Related papers: Mean Mesh Adaptation for Efficient CFD Simulations…
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
Lattice-Boltzmann methods are known for their simplicity, efficiency and ease of parallelization, usually relying on uniform Cartesian meshes with a strong bond between spatial and temporal discretization. This fact complicates the crucial…
Numerical models of the flow and wakes due to turbines operating within a real-scale offshore wind farm can lead to a prohibitively large computational cost, particularly when considering blade-resolved simulations. With the introduction of…
Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
A model hierarchy that is based on the one-dimensional isothermal Euler equations of fluid dynamics is used for the simulation and optimisation of gas flow through a pipeline network. Adaptive refinement strategies have the aim of bringing…
In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker-Planck operator for small-angle Coulomb collisions, a radiation damping operator, and a secondary knock-on (Boltzmann) collision source.…
The alternating direction method of multipliers (ADMM) is commonly used for distributed model fitting problems, but its performance and reliability depend strongly on user-defined penalty parameters. We study distributed ADMM methods that…
The dynamic behavior of jointed assemblies exhibiting friction nonlinearities features amplitude-dependent dissipation and stiffness. To develop numerical simulations for predictive and design purposes, macro-scale High Fidelity Models…
We study dendritic microstructure evolution using an adaptive grid, finite element method applied to a phase-field model. The computational complexity of our algorithm, per unit time, scales linearly with system size, rather than the…
Adaptive spatial meshing has proven invaluable for the accurate, efficient computation of solutions of time dependent partial differential equations. In a DA context the use of adaptive spatial meshes addresses several factors that place…
For the non-conforming Crouzeix-Raviart boundary elements from [Heuer, Sayas: Crouzeix-Raviart boundary elements, Numer. Math. 112, 2009], we develop and analyze a posteriori error estimators based on the $h-h/2$ methodology. We discuss the…
The typical size of computational meshes needed for realistic geometries and high-speed flow conditions makes Computational Fluid Dynamics (CFD) impractical for full-mission performance prediction and control. Reduced-Order Models (ROMs) in…
A three-dimensional (3-D) adaptive mesh refinement (AMR) cellular automata (CA) model is developed to simulate the equiaxed dendritic growth of pure substance. In order to reduce the mesh induced anisotropy by CA capture rules, a limited…
The implementation of machine learning in Internet of Things devices poses significant operational challenges due to limited energy and computation resources. In recent years, significant efforts have been made to implement simplified ML…
In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in costs in addition to minimizing a standard criterion. Conditional value-at-risk (CVaR) is a relatively new risk measure that…
Traditional simulation of complex mechanical systems relies on numerical solvers of Partial Differential Equations (PDEs), e.g., using the Finite Element Method (FEM). The FEM solvers frequently suffer from intensive computation cost and…
The Alternating Direction Method of Multipliers (ADMM) has gained significant attention across a broad spectrum of machine learning applications. Incorporating the over-relaxation technique shows potential for enhancing the convergence rate…
Reinforcement learning (RL) has emerged as a promising approach to automating decision processes. This paper explores the application of RL techniques to optimise the polynomial order in the computational mesh when using high-order solvers.…
In aircraft design, structural optimization and uncertainty quantification concerning transonic aeroelastic issues are computationally impractical, because the iterative process requires great number of aeroelastic analysis. Emerging…