Unified computational framework for the efficient solution of n-field coupled problems with monolithic schemes

摘要

In this paper, we propose and evaluate the performance of a unifiedcomputational framework for preconditioning systems of linear equationsresulting from the solution of coupled problems with monolithic schemes. Theframework is composed by promising application-specific preconditionerspresented previously in the literature with the common feature that they areable to be implemented for a generic coupled problem, involving an arbitrarynumber of fields, and to be used to solve a variety of applications. The firstselected preconditioner is based on a generic block Gauss-Seidel iteration foruncoupling the fields, and standard algebraic multigrid (AMG) methods forsolving the resulting uncoupled problems. The second preconditioner is based onthe semi-implicit method for pressure-linked equations (SIMPLE) which isextended here to deal with an arbitrary number of fields, and also results inuncoupled problems that can be solved with standard AMG. Finally, a moresophisticated preconditioner is considered which enforces the coupling at allAMG levels, in contrast to the other two techniques which resolve the couplingonly at the finest level. Our purpose is to show that these methods performsatisfactory in quite different scenarios apart from their originalapplications. To this end, we consider three very different coupled problems:thermo-structure interaction, fluid-structure interaction and a complex modelof the human lung. Numerical results show that these general purpose methodsare efficient and scalable in this range of applications.