Recent advances in multipreconditioned domain decomposition methods
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Multipreconditioned domain decomposition methods, such as Adaptive Multipreconditioned FETI [1] and Adaptive Multipreconditioned BDD [2], provide an efficient and robust alternative to adaptive coarse spaces [3]. These approaches combine a non-overlapping domain decomposition formulation with a multipreconditioned Krylov solver [4, 5]. For symmetric positive definite systems, an adaptive selection procedure makes it possible to retain only the most relevant preconditioners among the available candidates [6]. In non-overlapping domain decomposition methods, multipreconditioning naturally arises from the decomposition itself, as each subdomain contributes a candidate search direction. However, at large scale, the number of subdomains increases significantly, making the control of the memory footprint a critical issue. To address this challenge, a first improvement was proposed by aggregating subdomain search directions into multipreconditioning aggregates and by introducing an algorithm allowing these aggregates to evolve dynamically [7]. In this work, we propose two new contributions. First, we introduce a strategy to optimally weight the contribution of subdomain search directions. Second, we extend the framework to field-split multipreconditioning in order to handle multiphysics problem. New algorithms and large scale studies will be presented.
