Solution of elliptic partial differential equations by an optimization-based domain decomposition method

2000 ◽  
Vol 113 (2-3) ◽  
pp. 111-139 ◽  
Author(s):  
Max D. Gunzburger ◽  
Matthias Heinkenschloss ◽  
Hyesuk Kwon Lee
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential

Parallel Nesterov Domain Decomposition Method for Elliptic Partial Differential Equations

2020 ◽  
Vol 30 (01) ◽  
pp. 2050004
Author(s):  
Firmin Andzembe Okoubi ◽  
Jonas Koko
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Gradient Descent ◽  
Domain Decomposition Method ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Matrix Vector Multiplication ◽  
Constrained Convex Minimization Problem

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 [Formula: see text]. 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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