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We present a one-dimensional shear-force-driven droplet formation model with a flux-based error estimator. The model is derived using asymptotic expansion and a front-tracking method to simulate the droplet interface. The model is then…
The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…
The problem of the resolution of turbulent flows in adaptive mesh refinement (AMR) simulations is investigated by means of 3D hydrodynamical simulations in an idealised setup, representing a moving subcluster during a merger event. AMR…
Neural Radiance Fields and 3D Gaussian Splatting have advanced novel view synthesis, yet still rely on dense inputs and often degrade at extrapolated views. Recent approaches leverage generative models, such as diffusion models, to provide…
In order to reduce the computational cost of the simulation of electromagnetic responses in geophysical settings that involve highly heterogeneous media, we develop a multiscale finite volume method with oversampling for the quasi-static…
This paper presents a novel implicit scheme for the constraint resolution in real-time finite element simulations in the presence of contact and friction. Instead of using the standard motion correction scheme, we propose an iterative…
Over the last decade block-structured adaptive mesh refinement (SAMR) has found increasing use in large, publicly available codes and frameworks. SAMR frameworks have evolved along different paths. Some have stayed focused on specific…
High-order CFD is gathering a broadening interest as a future industrial tool, with one such approach being Flux Reconstruction (FR). However, due to the need to mesh complex geometries if FR is to displace current, lower order methods, FR…
The lack of fa\c{c}ade structures in photogrammetric mesh models renders them inadequate for meeting the demands of intricate applications. Moreover, these mesh models exhibit irregular surfaces with considerable geometric noise and texture…
Given the compact binary evolution problem of numerical relativity, in the finite-difference, block-based, adaptive mesh refinement context, choices must be made on how evolved fields are to be discretized. In GR-Athena++, the space-time…
This research presents the development of an innovative algorithm tailored for the adaptive sampling of residual points within the framework of Physics-Informed Neural Networks (PINNs). By addressing the limitations inherent in existing…
Deep neural networks are often not robust to semantically-irrelevant changes in the input. In this work we address the issue of robustness of state-of-the-art deep convolutional neural networks (CNNs) against commonly occurring distortions…
When a numerical simulation has to handle a physics problem with a wide range of time-dependent length scales, dynamically adaptive discretizations can be the method of choice. We present a major upgrade to the numerical relativity code…
We perform three-dimensional numerical relativity simulations of homogeneous and inhomogeneous expanding spacetimes, with a view towards quantifying non-linear effects from cosmological inhomogeneities. We demonstrate fourth-order…
Performing a stable, long duration simulation of driven MHD turbulence with a high thermal Mach number and a strong initial magnetic field is a challenge to high-order Godunov ideal MHD schemes because of the difficulty in guaranteeing…
Foundation models pretrained on large-scale natural images are widely adapted to various cross-domain low-resource downstream tasks, benefiting from generalizable and transferable patterns captured by their representations. However, these…
This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…
We consider convection-diffusion problems in time-dependent domains and present a space-time finite element method based on quadrature in time which is simple to implement and avoids remeshing procedures as the domain is moving. The…
Real-image super-resolution (Real-ISR) seeks to recover HR images from LR inputs with mixed, unknown degradations. While diffusion models surpass GANs in perceptual quality, they under-reconstruct high-frequency (HF) details due to a…
Multi-slice magnetic resonance images of the fetal brain are usually contaminated by severe and arbitrary fetal and maternal motion. Hence, stable and robust motion correction is necessary to reconstruct high-resolution 3D fetal brain…