Efficiency Based Adaptive Local Refinement for First-Order System Least-Squares Formulations
Efficiency Based Adaptive Local Refinement for First-Order System Least-Squares Formulations
复制标题
一阶系统最小二乘公式基于效率的自适应局部细化
DOI：
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发表时间：
2011
影响因子：
3.1
通讯作者：
Lei Tang
中科院分区：
文献类型：
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作者：
J. Adler;T. Manteuffel;S. McCormick;J. Nolting;J. Ruge;Lei Tang
本文结合嵌套迭代的代数多重网格方法，提出了一阶系统最小二乘有限元的自适应局部细化（ALR）策略。目标是以最少的计算成本和误差在所有元素上的几乎均匀分布达到一定的容错性。为了实现这一点，每个精化级别的精化决策都是基于考虑到减少错误和计算成本的优化效率度量来确定的。讨论了两种效率措施：预测误差减少和预测计算成本。这些方法首先应用于具有陡峭梯度的二维泊松问题，并将结果与[W. W.]中描述的基于阈值的方法进行比较。多夫勒，SIAM J. number。分析的。， 33(1996)，第1106-1124页。接下来，将这些方法应用于不可压缩、电阻磁流体动力学方程的二维简化模型。这些方程用于模拟大展弦比托卡马克的不稳定性。我们表明，通过在该系统上使用新的ALR策略，我们能够在相同的容错范围内，仅使用用于在均匀精细网格上近似解的计算成本的10%来解决物理问题。
In this paper, we propose new adaptive local refinement (ALR) strategies for first-order system least-squares finite elements in conjunction with algebraic multigrid methods in the context of nested iteration. The goal is to reach a certain error tolerance with the least amount of computational cost and nearly uniform distribution of the error over all elements. To accomplish this, the refinement decision at each refinement level is determined based on optimizing efficiency measures that take into account both error reduction and computational cost. Two efficiency measures are discussed: predicted error reduction and predicted computational cost. These methods are first applied to a two-dimensional (2D) Poisson problem with steep gradients, and the results are compared with the threshold-based methods described in [W. Dorfler, SIAM J. Numer. Anal., 33 (1996), pp. 1106-1124]. Next, these methods are applied to a 2D reduced model of the incompressible, resistive magnetohydrodynamic equations. These equations are used to simulate instabilities in a large aspect-ratio tokamak. We show that, by using the new ALR strategies on this system, we are able to resolve the physics using only 10 percent of the computational cost used to approximate the solutions on a uniformly refined mesh within the same error tolerance.