Computers and Mathematics with Applications A partially parallel-in-time fixed-stress splitting method for Biot’s consolidation model
Computers and Mathematics with Applications A partially parallel-in-time fixed-stress splitting method for Biot’s consolidation model
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计算机和数学及其应用 Biot 固结模型的部分时间并行固定应力分裂方法
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通讯作者：
M. Ferronato
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作者：
Caterina Millevoi;N. Spiezia;M. Ferronato
在这项工作中，我们研究了多孔介质中流动和流体力学耦合的平行时间迭代解，该解由Biot方程的双场公式模拟。特别地，我们提出了一种新版本的固定应力分裂法，作为这些问题的求解方法得到了广泛的应用。这种新方法忘记了时间变量的顺序性，而把时间方向作为并行化的进一步方向。对该方法进行了严格的收敛性分析，并通过数值实验验证了该算法的鲁棒性。
In this work, we study the parallel-in-time iterative solution of coupled flow and ge- omechanics in porous media, modelled by a two-field formulation of Biot’s equations. In particular, we propose a new version of the fixed-stress splitting method, which has been widely used as solution method of these problems. This new approach forgets about the sequential nature of the temporal variable and considers the time direction as a further directionforparallelization.Themethodispartiallyparallel-in-time.Wepresentarigorous convergence analysis of the method and numerical experiments to demonstrate the robust behaviour of the algorithm.