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We construct exact solutions that describe the near horizon region of extremal rotating black holes in Einstein-Born-Infeld theory. Using generalized Komar integrals, we extract the electric charge and angular momentum from the near horizon…
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…
A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac…
We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting in two disjoint domains. We…
We use the frequency and time domain Teukolsky formalism to calculate gravitational-wave fluxes from a spinning body on a bound eccentric equatorial orbit around a Kerr black hole. The spinning body is represented as a point particle…
The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…
Motivated by many applications in complex domains with boundaries exposed to large topological changes or deformations, fictitious domain methods regard the actual domain of interest as being embedded in a fixed Cartesian background. This…
Observations reveal that mass-transferring binary systems may have non-zero orbital eccentricities. The time-evolution of the orbital semi-major axis and eccentricity of mass-transferring eccentric binary systems is an important part of…
The detection of a pulsar (PSR) in a tight, relativistic orbit around a supermassive or intermediate mass black hole - such as those in the Galactic centre or in the centre of Globular clusters - would allow for precision tests of general…
Gravitational waves from inspiraling sub-solar mass compact objects would provide almost definitive evidence for the existence of primordial black holes. In this chapter, we explain why these exotic objects are interesting candidates for…
This paper recalls the principles of the finite-element methods (FEM) theory and declines its application in the EN-MME group, for the numerical modelling and study of particle accelerator equipment. Implicit and explicit methods are…
We use inverted finite elements method for approximating solutions of second order elliptic equations with non-constant coefficients varying to infinity in the exterior of a 2D bounded obstacle, when a Neumann boundary condition is…
The production of numerical relativity waveforms that describe quasicircular binary black hole mergers requires high-quality initial data, and an algorithm to iteratively reduce residual eccentricity. To date, these tools remain closed…
The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution…
Stationary axisymmetric binary systems of unequal co and counter-rotating extreme Kerr black holes apart by a conical singularity are studied. Both solutions are well identified as two $3$-parametric subfamilies of the Kinnersley-Chitre…
Extreme mass-ratio inspirals (EMRIs), comprising a stellar-mass compact object (CO) orbiting a supermassive black hole (BH), are key targets for future space-based gravitational-wave (GW) observatories. Incorporating the spin of the…
Systems of two black holes with unbound orbits can produce a diverse array of gravitational wave signals with rich morphology. This parameter space encompasses both hyperbolic orbit scattering events and dynamical captures, including…
We calculate puncture initial data corresponding to both single and binary black hole solutions of the constraint equations by means of a pseudo-spectral method applied in a single spatial domain. Introducing appropriate coordinates, these…
Future gravitational wave observatories can probe dark matter by detecting the dephasing in the waveform of binary black hole mergers induced by dark matter overdensities. Such a detection hinges on the accurate modelling of the dynamical…
In this paper, finite element method is applied to Leland's model for numerical simulation of option pricing with transaction costs. Spatial finite element models based on P1 and/or P2 elements are formulated in combination with a…