Development of a Stokes flow solver robust to large viscosity jumps using a Schur complement approach with mixed precision arithmetic

Furuichi, Mikito; May, David A.; Tackley, P. J.

doi:10.1016/j.jcp.2011.09.007

Cited by 65 publications

(48 citation statements)

References 28 publications

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“…This procedure of the mixed precision method is consistent with the idea that the preconditioner is used for a rough estimation of the real solution. The high precision calculation of full recurrence relation in GCR method is found to avoid the stagnation of convergence, and improves the robustness of the solver [3].…”

Section: Methodsmentioning

confidence: 99%

“…There have been many studies and developments of the solution procedure of Stokes flow problems toward realistically simulating mantle convection, for example, in the treatment of highly varying viscosity, nonlinear rheology, transport of material, spherical shell geometry and adaptive grid resolutions [1][2][3][4][5][6][7][8][9][10][11]. In addition, recent advances of the technology allow one to conduct high resolution simulations, in which the coupled system of geodynamical processes in different time and spatial scales -such as global mantle convection and local deformation of a tectonic plate -can be directly and consistently reproduced within the same numerical framework [e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In earlier studies, I and coworkers developed solution algorisms of the low diffusive advection, and the Stokes flow solver dealing with high viscosity contrast problems [1][2][3]. In this study, these techniques are applied to the problems of spherical Cartesian in three dimensions.…”

Section: Introductionmentioning

confidence: 99%

“…The surface of the object is advected by the CIP-CSLR method, which is based on a fully fixed Eulerian mesh and suitable for computation on the vector processors [19][20]. The illconditioned Stokes flow problems due to sticky air and rheological modeling are solved by the iterative solver utilizing a strong Schur complement preconditioner and mixed precision arithmetic [3,21].…”

Section: Introductionmentioning

confidence: 99%

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Numerical modeling of three dimensional self-gravitating Stokes flow problem with free surface

Furuchi

2011

Procedia Computer Science

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A solution code of the Stokes flow system in three dimensions under a self-gravitating field was developed with a free surface in order to simulate the long-time scale evolution of the solid earth system on the massively parallel-vector super computer Earth Simulator 2 (ES2). The largely deformable surface of a planetary body is represented by a sharp boundary of scalar color function, which is advected by the CIP-CLSR method. The self-gravitating field is calculated by the Poisson equation of the gravity potential. A low viscous material (sticky air) surrounding the planet mimics its free surface motion. In order to solve the ill conditioned Stokes problem of the finite difference discretization on a staggered grid, I employ the iterative Stokes flow solver, robust to large viscosity jumps, using a strong Schur complement preconditioner and mixed precision arithmetic utilizing the double-double method. In this paper, I present an overview of the numerical algorithms and the current parallel programming strategy for the efficient performance on ES2. In addition, preliminary results of the core formation simulation are demonstrated in three dimensions as an example of the target Stokes flow system of this simulation code.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical modeling of three dimensional self-gravitating Stokes flow problem with free surface

Furuchi

2011

Procedia Computer Science

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“…The rheology of the earth contains large viscosity variations occurring over short distances, and this poses a challenge for computational codes [25,24,30,22,10,6,16,9]. For example, experimental studies and observations of seismic anisotropy suggest that dislocation creep is the dominant deformation mechanism in the upper mantle [14,21,16].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional simulations of geometrically complex subduction with large viscosity variations

Jadamec

Billen

Kreylos

2012

Proceedings of the 1st Conference of the Extreme Science and Engineering Discovery Environment: Bridging From the eXtreme to Th

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The incorporation of geologic realism into numerical models of subduction is becoming increasingly necessary as observational and experimental constraints indicate plate boundaries are inherently three-dimensional (3D) in nature and contain large viscosity variations. However, large viscosity variations occurring over short distances pose a challenge for computational codes, and models with complex 3D geometries require substantially greater numbers of elements, increasing the computational demands. We modified a community mantle convection code, CitcomCU, to model realistic subduction zones that use an arbitrarily shaped 3D plate boundary interface and incorporate the effects of a strainrate dependent viscosity based on an experimentally derived flow law for olivine aggregates. Tests of this implementation on 3D models with a simple subduction zone geometry indicate that limiting the overall viscosity range in the model, as well as limiting the viscosity jump across an element, improves model runtime and convergence behavior, consistent with what has been shown previously. In addition, the choice of method and averaging scheme used to transfer the viscosity structure to the different levels in the multigrid solver can significantly improve model performance. These optimizations can improve model runtime by over 20%. 3D models of a subduction zone with a complex plate boundary geometry were then constructed, containing over 100 million finite element nodes with a local resolution of up to 2.35 km, and run on XSEDE. These complex 3D models, representative of the Alaska subduction zone-transform plate boundary, contain viscosity variations of up to seven orders of magnitude. The optimizations in solver parameters determined from the simple 3D models of subduction applied to the much larger and more complex models of an actual subduction zone im- * Corresponding author.Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. proved model convergence behavior and reduced runtimes by on the order of 25%. One scientific result from 3D models of Alaska is that a laterally variable mantle viscosity emerges in the mantle as a consequence of variations in the flow field, with localized velocities of greater than 80 cm/yr occurring close to the subduction zone where the negative buoyancy of the slab drives the flow. These results are a significant departure from the paradigm of two-dimensional (2D) models of subduction where the slab velocity is often fixed to surface plate motion. While the solver parameter optimization can improve model performance, the results also demonstrate the need for new solvers to keep pace with the demands for increasingly complex numerical...

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Robust coupled fluid‐particle simulation scheme in Stokes‐flow regime: Toward the geodynamic simulation including granular media

Furuichi

Nishiura

2014

Geochem Geophys Geosyst

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We present a simulation scheme for solving high-viscosity fluid and particle dynamics in a coupled computational fluid dynamics and discrete element method (CFD-DEM) framework. This simulation scheme is intended to be used for geodynamical magmatic studies such as crystal settling at the melting roof of a magma chamber. The high-viscosity fluid is treated by the Stokes-flow approximation, where the fluid interacts with particles via the drag force in a cell-averaged manner. The particles are tracked with contact forces by DEM. To efficiently solve such Stokes-DEM coupled equations, we propose two key techniques. One is formulation of particle motion without the inertial term, allowing a larger time step at higher viscosities. The other is a semi-implicit treatment of the cell-averaged particle velocity in the fluid equation to stabilize the calculation. We simulate the settling particles in strongly viscous fluids in three dimensions and compare the results with the experimental and theoretical results. Our solution strategy is found to be robust and successfully captures the collective behavior of the particles. The simulation method presented here will be useful in various fields interested in long-term dynamics of high-viscosity granular media.

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Development of a Stokes flow solver robust to large viscosity jumps using a Schur complement approach with mixed precision arithmetic

Cited by 65 publications

References 28 publications

Numerical modeling of three dimensional self-gravitating Stokes flow problem with free surface

Numerical modeling of three dimensional self-gravitating Stokes flow problem with free surface

Three-dimensional simulations of geometrically complex subduction with large viscosity variations

Robust coupled fluid‐particle simulation scheme in Stokes‐flow regime: Toward the geodynamic simulation including granular media

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