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We consider fully discrete numerical approximations for axisymmetric Willmore flow that are unconditionally stable and work reliably without remeshing. We restrict our attention to surfaces without boundary, but allow for spontaneous…
Designing systems with large magnetic anisotropy energy (MAE) is desirable and critical for nanoscale magnetic devices. A recent breakthrough achieved the theoretical limit of the MAE for 3$d$ transition metal atoms by placing a single Co…
In this paper, we present exact divergence-free spectral method for solving the incompressible and resistive magneto-hydrodynamic (MHD) equations in two and three dimensions, as well as the efficient solution algorithm and unconditionally…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
We show that arbitrary 3D electromagnetic fields are transient solutions to Maxwell's equations and provide a simple equation to find how the field evolves over time. Multiple 3D fields can be realized at different times by superposing with…
Anisotropic rotation averaging has recently been explored as a natural extension of respective isotropic methods. In the anisotropic formulation, uncertainties of the estimated relative rotations -- obtained via standard two-view…
We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial…
In this note, two numerical methods of solving fractional differential equations (FDEs) are briefly described, namely predictor-corrector approach of Adams-Bashforth-Moulton type and multi-step generalized differential transform method…
We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…
For the evolution of a closed surface under anisotropic surface diffusion with a general anisotropic surface energy $\gamma(\boldsymbol{n})$ in three dimensions (3D), where $\boldsymbol{n}$ is the unit outward normal vector, by introducing…
The alternating direction multiplier method (ADMM) is widely used in computer graphics for solving optimization problems that can be nonsmooth and nonconvex. It converges quickly to an approximate solution, but can take a long time to…
Let $\mathcal{D}$ be the dictionary of Gaussian mixtures: the functions created by affine change of variables of a single Gaussian in $n$ dimensions. $\mathcal{D}$ is used pervasively in scientific applications to a degree that…
In plasma simulations, where the speed of light divided by a characteristic length is at a much higher frequency than other relevant parameters in the underlying system, such as the plasma frequency, implicit methods begin to play an…
The tractions that cells exert on a gel substrate from the observed displacements is an increasingly attractive and valuable information in biomedical experiments. The computation of these tractions requires in general the solution of an…
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…
We present an asymptotically and unconditionally stable numerical method to account for the momentum transfer between multiple species. Momentum is conserved to machine precision. This implies that the asymptotic equilibrium corresponds to…
In this paper, a time-domain discontinuous Galerkin (TDdG) finite element method for the full system of Maxwell's equations in optics and photonics is investigated, including a complete proof of a semi-discrete error estimate. The new…
Although FFT-based methods are renowned for their numerical efficiency and stability, traditional discretizations fail to capture material interfaces that are not aligned with the grid, resulting in suboptimal accuracy. To address this…
In this article, we analyse a stabilised equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a sub-domain, for example along the boundary of the domain,…
We have implemented and tested the method we have recently proposed [J. Phys. Chem. Lett. 10, 1537 (2019)] to treat dispersion interactions, which is derived from a supramolecular wavefunction constrained to leave the diagonal of the…