Abstract: Hydraulic fracturing simulations require the solution of strongly coupled, nonlinear, and often numerically stiff systems arising from the interaction of nonlocal rock elasticity, viscous fluid flow, and fracture propagation. In implicit formulations, a major computational bottleneck is the repeated solution of sparse linear algebraic equation systems at each Newton–Raphson iteration and time step. This work proposes a preconditioner for the reduced linear systems produced by a Newton–Raphson discretization that combines finite elements for the flow equations with a boundary-element treatment of the elasticity operator. The method approximates the inverse matrix using a Neumann series expansion built on a Jacobi preconditioner, so that applying the preconditioner reduces to a sequence of sparse matrix-vector multiplications without triangular substitutions. Numerical experiments on two hydraulic-fracture simulations with different grid sizes compare the proposed approach with ILU0 and evaluate CPU and GPU implementations of sparse matrix-vector products.

Cite: Manaev A.A. , Prokhorov D.I. , Chepelenkova V.D.
Parallel Preconditioner for Solving SLAE from the Hydraulic Fracturing Problem
Lobachevskii Journal of Mathematics. 2026. V.47. N8. P.3673–3682. DOI: 10.1134/S1995080226618862

Dates:

Submitted:	Apr 14, 2026
Accepted:	Apr 30, 2026

Identifiers: No identifiers

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