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

We present general purpose preconditioners for the efficient solution of quite general coupled problems using monolithic schemes. The proposed preconditioners form an unified framework that can be implemented for any generic coupled problem, involving an arbitrary number of fields, and be used to solve a large variety of applications. The preconditioners presented here are obtained by generalizing promising application-specific techniques presented pre- viously in the literature. The first one is based on a generic block Gauss-Seidel iteration for uncoupling the fields, and standard algebraic multigrid (AMG) methods for solving the resulting uncoupled problems. The second preconditioner is based on the SIMPLE method which is extended here to deal with an arbitrary number of fields, which also results in uncoupled problems that can be solved with standard AMG. Finally, a more sophisticated preconditioner is considered which enforces the coupling at all AMG levels, in contrast to the other two techniques which resolve the coupling only at the finest level. The versatility of the preconditioners is demonstrated considering three very different coupled problems: thermo-structure interaction, fluid-structure interaction and a complex model of the human lung. Numerical results show that the general purpose methods are efficient and scalable in a wide range of applications.     «

We present general purpose preconditioners for the efficient solution of quite general coupled problems using monolithic schemes. The proposed preconditioners form an unified framework that can be implemented for any generic coupled problem, involving an arbitrary number of fields, and be used to solve a large variety of applications. The preconditioners presented here are obtained by generalizing promising application-specific techniques presented pre- viously in the literature. The fi...     »