Artificial boundary conditions for the linear advection diffusion equation
Mathematics of Computation
Computational techniques for fluid dynamics
Computational techniques for fluid dynamics
Absorbing boundary conditions for domain decomposition
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
The optimized order 2 method: application to convection-diffusion problems
Future Generation Computer Systems - I. High Performance Numerical Methods and Applications. II. Performance Data Mining: Automated Diagnosis, Adaption, and Optimization
Optimized Schwarz Methods without Overlap for the Helmholtz Equation
SIAM Journal on Scientific Computing
Optimized Domain Decomposition Methods for the Spherical Laplacian
SIAM Journal on Numerical Analysis
Optimized Schwarz Waveform Relaxation for the Primitive Equations of the Ocean
SIAM Journal on Scientific Computing
The Optimized Schwarz Method with a Coarse Grid Correction
SIAM Journal on Scientific Computing
Algorithm 932: PANG: Software for nonmatching grid projections in 2D and 3D with linear complexity
ACM Transactions on Mathematical Software (TOMS)
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We are interested in solving time dependent problems using domain decomposition methods. In the classical approach, one discretizes first the time dimension and then one solves a sequence of steady problems by a domain decomposition method. In this paper, we treat directly the time dependent problem and we study a Schwarz waveform relaxation algorithm for the convection diffusion equation in two dimensions. We introduce the operators on the interfaces which minimize the convergence rate, resulting in an efficient method: numerical results illustrate the performances and show that the corresponding algorithms converge much faster than the classical one.