The deal.II library, Version 9.6
Here, this paper provides an overview of the new features of the finite element library deal.II, version 9.6.
97 MATHEMATICS AND COMPUTING↗
Engineering topics
Bangerth, Wolfgang
Publications and source records attributed to Bangerth, Wolfgang.
Democratizing uncertainty quantification
Uncertainty Quantification (UQ) is vital to safety-critical model-based analyses, but the widespread adoption of sophisticated UQ methods is limited by technical complexity. In this paper, we introduce UM-Bridge (the UQ and Modeling Bridge), a high-level abstraction and software protocol that facilitates universal interoperability of UQ software with simulation codes. It breaks down the technical complexity of advanced UQ applications and enables separation of concerns between experts. UM-Bridge democratizes UQ by allowing effective interdisciplinary collaboration, accelerating the development of advanced UQ methods, and making it easy to perform UQ analyses from prototype to High Performance Computing (HPC) scale. In addition, we present a library of ready-to-run UQ benchmark problems, all easily accessible through UM-Bridge. These benchmarks support UQ methodology research, enabling reproducible performance comparisons. We demonstrate UM-Bridge with several scientific applications, harnessing HPC resources even using UQ codes not designed with HPC support.
Benchmarks↗
The deal.II Library, Version 9.5
Here, this paper provides an overview of the new features of the finite element library deal.II, version 9.5.
97 MATHEMATICS AND COMPUTING↗
Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach
In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype $\mathrm{lr(0)_n}$ nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. Importantly, the paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
The deal.II library, Version 9.3
This paper provides an overview of the new features of the finite element library deal.II, version 9.3.
97 MATHEMATICS AND COMPUTING↗
The deal.II Library, Version 9.2
This work provides an overview of the new features of the finite element library deal.II, version 9.2.
97 MATHEMATICS AND COMPUTING↗
The DEAL.II finite element library: Design, features, and insights
DEAL.II is a state-of-the-art finite element library focused on generality, dimension-independent programming, parallelism, and extensibility. In this paper, we outline its primary design considerations and its sophisticated features such as distributed meshes, h p -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.
97 MATHEMATICS AND COMPUTING↗