The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
In this note, we introduce a new approach to study overlapping domain decomposition methods for optimal control systems governed by partial differential equations. The model considered in our paper is systems governed by wave equations. Our technique could be used for several other equations as well.
We present in this paper a proof of well-posedness and convergence for the parallel Schwarz Waveform Relaxation Algorithm adapted to an N-dimensional semilinear heat equation. Since the equation we study is an evolution one, each subproblem at each step has its own local existence time, we then determine a common existence time for every problem in any subdomain at any step. We also introduce a new technique: Exponential Decay Error Estimates, to prove the convergence of the Schwarz Methods, with...
In this paper, we introduce a new approach for the convergence problem of optimized Schwarz methods by studying a generalization of these methods for a semilinear elliptic equation. We study the behavior of the algorithm when the overlapping length is large.
Download Results (CSV)