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首页> 外文期刊>International Journal for Numerical Methods in Engineering >Numerical p-version refinement studies for the regularized stress-BEM
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Numerical p-version refinement studies for the regularized stress-BEM

机译：正则应力BEM的数值p版本细化研究

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摘要

In the development of the boundary element method (BEM) and the finite element method (FEM) researchers have typically selected similar basis functions. That is, both methods typically employ low-order interpolations such as piece-wise linear or piece-wise quadratic and rely on h-version refinement to increase accuracy as required. In the case of the FEM, the decision to use low-order elements is made for computational efficiency as an attractive compromise between local modeling accuracy and sparseness of the resulting linear system. However, in many BEM formulations, low-order elements may be the only practical choice given the complexity of using analytic integration formulae in conjunction with special integral interpretations. Unlike their efficient use in the FEM, fine meshes of low-order elements in the BEM are highly inefficient from a computational standpoint given the dense nature of BEM systems. Moreover, owing to singularities in the kernel functions, the BEM should be expected to benefit more so than the FEM from very high levels of local accuracy. Through the use of regularized algorithms which only require numerical integration, p-version refinement in the BEM is easily extended to include any set of basis functions with no significant increase in programming complexity. Numerical results show that by using interpolations as high as 12th and 16th order, one can expect reductions in error by as many as five orders of magnitude over comparable algorithms based on similar system size. For two-dimensional problems, it is also shown that, for a given level of error, one can expect reductions in system size by an order of magnitude, thus leading to a reduction in computational expense for conventional algorithms by three orders of magnitude.
机译：在边界元法（BEM）和有限元法（FEM）的发展中，研究人员通常选择相似的基函数。也就是说，两种方法通常都采用低阶插值法，例如逐段线性或逐段二次，并依赖于h版本细化以根据需要提高准确性。对于FEM，决定使用低阶元素是为了提高计算效率，这是在局部建模精度和所得线性系统的稀疏性之间的一种有吸引力的折衷方案。但是，在许多BEM公式中，考虑到使用解析积分公式结合特殊积分解释的复杂性，低阶元素可能是唯一的实际选择。不同于BEM在FEM中的有效使用，鉴于BEM系统的密集性质，从计算的角度来看，BEM中的低阶元素的精细网格效率非常低。此外，由于内核功能的奇异性，应该期望BEM比FEM受益于非常高的局部精度水平。通过使用仅需要数值积分的正则化算法，可以轻松扩展BEM中的p版本优化，使其包含任何基础函数集，而不会显着增加编程复杂性。数值结果表明，与基于相似系统大小的可比算法相比，通过使用高达12和16阶的插值，可以预期误差减少多达五个数量级。对于二维问题，还显示出，对于给定的错误级别，可以期望将系统大小减少一个数量级，从而导致传统算法的计算开销减少三个数量级。

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