A Class of Stable, Globally Noniterative, Nonoverlapping Domain Decomposition Algorithms for the Simulation of Parabolic Evolutionary Systems.
Date of Award
Doctor of Philosophy (PhD)
Donald H. Kraft
Parabolic systems are governed by time dependent partial differential equations. To obtain a high simulation quality that captures important features of a parabolic system requires solving the governing equation to an adequate accuracy, which necessitates a large sampling size in the spatial and temporal dimensions, and hence a large amount of simulation data and high computing cost. Domain decomposition is an effective method of divide-and-conquer paradigm that divides the problem domain into several subdomains, reducing the original problem into several smaller interdependent problems which can be solved in parallel. In this dissertation, we propose a class of stabilized explicit-implicit time marching (SEITM) domain decomposition algorithms for parabolic equations. Explicit-implicit time marching (EITM) algorithms are globally non-iterative nonoverlapping domain decomposition methods, which, when compared with Schwartz algorithm based parabolic solvers, are both computationally and communicationally efficient for each time step simulation but suffer from small time step size restrictions due to conditional stability. The proposed stabilization techniques in the SEITM algorithms retain the time-stepwise efficiency in computation and communication of the EITM algorithms but free the algorithms from small time step size restrictions, rendering SEITM algorithms excellent candidates for large scale parallel simulation problems. Three algorithms of the SEITM class are presented in this dissertation, which are mathematically analyzed and experimentally tested to show excellent numerical stability, computation and communication efficiencies, and high parallel speedup and scalability.
Zhuang, Yu, "A Class of Stable, Globally Noniterative, Nonoverlapping Domain Decomposition Algorithms for the Simulation of Parabolic Evolutionary Systems." (2000). LSU Historical Dissertations and Theses. 7406.