Related papers: A New Way to Make Waves

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D…

We present an improved spectral algorithm for Cauchy-characteristic extraction and characteristic evolution of gravitational waves in numerical relativity. The new algorithms improve spectral convergence both at the poles of the…

This thesis investigates algorithms regarding their applicability for highly nonlinear model fitting on big datasets. Various mathematical methods are presented with which a model fit using the least squares criterion is possible. Special…

This manuscript is a lightly reformatted version of my 2017 PhD thesis. I am posting it on arXiv at the request of my advisor, Sergiu Klainerman, who noted that it has been useful to some students. The content largely reflects the thesis in…

The Cauchy+characteristic matching (CCM) problem for the scalar wave equation is investigated in the background geometry of a Schwarzschild black hole. Previously reported work developed the CCM framework for the coupled…

We present the first results in a new program intended to make the best use of all available technologies to provide an effective understanding of waves from inspiralling black hole binaries in time for imminent observations. In particular,…

We undertake a systematic review of some results concerning local well-posedness of the Cauchy problem for certain systems of nonlinear wave equations, with minimal regularity assumptions on the initial data. Moreover we provide a…

The topic of this paper are nonlinear traveling waves occuring in a system of damped waves equations in one space variable. We extend the freezing method from first to second order equations in time. When applied to a Cauchy problem, this…

This thesis describes the application of numerical techniques to solve Einstein's field equations in three distinct cases. First we present the first long-term stable second order convergent Cauchy characteristic matching code in…

This paper aims to give a refined wave breaking description of the Cauchy problem to the one-dimensional nonlinear shallow water equations providing a sharp estimate of the lifespan of the solutions depending on the amplitude and topography…

Cauchy-characteristic matching (CCM) is a numerical-relativity technique that solves Einstein's equations on an effectively infinite computational domain, thereby eliminating systematic errors associated with artificial boundary conditions.…

We consider the Cauchy problem with smooth and compactly supported initial data for the wave equation in a general class of spherically symmetric geometries which are globally smooth and asymptotically flat. Under certain mild conditions on…

We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply-connected fluid domain that includes…

We construct solutions to nonlinear wave equations that are singular along a prescribed noncharacteristic hypersurface which is the graph of a function satisfying not the Eikonal but another partial differential equation of the first order.…

We study the local existence of strong solutions for the cubic nonlinear wave equation with data in $H^s(M)$, $s<1/2$, where $M$ is a three dimensional compact riemannian manifold. This problem is supercritical and can be shown to be…

In this paper, the existence, the uniqueness and estimates of solution to the integral Cauchy problem for linear and nonlinear abstract wave equations are proved. The equation includes a linear operator A defined in a Banach space E, in…

We present a new method for treating the inner Cauchy boundary of a black hole spacetime by matching to a characteristic evolution. We discuss the advantages and disadvantages of such a scheme relative to Cauchy-only approaches. A prototype…

We consider the Cauchy problem for the wave equation on a non-globally hyperbolic manifold of the special form (Minkowski plane with a handle) containing closed timelike curves (time machines). We prove that the classical solution of the…

We deal with the Cauchy problem for a perturbed wave equation in the half-plane with data given on a part of the space-time boundary. The equation in consideration describes a wave process in a laterally inhomogeneous medium. We propose a…

We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of…