Parallel Nesterov Domain Decomposition Method for Elliptic Partial Differential Equations
Abstract
We study a parallel non-overlapping domain decomposition method, based on the Nesterov accelerated gradient descent, for the numerical approximation of elliptic partial differential equations. The problem is reformulated as a constrained (convex) minimization problem with the interface continuity conditions as constraints. The resulting domain decomposition method is an accelerated projected gradient descent with convergence rate . At each iteration, the proposed method needs only one matrix/vector multiplication. Numerical experiments show that significant (standard and scaled) speed-ups can be obtained.
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