This paper presents a hybrid scheduling strategy for the parallel solution of linear systems using the multifrontal method. The approach combines static and dynamic scheduling to optimize both workload and memory usage. The static phase uses an optimistic scenario to estimate memory requirements, which is then relaxed during the dynamic phase to allow for more flexible task scheduling. The authors propose a new scheduler that incorporates these constraints, improving performance by allowing for better decision-making in the presence of memory limitations. Experimental results on large sparse matrices demonstrate that the hybrid approach significantly reduces memory usage and factorization time compared to a standard approach, even under tight memory constraints. The benefits are more pronounced for symmetric matrices, with a notable improvement in factorization time on 128 processors. The paper also discusses future improvements, including better exploitation of SMP node information and more sophisticated task selection strategies.This paper presents a hybrid scheduling strategy for the parallel solution of linear systems using the multifrontal method. The approach combines static and dynamic scheduling to optimize both workload and memory usage. The static phase uses an optimistic scenario to estimate memory requirements, which is then relaxed during the dynamic phase to allow for more flexible task scheduling. The authors propose a new scheduler that incorporates these constraints, improving performance by allowing for better decision-making in the presence of memory limitations. Experimental results on large sparse matrices demonstrate that the hybrid approach significantly reduces memory usage and factorization time compared to a standard approach, even under tight memory constraints. The benefits are more pronounced for symmetric matrices, with a notable improvement in factorization time on 128 processors. The paper also discusses future improvements, including better exploitation of SMP node information and more sophisticated task selection strategies.