Analysis of the Efficiency PETSc and PETIGA Libraries in Solving the Problem of Crystal Growth

We present an analysis of high performance computational method for solving the problem of crystal grows. The method uses PETSc and PETIGA C-language based libraries and supports parallel computing. The evolution of calculation process was studied in series of special computations are obtained on innovative mobile cluster platform, which provides exclusive system tuning abilities. The results of research confirm the high efficiency of the proposed algorithm on multi-core computer systems and allow us to recommend the use of PETSc and PETIGA for solving high order differential equations.

[1]  Peter Galenko,et al.  Phase-field-crystal and Swift-Hohenberg equations with fast dynamics. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Martin Grant,et al.  Modeling elasticity in crystal growth. , 2001, Physical review letters.

[3]  Lisandro Dalcin,et al.  PetIGA: High-Performance Isogeometric Analysis , 2013, ArXiv.

[4]  G. Tóth,et al.  Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2D and 3D , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[5]  M. Grant,et al.  Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Xesús Nogueira,et al.  An unconditionally energy-stable method for the phase field crystal equation , 2012 .

[7]  William Gropp,et al.  PETSc Users Manual Revision 3.4 , 2016 .

[8]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[9]  T. Hughes,et al.  Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations , 2010 .

[10]  T. Hughes,et al.  Isogeometric analysis of the Cahn–Hilliard phase-field model , 2008 .

[11]  László Gránásy,et al.  Advanced operator splitting-based semi-implicit spectral method to solve the binary phase-field crystal equations with variable coefficients , 2009, J. Comput. Phys..

[12]  Ilya Starodumov,et al.  Three dimensional structures predicted by the modified phase field crystal equation , 2016 .

[13]  Unconditionally stable method and numerical solution of the hyperbolic phase-field crystal equation. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Jianfei Zhang.  A PETSc-Based Parallel Implementation of Finite Element Method for Elasticity Problems , 2015 .