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Reconstructing the structure of thin films and multilayers from measurements of scattered X-rays or neutrons is key to progress in physics, chemistry, and biology. However, finding all structures compatible with reflectometry data is…
Richardson extrapolation is applied to a simple first-order upwind difference scheme for the approximation of solutions of singularly perturbed convection-diffusion problems in one dimension. Robust a posteriori error bounds are derived for…
We present details of a new numerical code designed to study the formation and evaporation of 2-dimensional black holes within the CGHS model. We explain several elements of the scheme that are crucial to resolve the late-time behavior of…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
The very high spatial resolution provided by Adaptive Optics assisted spectroscopic observations at 8m-class telescopes (e.g. with SINFONI at the VLT) will allow to greatly increase the number of direct black hole (BH) mass measurements…
Lagrangian trajectory or particle dispersion models as well as semi-Lagrangian advection schemes require meteorological data such as wind, temperature and geopotential at the exact spatio-temporal locations of the particles that move…
Recent developments in post-Minkowksian (PM) calculations have led to a fast-growing body of weak-field perturbative information. As such, there is major interest within the gravitational wave community as to how this information can be…
The development of novel materials in recent years has been accelerated greatly by the use of computational modelling techniques aimed at elucidating the complex physics controlling microstructure formation in materials, the properties of…
Deep learning (DL) inverse techniques have increased the speed of artificial electromagnetic material (AEM) design and improved the quality of resulting devices. Many DL inverse techniques have succeeded on a number of AEM design tasks, but…
A number of key scientific computing applications that are based upon tensor-product grid constructions, such as numerical weather prediction (NWP) and combustion simulations, require property-preserving interpolation. Essentially…
A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant…
It has long been thought that black hole accretion flows are driven by magnetohydrodynamic (MHD) turbulence, and there are now many general relativistic global simulations illustrating the dynamics of this process. However, many challenges…
Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many…
Artificial neural networks, widely recognised for their role in machine learning, are now transforming the study of ordinary differential equations (ODEs), bridging data-driven modelling with classical dynamical systems and enabling the…
In this paper, we propose a novel $hr$-adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional $h$-adaptive finite element method is interpolating the finite element…
The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…
Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy --- simply increase the order $N$ of the Lagrange interpolating polynomial and the mathematics of convergence automates the distribution of the grid points.…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
We introduce a higher order phase averaging method for nonlinear oscillatory systems. Phase averaging is a technique to filter fast motions from the dynamics whilst still accounting for their effect on the slow dynamics. Phase averaging is…
Gravitational-wave astronomy can give us access to the structure of black holes, potentially probing microscopic or even Planckian corrections at the horizon scale, as those predicted by some quantum-gravity models of exotic compact…