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Original Articles

On the Use of Symmetrized Transport Equation in Goal-Oriented Adaptivity

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References

  • Adams, M. P., Adams, M. L., Hawkins, W. D., Smith, T., Rauchwerger, L., Amato, N. M., Bailey, T. S., Falgout, R. D. (2013). Provably Optimal Parallel Transport Sweeps on Regular Grids. In The International Conference on Mathematics and Computational (M&C) Methods Applied to Nuclear Science and Engineering, Sun Valley, Idaho, USA, May 2013. American Nuclear Society.
  • Agoshkov, V. I. (1998). Boundary Value Problems for Transport Equations. Birkhäuser, Boston: Modeling and Simulation in Science, Engineering and Technology.
  • Alnæs, M. S., Logg, A., Ölgaard, K. B., Rognes, M. E., Wells, G. N. (March 2014). Unified form language: A domain-specific language for weak formulations of partial differential equations. ACM Trans. Math. Softw. 40(2):9:1–9:37.
  • Balay, S. A., Adams, M. F., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Eijkhout, V., Gropp, W. D., Kaushik, D., Knepley, M. G., McInnes, L. C., Rupp, K., Smith, B. F., Zampini, S., Zhang, H. (2015). PETSc Web page. http://www.mcs.anl.gov/petsc.
  • Bangerth, W., Rannacher, R. (2003). Adaptive Finite Element Methods for Differential Equations. Birkhäuser Basel: Birkhäuser Verlag.
  • Becker, R., Rannacher, R. (1996). A feed-back approach to error control in finite element methods: Basic analysis and examples. East-West J. Numer. Math 4:237–264.
  • Boffi, D., Brezzi, F., Fortin, M. (2013). Mixed Finite Element Methods and Applications. Springer, Berlin, Heidelberg: Springer Series in Computational Mathematics.
  • Brenner, S., Scott, L. R. (2013). The Mathematical Theory of Finite Element Methods. Springer, New York: Texts in Applied Mathematics.
  • Dautray, R., Lions, J.-L. (2000). Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 6 – Evolution Problems II. Verlag Berlin Heidelberg, Germany: Springer.
  • De Oliveira, C. R. E., Eaton, M. D., Umpleby, A. P., and Pain, C. C. (2001). Finite element-spherical harmonics solutions of the 3D Kobayashi benchmarks with ray-tracing void treatment. Prog. Nucl. Energy 39(2):243–261.
  • Gesh, C. J., Adams, M. L. (2001). Finite element solutions of second-order forms of the transport equation at the interface between diffusive and non-diffusive regions. In Proceedings ANS International Meeting on Mathematical Methods for Nuclear Applications: M&C, M&C 2001, Salt Lake City, Utah, USA, September 2001. pp. 1–15.
  • Heimsund, B.-O., Tai, X.-Ch., Wang, J. (April 2002). Superconvergence for the gradient of finite element approximations by l2 projections. SIAM J. Numer. Anal. 40(4):1263–1280.
  • Jansson, J., Hoffman, J., Spuhler, J., Degirmenci, C. (2013). Automated error control in finite element methods with applications in fluid flow. Technical report, KTH-CTL.
  • Lathouwers, D. (2011). Goal-oriented spatial adaptivity for the SN equations on unstructured triangular meshes. Ann. Nucl. Energy 38(6):1373–1381.
  • Lewis, E. E., Miller, W. F. (1984). Computational Methods of Neutron Transport. New York, NY: John Wiley and Sons.
  • Logg, A., Wells, G. N., Hake, J. (2012). DOLFIN: a C++/Python Finite Element Library. Verlag Berlin Heidelberg, Germany: Springer.
  • Marchuk, G. I., Agoshkov, V. I. (1981). Kinetic equations and variational principles. SIAM J. Numer. Anal. 18(2):242–261.
  • Möller, M., Kuzmin, D. (2006). Adaptive mesh refinement for high-resolution finite element schemes. Int. J. Numer. Metho. Fluids 52(5):545–569.
  • Morel, J. E., McGhee, J. M. (1995). A diffusion-synthetic acceleration technique for the even-parity SN equations with anisotropic scattering. Nucl. Sci. Eng. 120(3):147–164.
  • Morel, J. E., McGhee, J. M. (1999). A self-adjoint angular flux equation. Nucl. Sci. Eng. 132(3):312–325.
  • Vladimirov, V. S. (1963). Mathematical Problems in the One-Velocity Theory of Particle Transport. Atomic Energy of Canada Limited, Canada.
  • Wang, Y., Ragusa, J. C. (2011). Standard and goal-oriented adaptive mesh refinement applied to radiation transport on 2d unstructured triangular meshes. J. Comput. Phys. 230(3):763–788.

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