Title: The Parallel Algorithms of Series Solution under Precise Integration for Nonlinear Dynamic Equations
Abstract: Nonlinear dynamic equations can be changed into one order differential equations.The solution of the equations is composed of two parts: the homogeneous solution caused by the initial value and the particular solution caused by the loading item.The first part of computation is based on the precise solution of exponential matrix,and the second part is solved by series solution.Three parallel algorithms were presented.For every item of the series solution, the first algorithm calculates one linear combination of several vectors,and then one matrix-vector product.The second algorithm has the principle of the first algorithm,but the second algorithm changes power of matrix into product of matrix.The third algorithm calculates several matrix-vector products,and then one linear combination of several vectors.The first algorithm has the best parallel efficiency.But it needs a great deal of memory and is not benefit to large-scale question.Based on the sparse transform of dynamic equations,the second and third algorithms improve the deficiency of the first algorithm.In general,the third algorithm spends less time than the second algorithm,because the third algorithm calculates every item of series solution on the basis of its preceding(item.) Finally,these algorithms were demonstrated by a numerical example and have higher speedup.
Publication Year: 2006
Publication Date: 2006-01-01
Language: en
Type: article
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