A multigrid waveform relaxation method for solving the poroelasticity equations

Journal Article · Sat Sep 15 04:00:00 EDT 2018 · Computational and Applied Mathematics

DOI:https://doi.org/10.1007/S40314-018-0603-9· OSTI ID:22769221

Pinto, M. A. V., ^[1]

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1. Federal University of Paraná, Department of Mechanical Engineering (Brazil)

In this work, a multigrid waveform relaxation method is proposed for solving a collocated finite difference discretization of the linear Biot’s model. This gives rise to the first space–time multigrid solver for poroelasticity equations in the literature. The waveform relaxation iteration is based on a point-wise Vanka smoother that couples the pressure variable at a grid-point with the displacements around it. A semi-algebraic mode analysis is proposed to theoretically analyze the convergence of the multigrid waveform relaxation algorithm. This analysis is novel since it combines the semi-algebraic analysis, suitable for parabolic problems, with the non-standard analysis for overlapping smoothers. The practical utility of the method is illustrated through several numerical experiments in one and two dimensions.

• OSTI ID: 22769221
• Journal Information: Computational and Applied Mathematics, Journal Name: Computational and Applied Mathematics Journal Issue: 4 Vol. 37; ISSN 0101-8205
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ALGORITHMS
CONVERGENCE
EQUATIONS
RELAXATION
WAVE FORMS