Dynamic Load Balancing for the Parallel, Adaptive, Multigrid Solution of Implicit Phase-Field Simulations

In this paper we assess the performance of a selection of load balancing strategies for a parallel, adaptive multigrid solver that has been developed for the implicit solution of phase-field problems. The strategies considered include a number of standard approaches and a new technique that we propose specifically for multigrid solvers. This technique takes account of the sequential nature of the grid correction used in multiplicative multilevel algorithms such as multigrid. The paper focuses on two phase-field example problems which model the rapid solidification of an undercooled binary alloy: using isothermal and non-isothermal models respectively. We undertake a systematic comparison of the different load-balancing strategies for a selection of different adaptive mesh scenarios. We conclude that the optimal choice of load-balancing strategy depends critically on the computation to communication ratio of the parallel multigrid solver, and that in the computation-dominated limit our proposed technique is typically the most effective of those considered.

[1]  P. Jimack,et al.  A new approach to multi-phase formulation for the solidification of alloys , 2012 .

[2]  Nathan Ida,et al.  Introduction to the Finite Element Method , 1997 .

[3]  Peter K. Jimack,et al.  Three dimensional thermal-solute phase field simulation of binary alloy solidification , 2014, J. Comput. Phys..

[4]  D. Brandt,et al.  Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .

[5]  G E Karniadakis,et al.  Flow instability and wall shear stress variation in intracranial aneurysms , 2010, Journal of The Royal Society Interface.

[6]  Wenqiang Feng,et al.  A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-cartesian grids , 2018, J. Comput. Phys..

[7]  Peter K. Jimack,et al.  On the fully implicit solution of a phase-field model for binary alloy solidification in three dimensions , 2012 .

[8]  Ümit V. Çatalyürek,et al.  A framework for scalable greedy coloring on distributed-memory parallel computers , 2008, J. Parallel Distributed Comput..

[9]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[10]  T. Pusztai,et al.  Consistent multiphase-field theory for interface driven multidomain dynamics , 2015, 1508.04311.

[11]  Hans Leo Lukas,et al.  Computational Thermodynamics: Basis , 2007 .

[12]  Peter K. Jimack,et al.  An optimally efficient technique for the solution of systems of nonlinear parabolic partial differential equations , 2017, Adv. Eng. Softw..

[13]  G. Smith,et al.  Numerical Solution of Partial Differential Equations: Finite Difference Methods , 1978 .

[14]  Courtenay T. Vaughan,et al.  Zoltan data management services for parallel dynamic applications , 2002, Comput. Sci. Eng..

[15]  George Karypis,et al.  Parmetis parallel graph partitioning and sparse matrix ordering library , 1997 .

[16]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[17]  Martin Berzins,et al.  A comparison of some dynamic load-balancing algorithms for a parallel adaptive flow solver , 2000, Parallel Comput..

[18]  Peter MacNeice,et al.  Paramesh: A Parallel Adaptive Mesh Refinement Community Toolkit , 2013 .

[19]  Roy D. Williams,et al.  Performance of dynamic load balancing algorithms for unstructured mesh calculations , 1991, Concurr. Pract. Exp..

[20]  Peter K. Jimack,et al.  An adaptive, fully implicit multigrid phase-field model for the quantitative simulation of non-isothermal binary alloy solidification , 2008 .

[21]  N. Goldenfeld,et al.  Adaptive Mesh Refinement Computation of Solidification Microstructures Using Dynamic Data Structures , 1998, cond-mat/9808216.

[22]  P. Jimack,et al.  Bracket formalism applied to phase field models of alloy solidification , 2017 .

[23]  J. Strikwerda.  Finite Difference Schemes and Partial Differential Equations , 1989 .

[24]  A. Iserles.  A First Course in the Numerical Analysis of Differential Equations: Stiff equations , 2008 .