Galerkin-collocation domain decomposition method for arbitrary binary black holes

Chebyshev Collocation Method for Shallow Water Models with Domain Decomposition

The spectral methods seek the numerical solutions by a set of known polynomials. The main advantage of using spectral methods for solving atmospheric problems is the high efficiency and conservations of important quadratic quantities such as kinetic energy and enstrophy. Namely, we can get very high accuracy through the exponential convergence. The conservation of the quadratic quantities are i...

Domain Decomposition Preconditioners for Hermite Collocation Problems

Approximate initial data for binary black holes

We construct approximate analytical solutions to the constraint equations of general relativity for binary black holes of arbitrary mass ratio in quasicircular orbit. We adopt the puncture method to solve the constraint equations in the transverse-traceless decomposition and consider perturbations of Schwarzschild black holes caused by boosts and the presence of a binary companion. A superposit...

Galerkin domain decomposition procedures for parabolic equations on rectangular domain

Galerkin domain decomposition procedures for parabolic equations with three cases of boundary conditions on rectangular domain are discussed. These procedures are non-iterative and non-overlapping ones. They rely on implicit Galerkin method in the sub-domains and integral mean method on the inter-domain boundaries to present explicit flux calculation. Thus, the parallelism can be achieved by th...

A Collocation-i/ '-Galerkin Method for Some Elliptic Equations

A collocation-//"'-Galerkin method is defined for some elliptic boundary value problems on a rectangle. The method uses tensor products of discontinuous piecewise polynomial spaces and collocation based on Jacobi points with weight function >c2(l x)2. Optimal order of L2 rates of convergence is established for the approximation solution. A numerical example which confirms these results is prese...