Algebraic preconditioning for Biot-Barenblatt poroelastic systems

Abstract

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Robust block diagonal preconditioners for poroelastic problems with strongly heterogeneous material

“…One can see that the estimates of and are independent of $$$ \tau $$$, $$$ h $$$ and $$$ k $$$. We note that an alternative derivation of estimate (47) can be found in References 26,30.…”

“…The related numerical solution methods can be divided into block‐splitting methods with Uzawa‐type algorithms 22–25 and preconditioned Krylov methods, applied on the original monolithic algebraic system 26,27 . The related preconditioners reflect the block structure and are based on Schur complements 16,28–31 . In fact, such preconditioners also decouple the poroelastic systems and shift the main computational workload to solving modified single‐field systems.…”

“…26,27 The related preconditioners reflect the block structure and are based on Schur complements. 16,[28][29][30][31] In fact, such preconditioners also decouple the poroelastic systems and shift the main computational workload to solving modified single-field systems. This is a common feature of the preconditioned Krylov methods and the block-splitting methods.…”