Article
Mathematics, Applied
Daniel Arndt, Wolfgang Bangerth, Bruno Blais, Marc Fehling, Rene Gassmoller, Timo Heister, Luca Heltai, Uwe Koecher, Martin Kronbichler, Matthias Maier, Peter Munch, Jean-Paul Pelteret, Sebastian Proell, Konrad Simon, Bruno Turcksin, David Wells, Jiaqi Zhang
Summary: This paper provides an overview of the new features in version 9.3 of the finite element library deal.II.
JOURNAL OF NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Daniel Arndt, Wolfgang Bangerth, Denis Davydov, Timo Heister, Luca Heltai, Martin Kronbichler, Matthias Maier, Jean-Paul Pelteret, Bruno Turcksin, David Wells
Summary: DEAL.II is a state-of-the-art finite element library that focuses on generality, dimension-independent programming, parallelism, and extensibility. It includes sophisticated features such as distributed meshes, hp-adaptivity, support for complex geometries, and matrix-free algorithms. Additionally, DEAL.II is not just a software library but also a diverse worldwide community of developers and users, serving as an educational platform.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Daniel Arndt, Wolfgang Bangerth, Maximilian Bergbauer, Marco Feder, Marc Fehling, Johannes Heinz, Timo Heister, Luca Heltai, Martin Kronbichler, Matthias Maier, Peter Munch, Jean-Paul Pelteret, Bruno Turcksin, David Wells, Stefano Zampini
Summary: This paper provides an overview of the new features introduced in version 9.5 of the finite element library deal.II.
JOURNAL OF NUMERICAL MATHEMATICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Alberto Paganini, Florian Wechsung
Summary: Fireshape is an open-source automated shape optimization toolbox designed for the finite element software Firedrake. It utilizes the moving mesh method, allowing users with minimal shape optimization knowledge to easily tackle challenging shape optimization problems constrained by partial differential equations (PDEs).
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2021)
Article
Computer Science, Software Engineering
Stefan Frei, Thomas Richter, Thomas Wick
Summary: LocModFE is a software package implementing a locally modified finite element method for accurate interface problem solutions. Originally developed in Gascoigne 3d, it has been rewritten in deal.II, making it accessible to users worldwide with potential for future extensions like parallel computing and mesh adaptivity.
Article
Computer Science, Interdisciplinary Applications
Francesc Verdugo, Santiago Badia
Summary: This paper presents the software design of Gridap, a finite element library written in Julia. Gridap provides various discretization techniques for numerical approximation of mathematical models governed by Partial Differential Equations (PDEs). The library leverages Julia's just-in-time compiler to build efficient code for specific problems, eliminating the need for different languages for back-end and front-end. Gridap also offers a low-level API that is modular and extensible. The main contributions of this paper are the introduction of novel software abstractions and a performance comparison with FEniCS, demonstrating comparable performance.
COMPUTER PHYSICS COMMUNICATIONS
(2022)
Article
Mathematics, Applied
Daniel Arndt, Wolfgang Bangerth, Marco Feder, Marc Fehling, Rene Gassmoller, Timo Heister, Luca Heltai, Martin Kronbichler, Matthias Maier, Peter Munch, Jean-Paul Pelteret, Simon Sticko, Bruno Turcksin, David Wells
Summary: This paper mainly provides an overview of the new features of the finite element library deal.II, version 9.4.
JOURNAL OF NUMERICAL MATHEMATICS
(2022)
Article
Mathematics, Applied
Santiago Badia, Eric Neiva, Francesc Verdugo
Summary: This work presents a novel formulation for solving partial differential equations using finite element methods on unfitted meshes, showing enhanced stability and convergence results with the aggregated finite element method. By modifying the definition of extension operators, the proposed method achieves stable and convergent high-order approximations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
Nicolas Barnafi, Gabriel N. Gatica, Daniel E. Hurtado, Willian Miranda, Ricardo Ruiz-Baier
Summary: This work presents new primal and dual-mixed finite element methods for deformable image registration, considering the continuity of the similarity measure and ellipticity of the regularizer. By modifying the original model to incorporate additional degrees of freedom from the regularizer's kernel, ellipticity is granted on the entire solution space. The well-posedness of extended formulations and error estimates with convergence rates are proven, with numerical examples demonstrating the efficiency of the methods in registration tasks, particularly for translations and rotations.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2021)
Article
Computer Science, Software Engineering
Georgios Papanikos, Catherine E. Powell, David J. Silvester
Summary: IFISS is a MATLAB finite element software package for studying strategies for solving partial differential equations. IFISS3D is a new add-on toolbox that extends the capabilities of IFISS to three-dimensional elliptic PDEs. This open-source MATLAB framework provides a computational laboratory for experimentation and exploration of finite element approximation and error estimation, as well as iterative solvers. It is an important teaching tool and resource for researchers.
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
(2023)
Article
Mechanics
Jie Yang, Ping Li, Yi Zhang, Yanchuan Hui, Lihua Xu, Noureddine Damil, Heng Hu
Summary: The coupling of model-free data-driven computing and model-driven computing has recently been proposed to combine data-driven and traditional finite element methods in the same mesh. This article aims to prove that these two computing methods can share the same distance-based functional and can be freely converted to each other, providing the basis for data-model-coupling computing. The effectiveness of the proposed coupling strategy is demonstrated through the analysis of crack propagation problems in various composite materials and structures.
COMPOSITE STRUCTURES
(2023)
Article
Mathematics, Applied
Stefan Sauter
Summary: In this paper, the discretization of the two-dimensional stationary Stokes equation using CrouzeixRaviart elements for the velocity of polynomial order k >= 1 and discontinuous pressure approximations of order k - 1 is considered. The lower bound of the inf-sup constant is bounded independently of the mesh size and is shown to depend only logarithmically on k. The assumptions on the mesh are very mild: at least one inner vertex for odd k and more than a single triangle for even k.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Engineering, Manufacturing
Anton Evdokimov, Filip Jasiewicz, Nikolay Doynov, Ralf Ossenbrink, Vesselin Michailov
Summary: In this study, a heat source model was developed to calculate the intensity distribution on the workpiece surface based on beam and process parameters. The model's applicability was demonstrated through simulations of different laser hardening regimes.
JOURNAL OF MANUFACTURING PROCESSES
(2022)
Article
Multidisciplinary Sciences
Aline Suelen da Silva, Marcelo Henrique Lisboa Renno, Ana Clara Ribeiro Quitania, Adalberto Correa Cafe-Filho, Robert Neil Gerard Miller, Alderi Emidio de Araujo, Danilo Batista Pinho
Summary: Despite being the fourth largest cotton producer globally, Brazil's cotton yield has been affected by the incidence of ramularia leaf spot. Ramulariopsis pseudoglycines has been identified as the main causal agent of cotton RLS in Brazilian growing regions. The development of species-specific primers targeting the EF1-α gene provides an opportunity for extensive sampling worldwide to study the distribution of Ramulariopsis species.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics
Todd Arbogast, Chuning Wang
Summary: This paper introduces new families of direct serendipity and direct mixed finite elements defined on general planar, strictly convex polygons. The finite elements provide optimal approximation while using the minimal degrees of freedom. The paper proposes alternative ways to construct supplemental functions on the element, resulting in better accuracy and robustness in numerical tests.
Article
Mathematics, Applied
Andreas Rupp, Markus Gahn, Guido Kanschat
Summary: This paper introduces a general analytical framework for numerical approximation of partial differential equations (PDEs) on graphs and networks of surfaces, generalized by the term hypergraphs. By considering PDEs on hypergraphs as singular limits of PDEs on networks of thin domains, the paper proposes the use of hybrid finite element methods for formulating and solving these PDEs effectively.
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
(2022)
Article
Mathematics, Interdisciplinary Applications
Shahab Golshan, Peter Munch, Rene Gassmoeller, Martin Kronbichler, Bruno Blais
Summary: This article introduces a new open-source parallel discrete element method (DEM) software, Lethe-DEM, with load balancing capability for simulating granular materials. Several tests have been conducted to validate the feasibility and scalability of the software.
COMPUTATIONAL PARTICLE MECHANICS
(2023)
Article
Computer Science, Hardware & Architecture
Martin Kronbichler, Dmytro Sashko, Peter Munch
Summary: This work explores a variant of the conjugate gradient method and integrates it with high-order finite-element schemes, enabling fast matrix-free evaluation and cost-effective preconditioning. By utilizing data-dependency analysis and appropriate enumeration of degrees of freedom, the authors effectively optimize the CG iteration by interleaving vector updates and inner products with matrix-vector multiplication, resulting in significant performance improvements.
INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS
(2023)
Article
Mathematics, Applied
Daniel Arndt, Wolfgang Bangerth, Marco Feder, Marc Fehling, Rene Gassmoller, Timo Heister, Luca Heltai, Martin Kronbichler, Matthias Maier, Peter Munch, Jean-Paul Pelteret, Simon Sticko, Bruno Turcksin, David Wells
Summary: This paper mainly provides an overview of the new features of the finite element library deal.II, version 9.4.
JOURNAL OF NUMERICAL MATHEMATICS
(2022)
Article
Engineering, Biomedical
Jordan A. Brown, Jae H. Lee, Margaret Anne Smith, David R. Wells, Aaron Barrett, Charles Puelz, John P. Vavalle, Boyce E. Griffith
Summary: Transcatheter aortic valve replacement (TAVR) is a commonly used technique for aortic valve replacement, and computer modeling and simulation (CM&S) can assist in the design and approval process of TAVR devices. This study presents a computational fluid-structure interaction (FSI) model of TAVR using the immersed finite element-difference (IFED) method.
ANNALS OF BIOMEDICAL ENGINEERING
(2023)
Article
Mathematics, Applied
Peipei Lu, Andreas Rupp, Guido Kanschat
Summary: This article proves the uniform convergence of geometric multigrid V-cycle for hybridized discontinuous Galerkin methods, under a new set of assumptions on the injection operators. The method involves standard smoothers and local solvers, and the proofs utilize a weak version of elliptic regularity. The new assumptions allow for local injection operators on each coarse grid cell, and examples of admissible injection operators are provided.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2022)
Book Review
Information Science & Library Science
David Wells
JOURNAL OF THE AUSTRALIAN LIBRARY AND INFORMATION ASSOCIATION
(2023)
Article
Computer Science, Theory & Methods
Peter Munch, Timo Heister, Laura Prieto Saavedra, Martin Kronbichler
Summary: This work compares three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening (h-multigrid), and polynomial global coarsening (p-multigrid variant). The algorithms are integrated into the same framework-deal.II, enabling fair comparisons of implementation complexity, computational efficiency, and parallel scalability, as well as comparing with theoretical performance metrics. Serial and parallel simulations on up to 147,456 CPU cores are presented, showing that global-coarsening algorithms exhibit better parallel behavior due to improved load balance on expensive fine levels. In the serial case, the costs of applying hanging-node constraints may favor local smoothing despite slightly higher solver iterations. Results also suggest that decreasing the degree of elements first in hp-multigrid offers performance advantages due to cheaper transfer.
ACM TRANSACTIONS ON PARALLEL COMPUTING
(2023)
Article
Computer Science, Interdisciplinary Applications
David R. Wells, Ben Vadala-Roth, Jae H. Lee, Boyce E. Griffith
Summary: The IFED method is a computational approach for modeling fluid-structure interactions using finite element and finite difference techniques. This paper presents numerical and computational analyses of the effects of replacing the projection matrices in the force projection and IFED coupling operators with diagonal approximations. The results show that lumped mass matrices derived from nodal quadrature rules can be used with the IFED method, unlike standard FE methods.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Information Science & Library Science
David Wells, Anita Sallenbach
Summary: This article reviews ALIA's prediction in 2013 that library print and ebook collections would reach a 50:50 balance by 2020 and maintain it in the future, based on the experience at Curtin University Library. It revisits the findings of a 2015 article on the same topic and documents the situation at Curtin University Library as of 2022. The article describes changes in the ebook environment and user attitudes over the past 6 years, as well as developments in the Library's acquisition strategies and methods to increase ebook holdings, and provides a likely projection of the ebook and print book holdings situation at Curtin Library in 2050.
JOURNAL OF THE AUSTRALIAN LIBRARY AND INFORMATION ASSOCIATION
(2023)
Article
Computer Science, Interdisciplinary Applications
Ebrahim M. Kolahdouz, David R. Wells, Simone Rossi, Kenneth I. Aycock, Brent A. Craven, Boyce E. Griffith
Summary: This paper introduces a sharp-interface approach to simulating fluid-structure interaction involving flexible bodies. The approach combines the immersed Lagrangian-Eulerian (ILE) scheme with the immersed boundary (IB) method for better accuracy and flexibility. The paper presents the formulation, numerical approach, and validation of the algorithm through various benchmarks, including the modeling of a deformable blood clot.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Geochemistry & Geophysics
Arushi Saxena, Juliane Dannberg, Rene Gassmoeller, Menno Fraters, Timo Heister, Richard Styron
Summary: Mantle convection models provide insight into the forces driving plate motions on Earth. However, there is contradiction in existing studies on the balance of these forces and the impact of plate boundary geometry on surface deformation remains unknown. Our research shows that the plate boundary geometry of the Global Earthquake Model achieves the best fit to observed GPS data, highlighting the importance of discrete plate boundaries within oceans and distributed faults within continents.
JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH
(2023)
Article
Computer Science, Hardware & Architecture
Peter Munch, Martin Kronbichler
Summary: This contribution presents data-locality optimizations of the additive Schwarz method (ASM) based on the fast-diagonalization method defined on overlapping cell-centric and vertex-star patches in the context of high-order matrix-free finite-element computations on modern CPU-based hardware. The proposed efficient implementation of ASM adopts concepts known from cell-loop infrastructures for efficient operator evaluation, in particular, the storage of information per geometric entity and the cache-friendly interleaving of cell loops and vector updates as a means to increase data locality. Experimental results indicate that, despite being more costly, optimized implementations of the additive Schwarz method outperform optimized point-Jacobi preconditioners for simple problems.
INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS
(2023)
Article
Mathematics, Applied
Daniele Boffi, Andrea Cangiani, Marco Feder, Lucia Gastaldi, Luca Heltai
Summary: This paper systematically compares various numerical schemes for approximating interface problems, focusing on implementation aspects and analyzing the costs of different simulation phases.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
