Optimal and optimized domain decomposition methods on the sphere
نویسنده
چکیده
At the heart of numerical weather prediction algorithms lie a Laplace and positive definite Helmholtz problems on the sphere [12]. Recently, there has been interest in using finite elements [2] and domain decomposition methods [1, 10]. The Schwarz iteration [7, 8, 9] and its variants [9, 4, 5, 6, 3, 11] are popular domain decomposition methods. In this paper, we introduce improved transmission operators for the Laplace problem on the sphere. In section 2, we review the Laplace operator on the sphere and recall the Schwarz iteration and its convergence estimates, previously published in [1]; we also give a new semidiscrete estimate which is substantially similar to the continuous one. In section 3, we introduce the framework of the optimized Schwarz iteration and give optimized operators. In section 4, we present numerical results that agree with the theoretical predictions.
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