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We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…

Theoretical treatments of strong-field physics have long relied on the numerical solution of the time-dependent Schr\"odinger equation. The most effective such treatments utilize a discrete spatial representation---a grid. Since most…

An integral equation based scheme is presented for the fast and accurate computation of effective conductivities of two-component checkerboard-like composites with complicated unit cells at very high contrast ratios. The scheme extends…

We present a local and transferable machine learning approach capable of predicting the real-space density response of both molecules and periodic systems to external homogeneous electric fields. The new method, SALTER, builds on the…

We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of…

We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…

We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances…

We numerically explore the Newton-Raphson basins of convergence, related to the libration points (which act as attractors), in the planar circular restricted five-body problem (CR5BP). The evolution of the position and the linear stability…

We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…

We give a short survey of recent results on sparse-grid linear algorithms of approximate recovery and integration of functions possessing a unweighted or weighted Sobolev mixed smoothness based on their sampled values at a certain finite…

An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…

We present a closed analytical formula for the scattering intensity from charged hard sphere fluids with any arbitrary number of components. Our result is an extension to ionic systems of Vrij's analogous expression for uncharged hard…

In this paper, we propose an efficient quadratic interpolation formula utilizing solution gradients computed and stored at nodes and demonstrate its application to a third-order cell-centered finite-volume discretization on tetrahedral…

This paper investigates the problem of computing capacity-cost (C-C) functions for continuous channels. Motivated by the Kullback-Leibler divergence (KLD) proximal reformulation of the classical Blahut-Arimoto (BA) algorithm, the…

We present a finite volume scheme for modeling the diffusion of charged particles, specifically ions, in constrained geometries using a degenerate Poisson-Nernst-Planck system with size exclusion yielding cross-diffusion. Our method…

A new iterative solver is proposed to efficiently calculate the ground state electronic structure in Density Functional Theory calculations. This algorithm is particularly useful for simulating physical systems considered difficult to…

We consider the scattering of two-bosons with negative parity and spin 0 or 1. Starting from helicity partial-wave scattering amplitudes we derive transformations that eliminate all kinematical constraints. Such amplitudes are expected to…

Flow based models such as Real NVP are an extremely powerful approach to density estimation. However, existing flow based models are restricted to transforming continuous densities over a continuous input space into similarly continuous…

In this paper we develop a class of efficient Galerkin boundary element methods for the solution of two-dimensional exterior single-scattering problems. Our approach is based upon construction of Galerkin approximation spaces confined to…

We calculate the drag coefficient of a spherical particle suspended in a near-critical binary fluid mixture. To capture the scaling behavior associated with critical adsorption in the strong adsorption regime, we employ the framework of…