Domain Decomposition Algorithms for Linear Hyperbolic Equations
The use of parallel computers for solving partial differential equations is important in areas such as fluid dynamics, reservoir simulation, and structural analysis, where many of the problems of interest cannot be solved without the use of supercomputers. One technique for applying parallel computers to the solution of these problems is known as domain decomposition where the domain of interest is subdivided into several smaller subdomains and the task of solving the partial differential equation on each subdomain problem is assigned to a different processor. The global solution is then synthesized from the solutions computed on the individual subdomains. Much of the current work in the application of domain decomposition techniques has been in the area of elliptic partial differential equations, with very little attention being given to hyperbolic equations. We propose to use the methods of domain decomposition for the solution of linear hyperbolic equations. The idea of using overlapping domains is introduced in the context of linear hyperbolic equations to develop a domain decomposition algorithm which is shown to be well suited for parallel processors. The issues of communication costs and load balancing are addressed and a simple strategy for assigning jobs to processors to achieve load balancing is presented.
Citable link to this pagehttps://hdl.handle.net/1911/101630
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