Wave propagation software, computational science, and reproducible research

Wave propagation algorithms are a class of high-resolution finite volume methods for solving hyperbolic partial differential equations arising in diverse applications. The development and use of the clawpack software implementing these methods serves as a case study for a more general discussion of mathematical aspects of software development and the need for more reproducibility in computational research. Sample applications discussed include medical applications of shock waves and geophysical fluid dynamics modeling volcanoes and tsunamis. Mathematics Subject Classification (2000). Primary 65Y15; Secondary 74S10.

[1]  Y. P. Oludnenko,et al.  STRINGS IN THEη CARINAE NEBULA: HYPERSONIC RADIATIVE COSMIC BULLETS , 2003 .

[2]  Xiaoming Huo,et al.  Beamlab and Reproducible Research , 2004, Int. J. Wavelets Multiresolution Inf. Process..

[3]  S. Mitran,et al.  Strings in the η Carinae Nebula: Hypersonic Radiative Cosmic Bullets , 2003, astro-ph/0310007.

[4]  Lloyd N. Trefethen,et al.  Ten Digit Algorithms , 2005 .

[5]  S. Donell,et al.  Low-energy extracorporeal shock-wave treatment (ESWT) for tendinitis of the supraspinatus. , 2002, The Journal of bone and joint surgery. British volume.

[6]  Randall J. LeVeque,et al.  Stable boundary conditions for Cartesian grid calculations , 1990 .

[7]  Maryam Shayegan Hastings,et al.  She Does Math!: Mathematics and Computer Science , 1995 .

[8]  Michael Pinedo,et al.  GUIDELINES FOR REPORTING COMPUTATIONAL RESULTS IN IIE TRANSACTIONS , 1993 .

[9]  Garrett Birkhoff.  Mathematics and Computer Science , 1975 .

[10]  Costas E Synolakis,et al.  Tsunami: wave of change. , 2006, Scientific American.

[11]  Randall J. LeVeque,et al.  Wave propagation algorithms on curved manifolds with applications to relativistic hydrodynamics , 2002 .

[12]  Robert Gentleman,et al.  Statistical Analyses and Reproducible Research , 2007 .

[13]  Jack Dongarra,et al.  LINPACK Users' Guide , 1987 .

[14]  Randall J. LeVeque,et al.  High-Resolution Finite Volume Methods for Dusty Gas Jets and Plumes , 2006, SIAM J. Sci. Comput..

[15]  Jack J. Dongarra,et al.  Matrix Eigensystem Routines — EISPACK Guide Extension , 1977, Lecture Notes in Computer Science.

[16]  Patrick J. Roache,et al.  Verification and Validation in Computational Science and Engineering , 1998 .

[17]  W Schaden,et al.  Extracorporeal Shock Wave Therapy of Nonunion or Delayed Osseous Union , 2001, Clinical orthopaedics and related research.

[18]  D. Kohn,et al.  Extracorporal shock wave therapy in patients with tennis elbow and painful heel , 2000, Archives of Orthopaedic and Trauma Surgery.

[19]  James A. Rossmanith,et al.  A wave propagation method for hyperbolic systems on the sphere , 2006, J. Comput. Phys..

[20]  J. Fritze.  [Extracorporeal shockwave therapy (ESWT) in orthopedic indications: a selective review]. , 1998, Versicherungsmedizin.

[21]  R. Denlinger,et al.  Granular avalanches across irregular three‐dimensional terrain: 2. Experimental tests , 2004 .

[22]  Richard M. Iverson,et al.  Granular avalanches across irregular three-dimensional terrain: 1. Theory and computation , 2004 .

[23]  J. Borwein.  The SIAM 100-Digit challenge: a study in high-accuracy numerical computing , 1987 .

[24]  Donald E. Knuth,et al.  Computer Science and its Relation to Mathematics , 1974 .

[25]  Randall J. LeVeque,et al.  Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains , 2008, SIAM Rev..

[26]  William J. Rider,et al.  A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov , 2004 .

[27]  R. LeVeque.  Numerical methods for conservation laws , 1990 .

[28]  L. Trefethen.  Spectral Methods in MATLAB , 2000 .

[29]  Randall J. LeVeque,et al.  Wave propagation algorithms for multicomponent compressible flows with applications to volcanic jets , 2005 .

[30]  George E. Forsythe,et al.  Computer science and mathematics , 1970, SGCS.

[31]  Randall J. LeVeque,et al.  Cartesian meshes and adaptive mesh refinement for hyperbolic partial differential equations , 1990 .

[32]  Randall J. LeVeque,et al.  A wave propagation method for three-dimensional hyperbolic conservation laws , 2000 .

[33]  R. LeVeque,et al.  A wave propagation algorithm for hyperbolic systems on curved manifolds , 2004 .

[34]  R. LeVeque.  Wave Propagation Algorithms for Multidimensional Hyperbolic Systems , 1997 .

[35]  Chi-Wang Shu,et al.  High Order ENO and WENO Schemes for Computational Fluid Dynamics , 1999 .

[36]  M. Berger,et al.  Adaptive mesh refinement for hyperbolic partial differential equations , 1982 .

[37]  John M. Mulvey,et al.  On Reporting Computational Experiments with Mathematical Software , 1979, TOMS.

[38]  David L. Donoho,et al.  WaveLab and Reproducible Research , 1995 .

[39]  Richard Liska,et al.  Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations , 2003, SIAM J. Sci. Comput..

[40]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[41]  B. S. Garbow,et al.  Matrix Eigensystem Routines — EISPACK Guide , 1974, Lecture Notes in Computer Science.

[42]  Donald E. Knuth,et al.  Algorithmic Thinking and Mathematical Thinking , 1985 .

[43]  P. Colella,et al.  Local adaptive mesh refinement for shock hydrodynamics , 1989 .

[44]  Stephen G. Nash,et al.  Guidelines for reporting results of computational experiments. Report of the ad hoc committee , 1991, Math. Program..

[45]  Ralf Deiterding,et al.  Construction and Application of an AMR Algorithm for Distributed Memory Computers , 2005 .

[46]  Christopher J. Roy,et al.  Review of code and solution verification procedures for computational simulation , 2005 .

[47]  Matthias Schwab,et al.  Making scientific computations reproducible , 2000, Comput. Sci. Eng..