203 citations · 1.7k across the 51 of their papers we have counts for
36 papers · 1 filter
Towards solving General Relativity with Physics-Informed Neural Networks
Juan A. Carretero, Jorge F. Urbán, Fernando Abalos +4
Physics-Informed Neural Networks (PINNs) are a machine-learning framework for approximating solutions to systems of partial differential equations by constraining neural networks t…
Numerical simulations of divergence-type theories for conformal dissipative fluids
Pablo Montes, Marcelo E. Rubio, Oscar A. Reula
We present the first numerical simulations of the symmetric--hyperbolic theory for conformal dissipative relativistic fluids developed in [1]. In this theory, the information of th…
On the illposedness and stability of the relativistic heat equation
A. L. García-Perciante, Oscar. Reula
In this note we analyze, in terms of a simple example, the incompatibility of parabolic evolution and general covariance. For this we introduce a unit time-like four-vector and stu…
Generic instabilities in the relativistic Chapman-Enskog heat conduction law
A. L. Garcia-Perciante, Marcelo E. Rubio, Oscar A. Reula
We address the well-posedness of the Cauchy problem corresponding to the relativistic fluid equations, when coupled with the heat-flux constitutive relation arising within the rela…
On necessary and sufficient conditions for strong hyperbolicity
Fernando Abalos, Oscar Reula
In this work we study constant-coefficient first order systems of partial differential equations and give necessary and sufficient conditions for those systems to have a well posed…
A hyperbolic theory of relativistic conformal dissipative fluids
Luis Lehner, Oscar A. Reula, Marcelo E. Rubio
We develop a complete description of the class of conformal relativistic dissipative fluids of divergence form, following the formalism carried out by Geroch, Lindblom and Pennisi.…
A novel scheme for simulating the force-free equations: boundary conditions and the evolution of solutions towards stationarity
Federico Carrasco, Oscar Reula
Force-Free Electrodynamics (FFE) describes a particular regime of magnetically dominated relativistic plasmas, which arises on several astrophysical scenarios of interest such as p…
On the ill posedness of Force-Free Electrodynamics in Euler Potentials
Oscar A. Reula, Marcelo E. Rubio
We prove that the initial value problem for Force-free Electrodynamics in Euler variables is not well posed. We establish this result by showing that a well-posedness criterion pro…
Covariant Hyperbolization of Force-free Electrodynamics
Federico Carrasco, Oscar Reula
Force-Free Flectrodynamics (FFE) is a non-linear system of equations modeling the evolution of the electromagnetic field, in the presence of a magnetically dominated relativistic p…
Nonlinear electrodynamics as a symmetric hyperbolic system
Fernando Abalos, Federico Carrasco, Érico Goulart +1
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes cor…
The Initial-Boundary Value Problem in General Relativity
Oscar Reula, Olivier Sarbach
In this article we summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it.
On the well posedness of Robinson Trautman Maxwell solutions
Carlos Kozameh, Oscar Reula, Heinz-Otto Kreiss
We show that the so called Robinson-Trautman-Maxwell equations do not constitute a well posed initial value problem. That is, the dependence of the solution on the initial data is…
Well-posed initial-boundary value problem for the harmonic Einstein equations using energy estimates
H. -O. Kreiss, O. Reula, O. Sarbach +1
In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed…
AMR, stability and higher accuracy
Luis Lehner, Steven L. Liebling, Oscar Reula
Efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second order accurate adaptive mesh refinement or on defining higher order acc…
Multi-block simulations in general relativity: high order discretizations, numerical stability, and applications
Luis Lehner, Oscar Reula, Manuel Tiglio
The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve the problem of interest under this grid-structure one mus…
A model problem for the initial-boundary value formulation of Einstein's field equations
Oscar Reula, Olivier Sarbach
In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditi…
The discrete energy method in numerical relativity: Towards long-term stability
Luis Lehner, David Neilsen, Oscar Reula +1
The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipativ…
Strongly hyperbolic systems in General Relativity
Oscar Reula
We discuss several topics related to the notion of strong hyperbolicity which are of interest in general relativity. After introducing the concept and showing its relevance we prov…
Strongly hyperbolic second order Einstein's evolution equations
Gabriel Nagy, Omar E. Ortiz, Oscar A. Reula
BSSN-type evolution equations are discussed. The name refers to the Baumgarte, Shapiro, Shibata, and Nakamura version of the Einstein evolution equations, without introducing the c…
Summation by parts and dissipation for domains with excised regions
Gioel Calabrese, Luis Lehner, Oscar Reula +2
We discuss finite difference techniques for hyperbolic equations in non-trivial domains, as those that arise when simulating black hole spacetimes. In particular, we construct diss…
Novel finite-differencing techniques for numerical relativity: application to black hole excision
Gioel Calabrese, Luis Lehner, David Neilsen +4
We use rigorous techniques from numerical analysis of hyperbolic equations in bounded domains to construct stable finite-difference schemes for Numerical Relativity, in particular…
Well posed constraint-preserving boundary conditions for the linearized Einstein equations
Gioel Calabrese, Jorge Pullin, Oscar Reula +2
In the Cauchy problem of general relativity one considers initial data that satisfies certain constraints. The evolution equations guarantee that the evolved variables will satisfy…
On free evolution of self gravitating, spherically symmetric waves
Mirta S. Iriondo, Oscar A. Reula
We perform a numerical free evolution of a selfgravitating, spherically symmetric scalar field satisfying the wave equation. The evolution equations can be written in a very simple…
Well-posed forms of the 3+1 conformally-decomposed Einstein equations
Simonetta Frittelli, Oscar A. Reula
We show that well-posed, conformally-decomposed formulations of the 3+1 Einstein equations can be obtained by densitizing the lapse and by combining the constraints with the evolut…