Related papers: Characteristic Evolution and Matching
We consider nonlinear mutation selection models, known as replicator-mutator equations in evolutionary biology. They involve a nonlocal mutation kernel and a confining fitness potential. We prove that the long time behaviour of the Cauchy…
Stellar evolution codes play a major role in present-day astrophysics, yet they share common issues. In this work we seek to remedy some of those by the use of results from realistic and highly detailed 3D hydrodynamical simulations of…
The evolution of global binary black holes variables such as energy or linear momentum are mainly obtained by applying numerical methods near coalescence, post-Newtonian (PN) expansions, or a combination of both. In this paper, we use a…
A chain regularization method is combined with special purpose computer hardware to study the evolution of massive black hole binaries at the centers of galaxies. Preliminary results with up to N=260,000 particles are presented. The decay…
We discuss inverse problems to finding the time-dependent coefficient for the multidimensional Cauchy problems for both strictly hyperbolic equations and polyharmonic heat equations. We also extend our techniques to the general inverse…
We report new results which establish that the accurate 3-dimensional numerical simulation of generic single-black-hole spacetimes has been achieved by characteristic evolution with unlimited long term stability. Our results cover a…
We analyse the Cauchy problem on a characteristic cone, including its vertex, for the Einstein equations in arbitrary dimensions. We use a wave map gauge, solve the obtained constraints and show gauge conservation.
Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…
Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve…
We present a new technique for time-domain numerical evolution of the scalar field generated by a pointlike scalar charge orbiting a black hole. Time-domain evolution offers an efficient way for calculating black hole perturbations,…
Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
We discuss a coupled-cluster formalism for carrying out imaginary-time evolution from an arbitrary reference, and study the properties of the resulting evolution trajectories. The evolution converges to a solution of the standard…
Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a…
Although real-coded differential evolution (DE) algorithms can perform well on continuous optimization problems (CoOPs), it is still a challenging task to design an efficient binary-coded DE algorithm. Inspired by the learning mechanism of…
We present a general method of solving the Cauchy problem for a linear parabolic partial differential equation of evolution type with variable coefficients and demonstrate it on the equation with derivatives of orders two, one and zero. The…
We describe early success in the evolution of binary black hole spacetimes with a numerical code based on a generalization of harmonic coordinates. Indications are that with sufficient resolution this scheme is capable of evolving binary…
A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates…
We study the Cauchy problem for a class of linear evolution equations of arbitrary order with coefficients depending both on time and space variables. Under suitable decay assumptions on the coefficients of the lower order terms for $|x|$…
The characteristic formalism in numerical relativity, which has been developed to study gravitational waves, and the observer metric approach in observational cosmology both make use of coordinate systems based on null cones. In this paper,…