Artificial boundary conditions for the linear advection diffusion equation
Mathematics of Computation
Artificial boundary conditions for incompletely parabolic perturbations of hyperbolic systems
SIAM Journal on Mathematical Analysis
Waveform relaxation with overlapping splittings
SIAM Journal on Scientific Computing
Optimal Schwarz Waveform Relaxation for the One Dimensional Wave Equation
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Optimized Schwarz Waveform Relaxation Methods for Advection Reaction Diffusion Problems
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics
Schwarz Waveform Relaxation Algorithms for the Linear Viscous Equatorial Shallow Water Equations
SIAM Journal on Scientific Computing
Discrete transparent boundary conditions for parabolic systems
Mathematical and Computer Modelling: An International Journal
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In this article we are interested in the derivation of efficient domain decomposition methods for the viscous primitive equations of the ocean. We consider the rotating three-dimensional incompressible hydrostatic Navier-Stokes equations with free surface. Performing an asymptotic analysis of the system in the regime of small Rossby numbers, we compute an approximate Dirichlet to Neumann operator and build an optimized Schwarz waveform relaxation algorithm. We establish that the algorithm is well defined and provide numerical evidence of the convergence of the method.