Narrow Results

This paper develops sharp convergence rate estimates of the Schwarz alternating procedure. We do this for a model Poisson problem in one and two dimensions with multiple subdomains We then use these estimates to assess the serial and parallel complexity of the optimal Schwarz algorithm. We finish with a comparison of this optimal algorithm, using multigrid as the subdomain solver, and multigrid by itself, without domain decomposition.

We present a formulation and numerical solution procedure for heterogeneous atomistic-continuum representations of fluid flows. The ingredients from atomistic and continuum perspectives are non-equilibrium molecular dynamics and spectral element, respectively; the matching is provided by a classical procedure, the Schwarz alternating method with overlapping subdomains. The technique is applied to microscale flow of a dense fluid (supercritical argon) in a complex two-dimensional channel.

The Schwarz, Dirichlet, Neumann and a Robin boundary value problems are investigated in the upper right quater plane of the complex plane for the inhomogeneous Cauchy-Riemann equation.