Zhang, Yun; Huang, Zhigao; Zhou, Huamin; Li, Dequn A rapid BEM-based method for cooling simulation of injection molding. (English) Zbl 1403.80033 Eng. Anal. Bound. Elem. 52, 110-119 (2015). Summary: Cooling simulation is significant for optimization of the cooling system of injection molds. The boundary element method (BEM) is thought to be one of the best approaches suiting the steady-state cooling simulation. In spite of the merits of the BEM, the long computational time and the exorbitant memory requirement are two bottleneck problems in the current BEM-based cooling simulation method for industrial applications. The problems are caused by two reasons. One is the coupled heat transfer between the mold and the part and another is attributed to the inherent drawback of the BEM. In this article, the outer iteration, which is traditionally used to achieve consistency of boundary conditions on the mold cavity surface, is eliminated by introducing analytical solutions of the part temperature into the BEM equations. Then the dense coefficient matrix is sparsified by a combination of coefficient items using geometric topology. Moreover, parallel computing has been employed to speed up the computation. The case study showed that the sparse ratio reaches 7% with a temperature error of \(\pm 1°\)C and the total computational time is reduced by almost one order of magnitude simultaneously. MSC: 80M15 Boundary element methods applied to problems in thermodynamics and heat transfer 65N38 Boundary element methods for boundary value problems involving PDEs 80A22 Stefan problems, phase changes, etc. Keywords:injection molding; cooling simulation; boundary element method; steady-state thermal analysis; parallel computing PDFBibTeX XMLCite \textit{Y. Zhang} et al., Eng. Anal. Bound. Elem. 52, 110--119 (2015; Zbl 1403.80033) Full Text: DOI References: [1] Kwon, TH., Mold cooling system design using boundary element method, J Eng Ind Trans ASME, 110, 4, 384-394, (1988) [2] Chen, SC; Hu, S., Simulations of cycle-averaged mold surface temperature in mold-cooling process by boundary element method, Int Commun Heat Mass Transf, 18, 6, 823-832, (1991) [3] Chen S, Huang S, Jiang Z, Li H, Shen C. 3D Simulation and verification for mold temperature control technologies. Society of plastics engineers annual technical conference. Boston: Society of Plastics Engineers; 2005. p. 74-78. [4] Qiao, H., A systematic computer-aided approach to cooling system optimal design in plastic injection molding, Int J Mech Sci, 48, 4, 430-439, (2006) · Zbl 1192.80018 [5] Zhou, H; Li, D; Cui, S., Three-dimensional optimum design of the cooling lines of injection moulds based on boundary element design sensitivity analysis, P I Mech Eng B-J Eng, 216, 7, 1067-1071, (2002) [6] Himasekhar, K; Lottey, J; Wang, KK., CAE of mold cooling in injection molding using a three-dimensional numerical simulation, J Eng Ind Trans ASME, 114, 2, 213-221, (1992) [7] Hioe, Y; Chang, K-C; Zuyev, K; Bhagavatula, N; Castro, JM., A simplified approach to predict part temperature and “Minimum safe” cycle time, Polym Eng Sci, 48, 9, 1737-1746, (2008) [8] Tang, LQ; Chassapis, C; Manoochehri, S., Optimal cooling system design for multi-cavity injection molding, Finite Elem Anal Des, 26, 3, 229-251, (1997) · Zbl 0914.76058 [9] Tang, LQ; Pochiraju, K; Chassapis, C; Manoochehri, S., Three-dimensional transient mold cooling analysis based on Galerkin finite element formulation with a matrix-free conjugate gradient technique, Int J Numer Methods Eng, 39, 18, 3049-3064, (1996) · Zbl 0875.76255 [10] Chang, R-Y; Yang, W-H; Hsu, DC; Yang, V., Three-dimensional computer-aided mold cooling design for injection molding, Proceedings of the annual technical conference - ANTEC, conference proceedings society of plastics engineers. Nashville: Society of Plastics Engineers;, 656-660, (2003) [11] Cao, W; Shen, CY; Li, HM., Coupled part and mold temperature simulation for injection molding based on solid geometry, Polym-Plast Technol, 45, 4-6, 741-749, (2006) [12] Rezayat, M; Burton, TE., A boundary‐integral formulation for complex three‐dimensional geometries, Int J Numer Methods Eng, 29, 2, 263-273, (1990) · Zbl 0719.73042 [13] Zhou, H., Computer modeling for injection molding: simulation, optimization, and control, (2013), John Wiley & Sons Hoboken [14] Kassab, AJ; Divo, EA., Parallel domain decomposition boundary element method for large-scale heat transfer problems, Integr Meth Sci Eng, 117, (2006) · Zbl 1097.65120 [15] Erhart, K; Divo, E; Kassab, AJ., A parallel domain decomposition boundary element method technique for large-scale transient heat conduction problems, 247-256, (2004), Charlotte, NC, United States: American Society of Mechanical Engineers New York, NY 10016-5990, United States [16] Gamez, B; Ojeda, D; Divo, E; Kassab, A; Cerrolaza, M., Parallelized iterative domain decomposition boundary element method for thermoelasticity in piecewise non-homogeneous media, Eng Anal Bound Elem, 32, 12, 1061-1073, (2008) · Zbl 1244.74155 [17] Yang, YJ; Tang, HK., A parallelization technique for preconditioned boundary-element-method solvers, J Electromagnet Wave, 19, 6, 811-826, (2005) [18] Cunha, MTF; Telles, JCF; ALGA, Coutinho; Panetta, J., On the parallelization of boundary element codes using standard and portable libraries, Eng Anal Bound Elem, 28, 7, 893-902, (2004) · Zbl 1075.65140 [19] Wu TW, Lou G., Cheng CYR. Multithread BEM computation for packed silencers. Fourteenth international conference on boundary element technology, BETECH XIV, March 12, 2001-March 14, 2001. Orlando, FL, United States: WITPress; 2001. p. 133-41. [20] Buchau, A; Tsafak, SM; Hafla, W; Rucker, WM., Parallelization of a fast multipole boundary element method with cluster openmp, IEEE T Magn, 44, 6, 1338-1341, (2008) [21] Nishimura, N., Fast multipole accelerated boundary integral equation methods, Appl Mech Rev, 55, 4, 299-324, (2002) [22] Yoshida, K., Applications of fast multipole method to boundary integral equation method, (2001), Kyoto University Japan [23] Zhou, H; Zhang, Y; Wen, J; Li, D., An acceleration method for the BEM-based cooling simulation of injection molding, Eng Anal Bound Elem, 33, 8-9, 1022-1030, (2009) · Zbl 1244.80017 [24] Rezayat, M; Burton, TE., A boundary-integral formulation for complex three-dimensional geometries, Int J Numer Meth Eng, 29, 2, 263-273, (1990) · Zbl 0719.73042 [25] Park, S; Kwon, T., Thermal and design sensitivity analyses for cooling system of injection mold, part 1: thermal analysis, J Manuf Sci E-T ASME, 120, 287, (1998) [26] Park, S; Kwon, T., Thermal and design sensitivity analyses for cooling system of injection mold, part 2: design sensitivity analysis, J Manuf Sci E-T ASME, 120, 296, (1998) [27] Park, S; Kwon, T., Optimization method for steady conduction in special geometry using a boundary element method, Int J Numer Meth Eng, 43, 6, 1109-1126, (1998) · Zbl 0951.74050 [28] Cela, JM; Julia, A., High performance computing on boundary element simulations, Twenty-second international conference on the boundary elements method, 175-179, (2000), (BEM XXII, Sep 6 - 8 2000. Cambridge, United Kingdom: WITPress) [29] Cui, X; Li, BQ., A parallel Galerkin boundary element method for surface radiation and mixed heat transfer calculations in complex 3-D geometries, Int J Numer Methods Eng, 61, 12, (2004) [30] Erhart, K; Divo, E; Kassab, AJ., A parallel domain decomposition boundary element method approach for the solution of large-scale transient heat conduction problems, Eng Anal Bound Elem, 30, 7, 553-563, (2006) · Zbl 1195.80028 [31] Buchau, A; Hafla, W; Groh, F; Rucker, WM., Parallelized computation of compressed BEM matrices on multiprocessor computer clusters, Compel, 24, 2, 468-479, (2005) · Zbl 1135.78342 [32] Divo, E; Kassab, AJ; Rodriguez, F., Parallel domain decomposition approach for large-scale three-dimensional boundary-element models in linear and nonlinear heat conduction, Numer Heat Tr B-Fund, 44, 5, 417-437, (2003) [33] Saitoh, A; Kamitani, A., GMRES with new preconditioning for solving BEM-type linear system, IEEE T Magn, 40, 2 Part 2, 1084-1087, (2004) [34] Fischer, M; Perfahl, H; Gaul, L., Approximate inverse preconditioning for the fast multipole BEM in acoustics, Comput Visual Sci, 8, 3, 169-177, (2005) [35] Valente, FP; Pina, HL., Conjugate gradient methods for three-dimensional BEM systems of equations, Eng Anal Bound Elem, 30, 6, 441-449, (2006) · Zbl 1195.65160 [36] Chen, Z; Xiao, H., Preconditioned Krylov subspace methods solving dense nonsymmetric linear systems arising from BEM, Seventh international conference on computational science, 113-116, (2007), (Beijing: Springer Verlag) [37] Xiao, H; Chen, Z., Numerical experiments of preconditioned Krylov subspace methods solving the dense non-symmetric systems arising from BEM, Eng Anal Bound Elem, 31, 12, 1013-1023, (2007) · Zbl 1259.74073 [38] Rui, PL; Chen, RS., Sparse approximate inverse preconditioning of deflated block-GMRES algorithm for the fast monostatic RCS calculation, Int J Numer Model E, 21, 5, 297-307, (2008) · Zbl 1177.78055 [39] Young, DM., Iterative solution of large linear systems, (2003), Academic Press New York [40] Henz, JA; Himasekhar, K., Design sensitivities of mold-cooling CAE software: an experimental verification, Adv Polym Tech, 15, 1, 1-16, (1996) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.