论文标题
域分解和分配方法，用于混合有限元离散化的毛弹性系统
Domain decomposition and partitioning methods for mixed finite element discretizations of the Biot system of poroelasticity
论文作者
论文摘要
我们为混合形式的生物弹性生物系统开发了非重叠的域分解方法。固体变形是用具有弱应力对称性的混合三体配方建模的。用混合的Darcy配方对流体流进行建模。我们在子域界面上引入位移和压力lagrange乘数，分别施加了正常应力和正常速度的弱连续性。全局问题减少为Lagrange乘数的接口问题，该问题通过Krylov空间迭代方法解决。我们研究整体和分裂方法。在整体方法中，解决了一个耦合的位移压力界面问题，每次迭代都需要解决局部生物局问题的解决方案。我们表明，所得的接口操作员是正定的，并分析了迭代的收敛性。我们进一步研究了排出的分裂和固定应力生物分裂，在这种情况下，我们解决了需要弹性和达西解决的单独界面问题。我们分析了拆分配方的稳定性。提出了数值实验，以说明域分解方法的收敛性并比较其准确性和效率。
We develop non-overlapping domain decomposition methods for the Biot system of poroelasticity in a mixed form. The solid deformation is modeled with a mixed three-field formulation with weak stress symmetry. The fluid flow is modeled with a mixed Darcy formulation. We introduce displacement and pressure Lagrange multipliers on the subdomain interfaces to impose weakly continuity of normal stress and normal velocity, respectively. The global problem is reduced to an interface problem for the Lagrange multipliers, which is solved by a Krylov space iterative method. We study both monolithic and split methods. In the monolithic method, a coupled displacement-pressure interface problem is solved, with each iteration requiring the solution of local Biot problems. We show that the resulting interface operator is positive definite and analyze the convergence of the iteration. We further study drained split and fixed stress Biot splittings, in which case we solve separate interface problems requiring elasticity and Darcy solves. We analyze the stability of the split formulations. Numerical experiments are presented to illustrate the convergence of the domain decomposition methods and compare their accuracy and efficiency.
