A Continuous Finite Element-Based, Discontinuous Finite Element Method for S_N Transport

References

• N. SUKUMAR and E. A. MALSCH, “Recent Advances in the Construction of Polygonal Finite Element Interpolants,” Arch. Comput. Meth. Eng., 13, 129 (2006).
   Web of Science ®Google Scholar
• G. DAVIDSON and T. S. PALMER, “Finite Element Transport Using Wachspress Rational Basis Functions on Quadrilaterals in Diffusive Regions,” Proc. Topl. Mtg. Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications, Palais des Papes, Avignon, France, September 12–15, 2005 (2005).
   Google Scholar
• H. G. STONE and M. L. ADAMS, “A Piecewise Linear Finite Element Basis with Application to Particle Transport,” Proc. Topl. Mtg. Mathematical and Computational Sciences, A Century in Review—A Century Anew(M&C 2003), Gatlinburg, Tennessee, April 6–10, 2003, American Nuclear Society (2003).
   Google Scholar
• T. S. BAILEY, M. L. ADAMS, B. YANG, and M. R. ZIKA, “A Piecewise Linear Finite Element Discretization of the Diffusion Equation for Arbitrary Polyhedral Grids,” Proc. Topl. Mtg. Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications, Palais des Papes, Avignon, France, September 12–15, 2005 (2005).
   Google Scholar
• J. E. MOREL and J. S. WARSA, “An Sn Spatial Discretization Scheme for Tetrahedral Meshes,” Nucl. Sci. Eng., 151, 157 (2005).
   Web of Science ®Google Scholar
• J. E. MOREL, A. GONZALEZ-ALLER, and J. S. WARSA, “A Lumped Linear-Discontinuous Spatial Discretization Scheme for Triangular-Mesh Sn Calculations in r-z Geometry,” Nucl. Sci. Eng., 155, 168 (2007).
   Web of Science ®Google Scholar
• J. E. MOREL and J. S. WARSA, “A Lumped Bilinear-Discontinuous Sn Spatial Discretization for R-Z Quadrilateral Meshes,” Trans. Am. Nucl. Soc., 95, 873 (2006).
   Google Scholar
• J. E. MOREL and J. S. WARSA, “Spatial Finite-Element Lumping Techniques for the Quadrilateral Mesh Sn Equations in X-Y Geometry,” Nucl. Sci. Eng., 156, 325 (2007).
   Web of Science ®Google Scholar
• M. L. ADAMS, “Discontinuous Finite Element Transport Solutions in Thick Diffusive Problems,” Nucl. Sci. Eng., 137, 298 (2001).
   Web of Science ®Google Scholar
• J. S. WARSA, T. A. WAREING, and J. E. MOREL, “Krylov Iterative Methods and the Degraded Effectiveness of Diffusion Synthetic Acceleration for Multidimensional SN Calculations in Problems with Material Discontinuities,” Nucl. Sci. Eng., 147, 218 (2004).
   Web of Science ®Google Scholar
• M. L. ADAMS, “Deterministic Transport on an Arbitrarily-Connected Grid,” Advances in the Free-Lagrange Method (Lecture Notes in Physics), pp. 212–221 H. E. TREASE, M. J. FRITTS, and W. P. CROWLEY, Eds., Berlin-Heidelberg, Springer-Verlag (1991).
   Google Scholar
• E. E. LEWIS and W. F. MILLER, Computational Methods of Neutron Transport, John Wiley & Sons, New York (1984).
   Google Scholar
• G. H. MEISTERS, “Polygons Have Ears,” Am. Math. Mon., 82, 648 (1975).
   Web of Science ®Google Scholar
• S. HERTEL and K. MEHLHORN, “Fast Triangulation of the Plane with Respect to Simple Polygons,” Inf. Control, 64, 52 (1985).
   Google Scholar
• J. O’ROURKE, Computational Geometry in C, 2nd ed., Cambridge University Press, New York (1998).
   Google Scholar
• P. P. PÉBAY and T. J. BAKER, “Analysis of Triangle Quality Measures,” Math. Comput., 72, 1817 (2003).
   Google Scholar
• D. A. FIELD, “Qualitative Measures for Initial Meshes,” Int. J. Numer. Methods Eng., 47, 887 (2000).
   Web of Science ®Google Scholar
• J. R. SHEWCHUK, “What Is a Good Linear Element? Interpolation, Conditioning, and Quality Measures,” Proc. 11th Int. Meshing Roundtable, Ithaca, New York, September 15–18, 2002, pp. 115–126 (2002).
   Google Scholar
• A. LIU and B. JOE, “Relationship Between Tetrahedron Shape Measures,” BIT, 34, 268 (1994).
   Web of Science ®Google Scholar
• J. DOMPIERRE, P. LABBÉ, F. GUIBAULT, and R. CAMARERO, “Proposal of Benchmarks for 3D Unstructured Mesh Optimization,” CERCA R98-91, Centre de Recherche en Calcul Appliqué (Sep. 1998).
   Google Scholar
• E. W. LARSEN, J. E. MOREL, and W. F. MILLER, Jr., “Asymptotic Solutions of Numerical Transport Problems in Optically Thick, Diffusive Regimes I,” J. Comp. Phys., 69, 283 (1987).
   Web of Science ®Google Scholar
• E. W. LARSEN and J. E. MOREL, “Asymptotic Solutions of Numerical Transport Problems in Optically Thick, Diffusive Regimes II,” J. Comput. Phys., 83, 212 (1989).
   Web of Science ®Google Scholar
• T. A. WAREING, E. W. LARSEN, and M. L. ADAMS, “Diffusion Accelerated Discontinuous Finite Element Schemes for the Sn Equations in Slab and X-Y Geometries,” Proc. Int. Topl. Mtg. Advances in Mathematics, Computations, and Reactor Physics, Pittsburgh, Pennsylvania, April 28–May 2, 1991, pp. 11.1 2–1, American Nuclear Society (1991).
   Google Scholar
• J. S. WARSA, T. A. WAREING, and J. E. MOREL, “Fully Consistent Diffusion Synthetic Acceleration of Linear Discontinuous Sn Transport Discretizations on Unstructured Tetrahedral Meshes,” Nucl. Sci. Eng., 141, 236 (2002).
   Web of Science ®Google Scholar