Solve the Quasi-static Biot Problem on Shared Memory Systems with Various Processors

The quasi-static frequency domain Biot equation can be used to model loading of fluid-filled poroelastic materials in low-frequency case and to estimate effective frequency-dependent strain and stress relations. To numerically solve the Biot equation, we proposed an algorithm based on finite-difference approximation, iterative solution of the obtained system of linear algebraic equations (SLAE) and using field-split preconditioner technique. The basis of the iterative solver is the Biconjugate Gradient Stabilized (BCGStab); inverting the preconditioner is based on using the direct solver. In this paper, we present the results of implementation and testing the proposed algorithm on various shared memory systems. The experiments were performed on servers with Intel, AMD and Elbrus processors. The accuracy, memory and performance characteristics were measured. The results demonstrate robustness of the proposed algorithm on these architectures.