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Implementation of a fully-balanced periodic tridiagonal solver on a parallel distributed memory architecture

机译：在并行分布式内存体系结构上实现全平衡周期三对角线求解器

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While parallel computers offer significant computational performance, it is generally necessary to evaluate several programming strategies. Two programming strategies for a fairly common problem - a periodic tridiagonal solver - are developed and evaluated. Simple model calculations as well as timing results are presented to evaluate the various strategies. The particular tridiagonal solver evaluated is used in many computational fluid dynamic simulation codes. The feature that makes this algorithm unique is that these simulation codes usually require simultaneous solutions for multiple right-hand-sides (RHS) of the system of equations. Each RHS solutions is independent and thus can be computed in parallel. Thus a Gaussian elimination type algorithm can be used in a parallel computation and the more complicated approaches such as cyclic reduction are not required. The two strategies are a transpose strategy and a distributed solver strategy. For the transpose strategy, the data is moved so that a subset of all the RHS problems is solved on each of the several processors. This usually requires significant data movement between processor memories across a network. The second strategy attempts to have the algorithm allow the data across processor boundaries in a chained manner. This usually requires significantly less data movement. An approach to accomplish this second strategy in a near-perfect load-balanced manner is developed. In addition, an algorithm will be shown to directly transform a sequential Gaussian elimination type algorithm into the parallel chained, load-balanced algorithm.
机译：尽管并行计算机提供了显着的计算性能，但通常有必要评估几种编程策略。开发并评估了针对一个常见问题的两种编程策略-周期性三对角线求解器。给出了简单的模型计算以及时序结果，以评估各种策略。在许多计算流体动力学仿真代码中使用了评估的特定三对角线求解器。使该算法独特的功能是，这些仿真代码通常需要同时求解方程组的多个右侧（RHS）。每个RHS解决方案都是独立的，因此可以并行计算。因此，可以在并行计算中使用高斯消除类型算法，并且不需要诸如循环归约之类的更复杂的方法。这两个策略是转置策略和分布式求解器策略。对于转置策略，需要移动数据，以便在多个处理器中的每个处理器上解决所有RHS问题的子集。这通常需要整个网络中处理器内存之间的大量数据移动。第二种策略试图使算法以链式方式允许数据跨处理器边界。通常，这需要很少的数据移动。开发了一种以接近完美的负载平衡方式完成第二种策略的方法。此外，将显示一种算法，可以将顺序高斯消除类型算法直接转换为并行链接的负载平衡算法。

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