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In this article, we present Kinetic Transport Solver for Radiation Therapy (KiT-RT), an open source C++-based framework for solving kinetic equations in therapy applications available at https://github.com/CSMMLab/KiT-RT. This software framework aims to provide a collection of classical deterministic solvers for unstructured meshes that allow for easy extendability. Therefore, KiT-RT is a convenient base to test new numerical methods in various applications and compare them against conventional solvers. The implementation includes spherical harmonics, minimal entropy, neural minimal entropy, and discrete ordinates methods. Solution characteristics and efficiency are presented through several test cases ranging from radiation transport to electron radiation therapy. Due to the variety of included numerical methods and easy extendability, the presented open source code is attractive for both developers, who want a basis to build their numerical solvers, and users or application engineers, who want to gain experimental insights without directly interfering with the codebase. [ABSTRACT FROM AUTHOR]

Unsteady aerodynamic shape optimization presents new challenges in terms of sensitivity analysis of time-dependent objective functions. In this work, we consider periodic unsteady flows governed by the unsteady Reynolds-averaged Navier-Stokes (URANS) equations. Hence, the resulting output functions acting as objective or constraint functions of the optimization are themselves periodic with unknown period length, which may depend on the design parameter of said optimization. Sensitivity analysis on the time average of a function with these properties turns out to be difficult. Therefore, we explore methods to regularize the time average of such a function with the so-called windowing approach. Furthermore, we embed these regularizers into the discrete adjoint solver for the URANS equations of the multiphysics and optimization software SU2. Finally, we exhibit a comparison study between the classical nonregularized optimization procedure and the ones enhanced with regularizers of different smoothness, and we show that the latter result in a more robust optimization. [ABSTRACT FROM AUTHOR]

The multi-scale nature of gaseous flows poses tremendous difficulties for theoretical and numerical analysis. The Boltzmann equation, while possessing a wider applicability than hydrodynamic equations, requires significantly more computational resources due to the increased degrees of freedom in the model. The success of a hybrid fluid-kinetic flow solver for the study of multi-scale flows relies on accurate prediction of flow regimes. In this paper, we draw on binary classification in machine learning and propose the first neural network classifier to detect near-equilibrium and non-equilibrium flow regimes based on local flow conditions. Compared with classical semi-empirical criteria of continuum breakdown, the current method provides a data-driven alternative where the parameterized implicit function is trained by solutions of the Boltzmann equation. The ground-truth labels are derived rigorously from the deviation of particle distribution functions and the approximations based on the Chapman-Enskog ansatz. Therefore, no tunable parameter is needed in the criterion. Following the entropy closure of the Boltzmann moment system, a data generation strategy is developed to produce training and test sets. Numerical analysis shows its superiority over simulation-based samplings. A hybrid Boltzmann-Navier-Stokes flow solver is built correspondingly with an adaptive partition of local flow regimes. Numerical experiments including the one-dimensional Riemann problem, shear flow layer, and hypersonic flow around a circular cylinder are presented to validate the current scheme for simulating cross-scale and non-equilibrium flow physics. The quantitative comparison with a semi-empirical criterion and benchmark results demonstrates the capability of the current neural classifier to accurately predict continuum breakdown. The code for the data generator, hybrid solver, and neural network implementation is available in the open source repositories [1,2]. • The first neural network to predict equilibrium and non-equilibrium flow regimes is proposed. • A data generation strategy is developed based on the entropy closure theory of the Boltzmann equation. • The label of flow regime is rigorously derived with no tunable parameters. • A hybrid Boltzmann-Navier-Stokes flow solver is built upon the neural classifier. [ABSTRACT FROM AUTHOR]

We compare a first‐order stochastic swarm intelligence model called consensus‐based optimization (CBO), which may be used for the global optimization of a function in multiple dimensions, to other particle swarm algorithms for global optimization. CBO allows for passage to the mean‐field limit resulting in a nonlocal, degenerate, parabolic PDE. Exploiting tools from PDE analysis, it is possible to rigorously prove convergence results for the algorithm (see [3]). In the present article we discuss numerical results obtained with the Particle Swarm Optimization (PSO) [4], Wind‐Driven Optimization (WDO) [6] and CBO and show that CBO leads to very competitive results. [ABSTRACT FROM AUTHOR]