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PIFE-PIC: parallel immersed finite element particle-in-cell for 3-D kinetic simulations of plasma-material interactions. (English) Zbl 1483.65199

In this paper, the authors show the performance of a software package, called PIFE-PIC, developed by the authors for solving three space dimensional kinetic simulations of plasma-material interactions. The key ideas are to apply domain decomposition method and parallel computations. In particular, both the field equations and the particle equations are solved parallelly in overlapping subdomains. This can certainly provide a significant speed-up. The authors provide a set of numerical experiment to validate the performance of their software. The test set includes a large-scale simulation of plasma charging at a lunar crater. For some test cases, parallel efficiency up to approximately 110% superlinear speedup was achieved.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N75 Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs
35R05 PDEs with low regular coefficients and/or low regular data
65Y05 Parallel numerical computation
78A30 Electro- and magnetostatics
82D10 Statistical mechanics of plasmas
85A99 Astronomy and astrophysics
65-04 Software, source code, etc. for problems pertaining to numerical analysis

Software:

PIFE-PIC; IFE-PIC

References:

[1] S. Adjerid, N. Chaabane, T. Lin, and P. Yue, An immersed discontinuous finite element method for the Stokes problem with a moving interface, J. Comput. Appl. Math., 362 (2019), pp. 540-559. · Zbl 1458.76061
[2] S. Adjerid and T. Lin, \(p\)-th degree immersed finite element for boundary value problems with discontinuous coefficients, Appl. Numer. Math, 59 (2009), pp. 1303-1321. · Zbl 1177.65118
[3] S. Adjerid, T. Lin, and Q. Zhuang, Error estimates for an immersed finite element method for second order hyperbolic equations in inhomogeneous media, J. Sci. Comput., 84 (2020), p. 35. · Zbl 1452.65220
[4] S. Adjerid and K. Moon, An immersed discontinuous Galerkin method for acoustic wave propagation in inhomogeneous media, SIAM J. Sci. Comput., 41 (2019), pp. A139-A162. · Zbl 1407.65169
[5] J. Bai, Y. Cao, Y. Chu, and X. Zhang, An improved immersed finite element particle-in-cell method for plasma simulation, Comput. Math. Appl., 75 (2018), pp. 1887-1899. · Zbl 1409.82018
[6] J. Bai, Y. Cao, X.-M. He, and P. E, An implicit particle-in-cell model based on anisotropic immersed-finite-element method, Comput. Phys. Commun., 261 (2021), 107655. · Zbl 1527.76048
[7] J. Bai, Y. Cao, X.-M. He, H. Liu, and X. Yang, Modeling and an immersed finite element method for an interface wave equation, Comput. Math. Appl., 76 (2018), p. 1625-1638. · Zbl 1434.65172
[8] B. Smith, P. Bjørstad, and W. Gropp, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, Cambridge, 1996. · Zbl 0857.65126
[9] O. E. Berg, A lunar terminator configuration, Earth Planet. Sci. Lett., 39 (1978), pp. 377-381.
[10] O. E. Berg, F. F. Richardson, and H. Burton, Apollo 17 preliminary science report, Technical Report NASA SP-330, National Aeronautics and Space Administration, 1973.
[11] C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (Series in Plasma Physics), Institute of Physics Publishing, Bristol, UK, 1991.
[12] B. Camp, T. Lin, Y. Lin, and W. Sun, Quadratic immersed finite element spaces and their approximation capabilities, Adv. Comput. Math., 24 (2006), pp. 81-112. · Zbl 1095.65102
[13] H. Cao, Y. Cao, Y. Chu, X.-M. He, and T. Lin, A Huygens immersed-finite-element particle-in-cell method for modeling plasma-surface interactions with moving interface, Commun. Nonlinear Sci. Numer. Simul., 59 (2018), pp. 132-148. · Zbl 1524.35666
[14] W. Cao, X. Zhang, and Z. Zhang, Superconvergence of immersed finite element methods for interface problems, Adv. Comput. Math., 43 (2017), pp. 795-821. · Zbl 1380.65365
[15] Y. Cao, Y. Chu, X.-M. He, and T. Lin, An iterative immersed finite element method for an electric potential interface problem based on given surface electric quantity, J. Comput. Phys., 281 (2015), pp. 82-95. · Zbl 1351.78045
[16] Y. Cao, Y. Chu, X. Zhang, and X. Zhang, Immersed finite element methods for unbounded interface problems with periodic structures, J. Comput. Appl. Math., 307 (2016), pp. 72-81. · Zbl 1382.78017
[17] Y. Chu, Y. Cao, X.-M. He, and M. Luo, Asymptotic boundary conditions with immersed finite elements for interface magnetostatic/electrostatic field problems with open boundary, Comput. Phys. Commun., 182 (2011), pp. 2331-2338. · Zbl 1308.78006
[18] Y. Chu, D. Han, Y. Cao, X.-M. He, and J. Wang, An immersed-finite-element particle-in-cell simulation tool for plasma surface interaction, Int. J. Numer. Anal. Model., 14 (2017), pp. 175-200. · Zbl 1365.76112
[19] G. L. Delzanno and X.-Z. Tang, Comparison of dust charging between orbital-motion-limited theory and particle-in-cell simulations, Phys. Plasmas, 22 (2015), 113703.
[20] D. Depew, D. Han, J. Wang, X.-M. He, and T. Lin, Immersed-Finite-Element Particle-In-Cell simulations of lunar surface charging, #199, Proceedings of the 13th Spacecraft Charging Technology Conference, Pasadena, California, June 23-27, 2014.
[21] R. E. Ewing, Z. Li, T. Lin, and Y. Lin, The immersed finite volume element methods for the elliptic interface problems. Modelling ’98 (Prague), Math. Comput. Simulation, 50 (1999), pp. 63-76. · Zbl 1027.65155
[22] W. Feng, X.-M. He, Y. Lin, and X. Zhang, Immersed finite element method for interface problems with algebraic multigrid solver, Commun. Comput. Phys., 15 (2014), pp. 1045-1067. · Zbl 1388.65177
[23] J. W. Freeman and M. Ibrahim, Lunar electric fields, surface potential and associated plasma sheaths, The Moon, 14 (1975), pp. 103-114.
[24] Y. Gong, B. Li, and Z. Li, Immersed-interface finite-element methods for elliptic interface problems with non-homogeneous jump conditions, SIAM J. Numer. Anal., 46 (2008), pp. 472-495. · Zbl 1160.65061
[25] R. Guo and T. Lin, A group of immersed finite-element spaces for elliptic interface problems, IMA J. Numer. Anal., 39 (2019), pp. 482-511. · Zbl 1483.65184
[26] R. Guo and T. Lin, A higher degree immersed finite element method based on a Cauchy extension for elliptic interface problems, SIAM J. Numer. Anal., 57 (2019), pp. 1545-1573. · Zbl 1420.65122
[27] R. Guo and T. Lin, An immersed finite element method for elliptic interface problems in three dimensions, J. Comput. Phys., 414 (2020), 109478. · Zbl 1440.65207
[28] R. Guo, T. Lin, and Y. Lin, Error estimates for a partially penalized immersed finite element method for elasticity interface problems, ESAIM Math. Model. Numer. Anal., 54 (2020), pp. 1-24. · Zbl 1442.74228
[29] R. Guo, T. Lin, and Q. Zhuang, Improved error estimation for the partially penalized immersed finite element methods for elliptic interface problems, Int. J. Numer. Anal. Mod., 16 (2019), pp. 575-589. · Zbl 1427.65361
[30] R. Guo and X. Zhang, Solving three-dimensional interface problems with immersed finite elements: A-priori error analysis, J. Comput. Phys., 441 (2021), 110445. · Zbl 07513824
[31] J. Guzmán, M. A. Sánchez, and M. Sarkis, Higher-order finite element methods for elliptic problems with interfaces, ESAIM Math. Model. Numer. Anal., 50 (2016), pp. 1561-1583. · Zbl 1353.65120
[32] J. S. Halekas, G. T. Delory, D. A. Brain, R. P. Lin, M. O. Fillingim, C. O. Lee, R. A. Mewaldt, T. J. Stubbs, W. M. Farrell, and M. K. Hudson, Extreme lunar surface charging during solar energetic particle events, Geophys. Res. Lett., 34 (2007), L02111.
[33] J. S. Halekas, G. T. Delory, R. P. Lin, T. J. Stubbs, and W. M. Farrell, Lunar prospector observations of the electrostatic potential of the lunar surface and its response to incident currents, J. Geophys. Res., 113 (2008), A09102.
[34] J. S. Halekas, Y. Saito, G. T. Delory, and W. M. Farrell, New views of the lunar plasma environment, Planet. Space Sci., 59 (2011), pp. 1681-1694.
[35] D. Han, Particle-in-Cell Simulations of Plasma Interactions with Asteroidal and Lunar Surfaces, PhD thesis, University of Southern California, 2015.
[36] D. Han and J. Wang, 3-D fully-kinetic particle-in-cell simulations of small asteroid charging in the solar wind, IEEE Trans. Plasma Sci., 47 (2019), pp. 3682-3688.
[37] D. Han, J. Wang, and X.-M. He, A non-homogeneous immersed-finite-element particle-in-cell method for modeling dielectric surface charging in plasmas, IEEE Trans. Plasma Sci., 44 (2016), pp. 1326-1332.
[38] D. Han, J. Wang, and X.-M. He, Immersed-finite-element particle-in-cell simulations of plasma charging at lunar terminator, J. Spacecraft Rockets, 55 (2018), pp. 1490-1497.
[39] D. Han, P. Wang, X.-M. He, T. Lin, and J. Wang, A 3D immersed finite element method with non-homogeneous interface flux jump for applications in particle-in-cell simulations of plasma-lunar surface interactions, J. Comput. Phys., 321 (2016), pp. 965-980. · Zbl 1349.76212
[40] C. He and X. Zhang, Residual-based a posteriori error estimation for immersed finite element methods, J. Sci. Comput., 81 (2019), pp. 2051-2079. · Zbl 1429.65276
[41] X.-M. He, Bilinear immersed finite elements for interface problems, Ph.D. Dissertation, Virginia Polytechnic Institute and State University, (2009).
[42] X.-M. He, T. Lin, and Y. Lin, Approximation capability of a bilinear immersed finite element space, Numer. Methods Partial Differential Equations, 24 (2008), pp. 1265-1300. · Zbl 1154.65090
[43] X.-M. He, T. Lin, and Y. Lin, A bilinear immersed finite volume element method for the diffusion equation with discontinuous coefficients, dedicated to Richard E. Ewing on the occasion of his 60th birthday, Commun. Comput. Phys., 6 (2009), pp. 185-202. · Zbl 1364.65225
[44] X.-M. He, T. Lin, and Y. Lin, Interior penalty bilinear IFE discontinuous Galerkin methods for elliptic equations with discontinuous coefficient, dedicated to David Russell’s 70th birthday, J. Syst. Sci. Complex., 23 (2010), pp. 467-483. · Zbl 1205.35010
[45] X.-M. He, T. Lin, and Y. Lin, Immersed finite element methods for elliptic interface problems with non-homogeneous jump conditions, Int. J. Numer. Anal. Model., 8 (2011), pp. 284-301. · Zbl 1211.65155
[46] X.-M. He, T. Lin, and Y. Lin, The convergence of the bilinear and linear immersed finite element solutions to interface problems, Numer. Methods Partial Differential Equations, 28 (2012), pp. 312-330. · Zbl 1241.65090
[47] X.-M. He, T. Lin, and Y. Lin, A selective immersed discontinuous Galerkin method for elliptic interface problems, Math. Methods Appl. Sci., 37 (2014), pp. 983-1002. · Zbl 1292.65126
[48] X.-M. He, T. Lin, Y. Lin, and X. Zhang, Immersed finite element methods for parabolic equations with moving interface, Numer. Methods Partial Differential Equations, 29 (2013), pp. 619-646. · Zbl 1266.65165
[49] G. H. Heiken, D. T. Vaniman, and B. M. French, Lunar Sourcebook: A User’s Guide to the Moon, Cambridge University Press, Cambridge, 1991.
[50] R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles, Adam Hilger, London, 1988. · Zbl 0662.76002
[51] J. D. Jackson, Classical electrodynamics, 3rd ed., Wiley, New York, 1999. · Zbl 0920.00012
[52] H. Jian, Y. Chu, H. Cao, Y. Cao, X.-M. He, and G. Xia, Three-dimensional IFE-PIC numerical simulation of background pressure’s effect on accelerator grid impingement current for ion optics, Vacuum, 116 (2015), pp. 130-138.
[53] R. Kafafy, T. Lin, Y. Lin, and J. Wang, Three-dimensional immersed finite element methods for electric field simulation in composite materials, Int. J. Numer. Meth. Engrg., 64 (2005), pp. 940-972. · Zbl 1122.78018
[54] R. Kafafy and J. Wang, Whole subscale ion optics simulation: Direct ion impingement and electron backstreaming, in 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA 2005-3691, Tucson, Arizona, July 2005.
[55] R. Kafafy and J. Wang, Whole ion optics gridlet simulations using a hybrid-grid immersed-finite-element particle-in-cell code, J. Propul. Power, 23 (2007), pp. 59-68.
[56] R. I. Kafafy and J. Wang, A hybrid grid immersed finite element particle-in-cell algorithm for modeling spacecraft-plasma interactions, IEEE Trans. Plasma Sci., 34 (2006), pp. 2114-2124.
[57] D. Kwak, S. Jin, and D. Kyeong, A stabilized P1-nonconforming immersed finite element method for the interface elasticity problems, ESAIM Math. Model. Numer. Anal., 51 (2017), pp. 187-207. · Zbl 1381.74199
[58] Z. Li, The immersed interface method using a finite element formulation, Appl. Numer. Math., 27 (1998), pp. 253-267. · Zbl 0936.65091
[59] Z. Li, T. Lin, Y. Lin, and R. C. Rogers, An immersed finite element space and its approximation capability, Numer. Methods Partial Differential Equations, 20 (2004), pp. 338-367. · Zbl 1057.65085
[60] Z. Li, T. Lin, and X. Wu, New Cartesian grid methods for interface problems using the finite element formulation, Numer. Math., 96 (2003), pp. 61-98. · Zbl 1055.65130
[61] T. Lin, Y. Lin, and X. Zhang, Partially penalized immersed finite element methods for elliptic interface problems, SIAM J. Numer. Anal., 53 (2015), pp. 1121-1144. · Zbl 1316.65104
[62] T. Lin, D. Sheen, and X. Zhang, A locking-free immersed finite element method for planar elasticity interface problems, J. Comput. Phys., 247 (2013), pp. 228-247. · Zbl 1349.74328
[63] T. Lin, D. Sheen, and X. Zhang, A nonconforming immersed finite element method for elliptic interface problems, J. Sci. Comput., 79 (2019), pp. 442-463. · Zbl 1415.65260
[64] T. Lin, Q. Yang, and X. Zhang, A priori error estimates for some discontinuous Galerkin immersed finite element methods, J. Sci. Comput., 65 (2015), pp. 875-894. · Zbl 1331.65154
[65] C. Lu, J. Wan, Y. Cao, and X.-M. He, A fully decoupled iterative method with three-dimensional anisotropic immersed finite elements for Kaufman-type discharge problems, Comput. Meth. Appl. Mech. Eng., 372 (2020), 113345. · Zbl 1506.65010
[66] C. Lu, Z. Yang, J. Bai, Y. Cao, and X.-M. He, Three-dimensional immersed finite element method for anisotropic magnetostatic/electrostatic interface problems with non-homogeneous flux jump, Int. J. Numer. Meth. Eng., 121 (2020), pp. 2107-2127. · Zbl 07843285
[67] D. Lund, J. Zhao, A. Lamb, and D. Han, Fully Kinetic PIFE-PIC Simulations of Plasma Charging at Lunar Craters, in AIAA SciTech 2020, AIAA 2020-1549, Orlando, Florida, January 6-10, 2020.
[68] D. S. McKay, G. Heiken, A. Basu, G. Blanford, S. Simon, R. Reedy, B. M. French, and J. Papike, Chapter 7: The lunar regolith, in Lunar Sourcebook: A User’s Guide to the Moon, Cambridge University Press, Cambridge, 1991, pp. 285-356.
[69] NASA-JPL, Moon Trek, trek, http://nasa.gov/moon (15 July 2020).
[70] A. R. Poppe, M. Piquette, A. Likhanskii, and M. Horányi, The effect of surface topography on the lunar photoelectron sheath and electrostatic dust transport, Icarus, 221 (2012), pp. 135-146.
[71] T. Preusser, M. Rumpf, S. Sauter, and L. O. Schwen, 3D composite finite elements for elliptic boundary value problems with discontinuous coefficients, SIAM J. Sci. Comput., 33 (2011), pp. 2115-2143. · Zbl 1237.65129
[72] D. L. Reasoner and W. J. Burke, Characteristics of the lunar photoelectron layer in the geomagnetic tail, J. Geophys. Res., 77 (1972), pp. 6671-6687.
[73] Y. G. Shkuratov and N. V. Bondarenko, Regolith layer thickness mapping of the moon by radar and optical data, Icarus, 149 (2001), pp. 329-338.
[74] T. J. Stubbs, J. S. Halekas, W. M. Farrell, and R. R. Vondrak, Lunar surface charging: A global perspective using lunar prospector data, in Workshop on Dust in Planetary Systems (ESA SP-643), H. Krueger and A. Graps, eds., Kauai, Hawaii, USA, September 26-30, 2005, pp. 181-184.
[75] X.-Z. Tang and G. L. Delzanno, Orbital-motion-limited theory of dust charging and plasma response, Phys. Plasmas, 21 (2014), p. 123708.
[76] D. Han and J. Wang, Simulations of Ion Thruster Plume Contamination with A Whole Grid Sputtered Mo Source Model, in 49th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA 2013-3888, San Jose, California, July 14 - 17, 2013.
[77] S. Vallaghè and T. Papadopoulo, A trilinear immersed finite element method for solving the electroencephalography forward problem, SIAM J. Sci. Comput., 32 (2010), pp. 2379-2394. · Zbl 1214.92046
[78] C. Wang, P. Sun, and Z. Li, An iterative approach for constructing immersed finite element spaces and applications to interface problems, Int. J. Numer. Anal. Model., 16 (2019), pp. 167-191. · Zbl 1408.65090
[79] J. Wang, Y. Cao, R. Kafafy, J. Pierru, and V. K. Decyk, Simulations of ion thruster plume-spacecraft interactions on parallel supercomputer, IEEE Trans. Plasma Sci., 34 (2006), pp. 2148-2158.
[80] J. Wang, X.-M. He, and Y. Cao, Modeling spacecraft charging and charged dust particle interactions on lunar surface, in Proceedings of the 10th Spacecraft Charging Technology Conference, Biarritz, France, 2007.
[81] J. Wang, X.-M. He, and Y. Cao, Modeling electrostatic levitation of dusts on lunar surface, IEEE Trans. Plasma Sci., 36 (2008), pp. 2459-2466.
[82] R. Willis, M. Anderegg, B. Feuerbacher, and B. Fitton, Photoemission and secondary electron emission from lunar surface material, in Photon and Particle Interactions with Surfaces in Space, R. Grard, ed., Astrophysics and Space Science Library 37, Springer, Amsterdam, 1973.
[83] W. Yu, D. Han, and J. Wang, Numerical Simulations of Dust Dynamics Around Small Asteroids, IEEE Trans. Plasma Sci., 47 (2019), pp. 3724-3730.
[84] W. Yu, J. J. Wang, and D. Han, Numerical Modeling of Dust Dynamics Around Small Asteroids, in AIAA SPACE Forum 2016, AIAA 2016-5447, Long Beach, California, September 13-16, 2016.
[85] H. Zhang, T. Lin, and Y. Lin, Linear and quadratic immersed finite element methods for the multi-layer porous wall model for coronary drug-eluting stents, Int. J. Numer. Anal. Mod., 15 (2018), pp. 48-73. · Zbl 1406.76054
[86] Q. Zhang, K. Ito, Z. Li, and Z. Zhang, Immersed finite elements for optimal control problems of elliptic PDEs with interfaces, J. Comput. Phys., 298 (2015), pp. 305-319. · Zbl 1349.65638
[87] X. Zhang, Nonconforming immersed finite element methods for interface problems, Ph.D. Dissertation, Virginia Polytechnic Institute and State University, 2013.
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