adaptive Finite Element Software
• Smoothers with localized residual computations for geometric multigrid methods
• High-accuracy numerical models of Brownian thermal noise in thin mirror coatings
• Hyperbolic Diffusion in Flux Reconstruction: Optimisation through Kernel Fusion within Tensor-Product Elements
• A computational study of nematic core structure and disclination interactions in elastically anisotropic nematics
• Sapphire++: A particle transport code combining a spherical harmonic expansion and the discontinuous Galerkin method
• Constriction of actin rings by passive crosslinkers
• R3MG: R-tree based agglomeration of polytopal grids with applications to multilevel methods
• Model hierarchies and higher-order discretisation of time-dependent thin-film free boundary problems with dynamic contact angle
• Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems
• Lorentz Resonance in the Homogenization of Plasmonic Crystals
• An HPC-Based Hydrothermal Finite Element Simulator for Modeling Underground Response to Community-Scale Geothermal Energy Production
• Learning Hidden Physics and System Parameters with Deep Operator Networks
• A cross-diffusion system modelling rivaling gangs: global existence of bounded solutions and FCT stabilization for numerical simulation
• Physics-Based Modeling and Predictive Simulation of Powder Bed Fusion Additive Manufacturing Across Length Scales
• Phase-field modeling of rock fractures with roughness
• Scalable augmented Lagrangian preconditioners for fictitious domain problems
• Scalar Quasi-Normal Modes in Black Hole Gravitational Lensing
• Deciphering the gamma-ray emission in the Cygnus region
• Parallel simulation and adaptive mesh refinement for 3D elastostatic contact mechanics problems between deformable bodies
• Improving Interoperability in Scientific Computing via MaRDI Open Interfaces
• Numerical Calculation of Electric Field Enhancement in Neutron Traps with Rough Walls Coated with Superfluid Helium