LeVeque research group publications

  1. Logically Rectangular Finite Volume Methods with Adaptive Refinement on the Sphere 
    by M. J. Berger and D. A. Calhoun, and C. Helzel, and R. J. LeVeque Phil. Trans. R. Soc. A 2009 367, 4483-4496.
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  2. CSE 2009: Python for Scientific Computing at CSE 2009 
    by F. Perez, H. P. Langtangen, and R. LeVeque SIAM News 42, Number 5, June 15, 2009.
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  3. Python Tools for Reproducible Research on Hyperbolic Problems 
    by R. J. LeVeque. Computing in Science and Engineering (CiSE) 11(2009), pp. 19-27. (Special issue on reproducible research.)
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  4. Correction to the article A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources by Vaughan et al. 
    by J. T. Beale, D. L. Chopp, R. J. LeVeque, and Zhilin Li Comm. Appl. Math. Comput. Sci. 3 (2008), pp. 95-100.
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  5. Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains 
    by Donna A. Calhoun, Christiane Helzel, and Randall J. LeVeque, SIAM Review 50 (2008), 723-752.
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  6. WENOCLAW: A higher order wave propagation method 
    by D. I. Ketcheson and R. J. LeVeque, To appear in Proceedings of the Eleventh Int’l Conference on Hyperbolic Problems, Lyon, 2006.
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  7. High-resolution finite volume methods for extracorporeal shock wave therapy 
    by K. Fagnan and R. J. LeVeque and T. J. Matula and B. MacConaghy To appear in Proceedings of the Eleventh Int’l Conference on Hyperbolic Problems, Lyon, 2006.
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  8. High resolution methods and adaptive refinement for tsunami propagation and inundation 
    by D. L. George and R. J. LeVeque, To appear in Proceedings of the Eleventh Int’l Conference on Hyperbolic Problems, Lyon, 2006.
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  9. A finite volume grid for solving hyperbolic problems on the sphere 
    by Donna A. Calhoun, Christiane Helzel, and Randall J. LeVeque, To appear in Proceedings of the Eleventh Int’l Conference on Hyperbolic Problems, Lyon, 2006.
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  10. Finite volume methods and adaptive refinement for global tsunami propagation and local inundation 
    by D. L. George and R. J. LeVeque, Science of Tsunami Hazards 24(2006), pp. 319-328.
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  11. Wave Propagation Software, Computational Science, and Reproducible Research 
    by R. J. LeVeque, Proceedings of the International Congress of Mathematicians (M Sanz-Sole, J. Soria, J. L. Varona and J. Verdera, eds.) Madrid, August 22-30, 2006, pp. 1227-1254
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  12. High-Resolution Finite Volume Methods for Dusty Gas Jets and Plumes 
    by M. Pelanti and R. J. LeVeque SIAM J. Sci. Comput. 28 (2006) 1335-1360.
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  13. High-resolution finite volume methods for the shallow water equations with bathymetry and dry states 
    by Randall J. LeVeque and David L. George To appear in Advanced Numerical Models for Simulationg Tsunami Waves and Runup, P. L-F. Liu, H. Yeh, C. Synolakis, eds., Advances in Coastal and Ocean Engineering, Vol 10, World Scientific, 2007, Proceedings of the Third International Workshop on Long-Wave Runup Models, Catalina, 2004.
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  14. A high-resolution rotated grid method for conservation laws with embedded geometries 
    by C. Helzel, M. J. Berger, and R. J. LeVeque, SIAM J. Sci. Comput. 26 (2005), pp. 785-809.
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  15. The dynamics of pressureless dust clouds and delta waves 
    by R. J. LeVeque, J. Hyperbolic Differential Equations, Vol 1 (2004), pp. 315-327.
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  16. An accuracy study of mesh refinement on mapped grids 
    by D. Calhoun and R. J. LeVeque, Adaptive Mesh Refinement – Theory And Applications: Proceedings of the Chicago Workshop on Adaptive Mesh Refinement Methods, September, 2003. (T. Plewa, Ed.), Springer Verlag, Lecture Notes in Computational Science and Engineering, Vol. 41 (2003) pp. 91-102.
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  17. A wave propagation algorithm for hyperbolic systems on curved manifolds, 
    by J. A. Rossmanith, D. S. Bale, and R. J. LeVeque J. Comput. Phys. 199 (2004), pp. 631-662.
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  18. H-box methods for the approximation of one-dimensional conservation laws on irregular grids 
    by M. J. Berger, C. Helzel and R. J. LeVeque SIAM J. Numer. Anal., 41 (2003), pp. 893-918.
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  19. Immersed Interface Methods for Incompressible Navier-Stokes Equations, 
    by Long Lee and R. J. LeVeque, SIAM J. Sci. Comput., 25 (2003), pp. 832-856.
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  20. A wave-propagation method for conservation laws with spatially varying flux functions
    , by D. S. Bale, R. J. LeVeque, S. Mitran, and J. A. Rossmanith, SIAM J. Sci. Comput 24 (2002), 955-978.
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  21. Phase Plane Behavior of Solitary Waves in Nonlinear Layered Media 
    by R. J. LeVeque and D. H. Yong, Proceedings of the 9′th Intl. Conf. on Hyperbolic Problems: Theory, Numerics, Applications , Caltech, (T. Hou and E. Tadmor, eds.) Springer, 2002, pp. 43-51.
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  22. Solitary Waves in Layered Nonlinear Media 
    by Randall J. LeVeque and Darryl H. Yong, SIAM J. Appl. Math., 63 (2003), pp. 1539-1560.
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  23. Wave-Propagation Methods and Software for Complex Applications 
    by Randall J. LeVeque and Sorin Mitran. To appear in the Proceedings of the Third International Symposium on Finite Volumes for Complex Applications, Porquerolles, France, June, 2002.
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  24. Some Traffic Flow Models Illustrating Interesting Hyperbolic Behavior 
    by R. J. LeVeque, technical report, July, 2001.
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  25. Finite Volume Methods for Nonlinear Elasticity in Heterogeneous Media 
    by R. J. LeVeque, Proceedings of the ICFD Conference on Numerical Methods for Fluid Dynamics, Oxford University, March, 2001.
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  26. A Class of Approximate Riemann Solvers and Their Relation to Relaxation Schemes 
    by R. J. LeVeque and M. Pelanti J. Comput. Phys. , 172 (2001), 572-591.
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  27. A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves 
    by C. Helzel, R. J. LeVeque, and G. Warnecke, SIAM J. Sci. Comput., 22 (2000) 1489-1510.
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  28. Fractional step methods applied to a chemotaxis model 
    by Rebecca Tyson, L.G. Stern, and Randall J. LeVeque Journal of Mathematical Biology , 41 (2000), pp. 455-475.
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  29. A wave propagation method for three-dimensional hyperbolic conservation laws 
    by Jan Olav Langseth and R. J. LeVeque, J. Comput. Phys. 165 (2000) pp. 126-166.
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  30. Cartesian Grid Methods for Fluid Flow in Complex Geometries, 
    by R. J. LeVeque and D. Calhoun, Appears in “Computational Modeling in Biological Fluid Dynamics”, (L. J. Fauci and S. Gueron, eds.) IMA Volumes in Mathematics and its Applications 124, pp. 117-143, Springer-Verlag, 2001. (Proceedings of an IMA Workshop January, 1999.)
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  31. Solving the advection-diffusion equation in irregular geometries 
    by D. Calhoun and R. J. LeVeque J. Comput. Phys., 156(2000) pp. 1-38.
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  32. High-resolution finite volume methods for acoustics in periodic or random media 
    by T. R. Fogarty and R. J. LeVeque, J. Acoust. Soc. Amer. 106 (1999) pp. 17-28.
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  33. Crack jump conditions for elliptic problems 
    by A. Wiegmann, Z. Li, and R. J. LeVeque Applied Mathematics Letters, 12,6 (1999), pp. 81-86
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  34. Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems 
    by Marsha J. Berger and Randall J. LeVeque SIAM J. Numer. Anal., 35(1998), pp. 2298-2316.
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  35. Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods: The Quasi-Steady Wave-Propagation Algorithm 
    by Randall J. LeVeque J. Comput. Phys., 146 (1998) 346-365.
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  36. Wave propagation algorithms for multi-dimensional hyperbolic systems 
    by R. J. LeVeque J. Comput. Phys., 131 (1997), pp. 327-353.
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  37. Two-Dimensional Front Tracking Based on High Resolution Wave Propagation Methods 
    by Randall J. LeVeque and Keh-Ming Shyue, J. Comput. Phys., 123 (1996), 354-368.
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  38. High-Resolution Conservative Algorithms for Advection in Incompressible Flow 
    by Randall LeVeque, SIAM J. Numer. Anal., 33 (1996), 627-665
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  39. The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources 
    by R. J. LeVeque and Z. Li SIAM J. Numer. Anal., 31(1994), pp. 1019-1044
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  40. Finite Volume Methods for Irregular One-Dimensional Grids 
    by M. J. Berger, R. J. LeVeque, and L. G. Stern, Proc. Symp. Appl. Math., 48 (1994) 255-259.
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  41. A Rotated Difference Scheme for Cartesian Grids in Complex Geometries 
    by M. Berger and R. J. LeVeque, AIAA Paper CP-91-1602, 1991
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  42. Stable boundary conditions for Cartesian grid calculations, 
    by M. Berger and R. J. LeVeque, Computing Systems in Engineering, 1 (1990) 305-311.
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  43. Cartesian meshes and adaptive mesh refinement for hyperbolic partial differential equations 
    by M. Berger and R. J. LeVeque, Proc. Third Int’l Conf. Hyperbolic Problems, Uppsala (B. Engquist and B. Gustafsson, editors), Studentlitteratur, Lund, 1990, pp. 67-73.
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  44. An adaptive Cartesian mesh algorithm for the Euler equations in arbitrary geometries 
    by M. Berger and R. LeVeque, AIAA-89-1930, 1989
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  45. High resolution finite volume methods on arbitrary grids via wave propagation 
    R. J. LeVeque, J. Comput. Phys., 78 (1988), 36-63.
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  46. Cartesian grid methods for flow in irregular regions 
    R. J. LeVeque, Num. Meth. Fl. Dyn. III (K. W. Morton and M. J. Baines, eds.), 1988, pp. 375-382.
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  47. A geometric approach to high resolution TVD schemes 
    by J. B. Goodman and R. J. LeVeque SIAM J. Numer. Anal. 25(1988), pp. 268-284.
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  48. Linear Difference Equations and Matrix Theorems 
    by Germund Dahquist and Randall LeVeque, KTH Lecture Notes, 1981.
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