Modeling/simulation of transient linear heat conduction problems via integrating a wide variety of space/time methods and choices

References

• S. Koshizuka and Y. Oka, “Moving-particle semi-implicit method for fragmentation of imcompressible fluid,” Nucl. Sci. Engin., vol. 123, no. 3, pp. 421–434, 1996. DOI: 10.13182/NSE96-A24205.
   Web of Science ®Google Scholar
• S. Koshizuka, A. Nobe, and Y. Oka, “Numerical analysis of breaking waves using the moving particle semi-implicit method,” Int. J. Numer. Meth. Fluids, vol. 26, no. 7, pp. 751–769, 1998. DOI: 10.1002/(SICI)1097-0363(19980415)26:7<751::AID-FLD671>3.0.CO;2-C.
   Web of Science ®Google Scholar
• S. Zhang, K. Morita, K. Fukuda, and N. Shirakawa, “An improved MPS method for numerical simulations of convective heat transfer problems,” Int. J. Numer. Meth. Fluids, vol. 51, no. 1, pp. 31–47, 2006. DOI: 10.1002/fld.1106.
   Web of Science ®Google Scholar
• R. Chen, Y. Oka, G. Li, and T. Matsuura, “Numerical investigation on melt freezing behavior in a tube by MPS method,” Nucl. Engin. Design, vol. 273, pp. 440–448, 2014. DOI: 10.1016/j.nucengdes.2014.03.049.
   Web of Science ®Google Scholar
• T. Xue, K. K. Tamma and X. Zhang, “A consistent moving particle system simulation method: applications to parabolic/hyperbolic heat conduction type problems,” Int. J. Heat Mass Transfer, vol. 101, pp. 365–372, 2016. DOI: 10.1016/j.ijheatmasstransfer.2016.05.020.
   Web of Science ®Google Scholar
• G. Lube, F. C. Otto and H. Müller, “A non-overlapping domain decomposition method for parabolic initial-boundary value problems,” Appl. Numer. Mathe., vol. 28, no. 2–4, pp. 359–369, 1998. DOI: 10.1016/S0168-9274(98)00053-1.
   Web of Science ®Google Scholar
• A. Auge, A. Kapurkin, G. Lube and F. C. Otto, A note on domain decomposition of singularly perturbed elliptic problems, in Proceedings of the Ninth International Conference on Domain Decomposition, Bergen, 1996.
   Google Scholar
• F. Confalonieri, A. Ghisi, G. Cocchetti, and A. Corigliano, “A domain decomposition approach for the simulation of fracture phenomena in polycrystalline microsystems,” Computer Methods Appl. Mech. Engin., vol. 277, pp. 180–218, 2014. DOI: 10.1016/j.cma.2014.04.007.
   Web of Science ®Google Scholar
• Z. Xiaogang and Z. Fang, “A coupled FE and boundary integral equation method based on exterior domain decomposition for fluid-structure interface problems,” Int. J. Solids Struct., vol. 31, no. 8, pp. 1047–1061, 1994. DOI: 10.1016/0020-7683(94)90163-5.
   Web of Science ®Google Scholar
• X. Feng, “Interface conditions and non-overlapping domain decomposition methods for a fluid-solid interaction problem,” Contemporary Mathe., vol. 218, pp. 417–424, 1998.
   Google Scholar
• E. Burman and P. Zunino, “A domain decomposition method based on weighted interior penalties for advection-diffusion-reaction problems,” SIAM J. Numer. Anal, vol. 44, no. 4, pp. 1612–1638, 2006. DOI: 10.1137/050634736.
   Web of Science ®Google Scholar
• B. F. Smith, “Domain decomposition algorithms for the partial differential equations of linear elasticity,” Ph.D. dissertation, Citeseer, 1990.
   Google Scholar
• A. Gravouil and A. Combescure, “Multi-time-step explicit-implicit method for non-linear structural dynamics,” Int. J. Numer. Meth. Engng, vol. 50, no. 1, pp. 199–225, 2001. DOI: 10.1002/1097-0207(20010110)50:1<199::AID-NME132>3.0.CO;2-A.
   Web of Science ®Google Scholar
• A. Prakash and K. Hjelmstad, “A FETI-based multi-time-step coupling method for Newmark schemes in structural dynamics,” Int. J. Numer. Meth. Engng, vol. 61, no. 13, pp. 2183–2204, 2004. DOI: 10.1002/nme.1136.
   Web of Science ®Google Scholar
• S. Karimi and K. B. Nakshatrala, “On multi-time-step monolithic coupling algorithms for elastodynamics,” J. Comput. Phys., vol. 273, pp. 671–705, 2014. DOI: 10.1016/j.jcp.2014.05.034.
   Web of Science ®Google Scholar
• K. B. Nakshatrala, K. D. Hjelmstad and D. A. Tortorelli, “A FETI-based domain decomposition technique for time-dependent first-order systems based on a DAE approach,” Int. J. Numer. Meth. Engng, vol. 75, no. 12, pp. 1385–1415, 2008. DOI: 10.1002/nme.2303.
   Web of Science ®Google Scholar
• H. M. Hilber, T. J. R. Hughes and R. L. Taylor, “Improved numerical dissipation for time integration algorithms in structural dynamics,” Earthquake Engng. Struct. Dyn, vol. 5, no. 3, pp. 283–292, 1977. DOI: 10.1002/eqe.4290050306.
   Web of Science ®Google Scholar
• J. Crank and P. Nicolson, “A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,” Math. Proc. Camb. Phil. Soc, vol. 43, no. 1, pp. 50–67, 1947. DOI: 10.1017/S0305004100023197.
   Web of Science ®Google Scholar
• T. Xue, X. Zhang and K. K. Tamma, “Generalized heat conduction model involving imperfect thermal contact surface: application of the GSSSS-1 differential-algebraic equation time integration,” Int. J. Heat Mass Transfer, vol. 116, pp. 889–896, 2018. DOI: 10.1016/j.ijheatmasstransfer.2017.09.081.
   Web of Science ®Google Scholar
• K. K. Tamma, X. Zhou and D. Sha, “The time dimension: A theory towards the evolution, classification, characterization and design of computational algorithms for transient/dynamic applications,” ARCO, vol. 7, no. 2, pp. 67–290, 2000. DOI: 10.1007/BF02736209.
   Google Scholar
• X. Zhou and K. K. Tamma, “Algorithms by design with illustrations to solid and structural mechanics/dynamics,” Int. J. Numer. Meth. Engng, vol. 66, no. 11, pp. 1738–1790, 2006. DOI: 10.1002/nme.1559.
   Web of Science ®Google Scholar
• X. Zhou and K. K. Tamma, “Design, analysis, and synthesis of generalized single step single solve and optimal algorithms for structural dynamics,” Int. J. Numer. Meth. Engng, vol. 59, no. 5, pp. 597–668, 2004. DOI: 10.1002/nme.873.
   Web of Science ®Google Scholar
• S. U. Masuri, M. Sellier, X. Zhou and K. K. Tamma, “Design of order-preserving algorithms for transient first-order systems with controllable numerical dissipation,” Int. J. Numer. Meth. Engng, vol. 88, no. 13, pp. 1411–1448, 2011. DOI: 10.1002/nme.3228.
   Web of Science ®Google Scholar
• J. Har and K. K. Tamma, Advances in Computational Dynamics of Particles, Materials and Structures. Chichester, UK: John Wiley & Sons, 2012.
   Google Scholar
• C. W. Gear, “Numerical initial value problems in ordinary differential equations,” Prentice-Hall Series Automatic Computation, 1971.
   Google Scholar
• W. L. Wood, M. Bossak and O. C. Zienkiewicz, “An alpha modification of newmark’s method,” Int. J. Numer. Meth. Engng, vol. 15, no. 10, pp. 1562–1566, 1980. DOI: 10.1002/nme.1620151011.
   Web of Science ®Google Scholar
• D. Tae and K. K. Tamma, “Towards a unified single analysis framework embedded with multiple spatial and time discretized methods for linear structural dynamics,” Comput. Modeling Engin. Sci., vol. 135, no. 2, pp. 843–885, 2023. DOI: 10.32604/cmes.2023.023071.
   Web of Science ®Google Scholar
• D. Tae and K. K. Tamma, “Computational differential algebraic equation framework and multi spatial and time discretizations preserving consistent second-order accuracy: nonlinear dynamics,” J. Appl. Mech., vol. 90, no. 1, pp. 10, 2023. DOI: 10.1115/1.4055955.
   Web of Science ®Google Scholar
• D. Maxam and K. K. Tamma, “A re-evaluation of overshooting in time integration schemes: the neglected effect of physical damping in the starting procedure,” Numer. Meth Engin., vol. 123, no. 12, pp. 2683–2704, 2022. DOI: 10.1002/nme.6955.
   Web of Science ®Google Scholar
• M. Shimada, S. U. Masuri and K. K. Tamma, “A novel design of an isochronous integration [integration] framework for first/second order multidisciplinary transient systems,” Int. J. Numer. Meth. Engng, vol. 102, no. 3–4, pp. 867–891, 2015. DOI: 10.1002/nme.4715.
   Web of Science ®Google Scholar
• M. Shimada, S. U. Masuri and K. K. Tamma, “Isochronous explicit time integration framework: illustration to thermal stress problems involving both first- and second-order transient systems,” J. Thermal Stresses, vol. 37, no. 9, pp. 1066–1079, 2014. DOI: 10.1080/01495739.2014.913397.
   Web of Science ®Google Scholar
• D. Maxam, R. Deokar and K. K. Tamma, “A unified computational methodology for dynamic thermoelasticity with multiple subdomains under the GSSSS framework involving differential algebraic equation systems,” J. Thermal Stresses, vol. 42, no. 1, pp. 163–184, 2019. DOI: 10.1080/01495739.2018.1536869.
   Web of Science ®Google Scholar
• D. Maxam, R. Deokar and K. K. Tamma, “The applicability of model order reduction based on proper orthogonal decomposition to problems in dynamic thermoelasticity with multiple subdomains,” J. Thermal Stresses, vol. 42, no. 6, pp. 744–768, 2019. DOI: 10.1080/01495739.2019.1581720.
   Web of Science ®Google Scholar