Related papers: Discontinuous collocation methods and gravitationa…
Accurate calculation of the motion of a compact object in a background spacetime induced by a supermassive black hole is required for the future detection of such binary systems by the gravitational-wave detector LISA. Reaching the desired…
Rapidly rotating black hole solutions in theories beyond general relativity play a key role in experimental gravity, as they allow us to compute observables in extreme spacetimes that deviate from the predictions of general relativity. Such…
Gravitational waves from the inspiral of a stellar-size black hole to a supermassive black hole can be accurately approximated by a point particle moving in a Kerr background. This paper presents progress on finding the electromagnetic and…
We develop a convergence theory of space-time discretizations for the linear, 2nd-order wave equation in polygonal domains $\Omega\subset\mathbb{R}^2$, possibly occupied by piecewise homogeneous media with different propagation speeds.…
Numerical relativity has traditionally been pursued via finite differencing. Here we explore pseudospectral collocation (PSC) as an alternative to finite differencing, focusing particularly on the solution of the Hamiltonian constraint (an…
Extreme mass-ratio inspirals (EMRIs) are expected to have considerable eccentricity when emitting gravitational waves (GWs) in the LISA band. Developing GW templates that remain phase accurate over these long inspirals requires the use of…
Variational phase-field models of fracture are widely used to simulate nucleation and propagation of cracks in brittle materials. They are based on the approximation of the solutions of free-discontinuity fracture energy by two smooth…
Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the "curse of dimensionality". This paper…
Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of shocks, and, more generally,…
With a view to developing a formalism that will be applicable at second perturbative order, we devise a new practical scheme for computing the gravitational self-force experienced by a point mass moving in a curved background spacetime. Our…
We obtain electrically charged black hole solutions of the Einstein equations in arbitrary dimensions with a nonlinear electrodynamics source. The matter source is deriving from a Lagrangian given by an arbitrary power of the Maxwell…
We study the problem of finding the resistors in a resistor network from measurements of the power dissipated by the resistors under different loads. We give sufficient conditions for local uniqueness, i.e. conditions that guarantee that…
This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC…
A compact object moving in curved spacetime interacts with its own gravitational field. This leads to both dissipative and conservative corrections to the motion, which can be interpreted as a self-force acting on the object. The original…
Detailed observations of phenomena involving black holes, be it via gravitational waves or more traditional electromagnetic means, can probe the strong field regime of the gravitational interaction. The prediction of features in such…
Partial differential equations with distributional sources---in particular, involving (derivatives of) delta distributions---have become increasingly ubiquitous in numerous areas of physics and applied mathematics. It is often of…
We compute the electromagnetic self-force acting on a charged particle held in place at a fixed position r outside a five-dimensional black hole described by the Schwarzschild-Tangherlini metric. Using a spherical-harmonic decomposition of…
Computable estimates for the error of finite element discretisations of parabolic problems in the $L^\infty(0,T; L^2)$ norm are developed, which exhibit constant effectivities (the ratio of the estimated error to the true error) with…
We introduce a new time-domain method for computing the self-force acting on a scalar particle in a Schwarzschild geometry. The principal feature of our method consists in the division of the spatial domain into several subdomains and…
Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is much…