### Table 7: Parallel execution times (in seconds) for the backward facing step, Parnass2 and Origin 200/2000. Parallel execution times (in seconds) for the channel ow, ( due to swapping) Parnass2 code does scale as well on Parnass2 as on the shared memory machine Origin 200/2000. Outlook. Currently there are several other parallel applications under develop- ment at our department, namely a hierarchical adaptive tree-code (TreeMol) for molecular dynamics [2], a smoothed particle hydrodynamics code [1] for astro- physics, an eigenvalue solver for Schrodinger apos;s equation [3] based on the sparse grid combination technique [6], a wavelet based Navier{Stokes solver [11] and a parallel algebraic multi-grid (AMG) solver [16, 4, 7]. Acknowledgements. The computing time on the Cray T3E-1200 and T3E- 600 was donated to the department by Cray Research.

1999

"... In PAGE 9: ...Table7... ..."

Cited by 4

### Table 1. Scientific and Engineering Codes Developed for Beowulf-class Computers, cont.

1998

"... In PAGE 6: ... Even in the short time that Beowulf-class computers have been available, a number of important scientific and engineering codes have been developed to perform real-world end user computations. Table1 below provides a representative list with an emphasis on but not limited to NASA-related applications: Table 1. Scientific and Engineering Codes Developed for Beowulf-class Computers Organization Code ARC Implicit CFD, FFTs, Multigrid NAS Benchmarks Caltech Astrophysical N-body Tree Codes, Simulation Result Analysis Codes, Smooth Particle Hydrodynamics Code, Vortex Dynamics, Reactive Chemical Flow Clemson Parallel File System, Gauss Siedel Sorting Drexel N-body Tree Code, SPH, Weather and Storm Front Modeling, Nuclear Shell Model Code, Particle Scattering GMU Combinatorial Optimizations GSFC, Drexel... In PAGE 6: ... Even in the short time that Beowulf-class computers have been available, a number of important scientific and engineering codes have been developed to perform real-world end user computations. Table 1 below provides a representative list with an emphasis on but not limited to NASA-related applications: Table1 . Scientific and Engineering Codes Developed for Beowulf-class Computers Organization Code ARC Implicit CFD, FFTs, Multigrid NAS Benchmarks Caltech Astrophysical N-body Tree Codes, Simulation Result Analysis Codes, Smooth Particle Hydrodynamics Code, Vortex Dynamics, Reactive Chemical Flow Clemson Parallel File System, Gauss Siedel Sorting Drexel N-body Tree Code, SPH, Weather and Storm Front Modeling, Nuclear Shell Model Code, Particle Scattering GMU Combinatorial Optimizations GSFC, Drexel... ..."

Cited by 4

### Table 1. Computation phases of a hydrodynamics simulation program

1999

"... In PAGE 4: ...2 Regrouping Algorithm Wenow illustrate the problem and the solution of data regrouping through an example of a hydrodynamics simulation program, which computes the movement of particles in some three-dimensional space. Table1 lists the six major compu- tation phases of the program as well as the attributes of particles used in each phase. Since the program stores an attribute of all particles in a separate array, di erent attributes do not share the same cache block.... ..."

Cited by 23

### Table 1. Mean dissociation time f of small flocs as simulated for various levels of hydrodynamic approximation [up to terms of order (a/ r) quot;]

"... In PAGE 4: ...865 mPa s (water at 300 K). Table1 lists values of the mean dissociation time t obtained by truncating the series expansion at various values of (air) quot;. (Terms of order F2 and F5 are identically zero even for liquid particles of finite viscosity.... ..."

### Table 1 Comparison between the theoretical and experimental results for smooth non- cohesive particles.

"... In PAGE 2: ...rojection of the base triangle on the horizontal plane (Fig. 1). This criterion gives the maximum angle of stability as c = 23:4o. As Table1 indicates, these predictions for c agree rather well with experimental measurements of r and m both for discs in 2D and spheres in 3D.... In PAGE 3: ... These measurements were also conducted after small quantities of oil were added to the spheres with liquid content tliq [12,13]. When no oil was added to the spheres, we found r(tliq=0) apos; 22o, in good agreement with pre- vious measurements (see Table1 ). As Fig.... ..."

### TABLE I. Comparison between the theoretical and exper- imental results for smooth non-cohesive particles D Material

1997

### Table 4: Bras for the three-dimensional projection of the FCHC model. The rst four rows are the hydrodynamic bras, and the last 14 present one choice for the kinetic bras.

1999

"... In PAGE 38: ... In fact, this weighting factor can be thought of as a direction-dependent particle mass mj, so that the three-dimensional projection of the FCHC model is as presented in Table 3. The model is required to conserve mass and three components of momentum, so that the four hydrodynamic bras are given by h jj = mj (114) h xjj = mjcjx (115) h yjj = mjcjy (116) h zjj = mjcjz: (117) These are shown in the rst four rows of Table4 in Appendix B, followed by a choice of twenty linearly independent kinetic bras. The corresponding kets are shown in Table 5 in Appendix B, and these can be used to construct a general analytic form for the state ket, jNi.... In PAGE 53: ... B Basis Bras and Kets for FCHC Model In this appendix, we present one possible choice for the bras and kets of the FCHC model for three-dimensional uid dynamics. The basis bras are shown in Table4 , and the basis kets are shown in Table 5.... In PAGE 54: ... The rst four rows are the hydrodynamic bras, and the last 14 present one choice for the kinetic bras. 1 48 0 B B B B B B B B B B B B B B B @ 16 8 8 16 8 8 16 8 8 16 8 8 16 8 8 16 8 8 12 0 24 12 0 0 12 0 0 12 0 12 12 0 0 12 0 12 24 12 36 24 12 12 24 12 12 24 12 12 24 12 12 24 12 12 6 6 6 6 18 18 6 6 6 6 0 6 6 6 6 6 0 6 36 12 12 12 12 12 36 12 12 60 24 12 36 12 12 60 24 12 0 0 0 48 36 12 0 0 0 24 18 6 0 0 0 24 18 6 29 7 19 5 11 5 5 7 1 29 16 13 29 7 1 29 16 13 14 10 10 10 14 2 10 14 2 14 10 4 14 10 2 14 10 4 6 6 18 6 6 6 6 18 18 6 0 6 6 6 6 6 0 6 18 6 6 6 6 6 18 6 6 18 12 6 18 6 18 42 12 6 9 3 15 15 15 9 9 3 3 9 0 9 9 3 3 33 24 9 36 12 60 36 12 12 36 12 12 36 0 36 36 12 12 36 24 12 22 2 22 26 22 14 2 2 14 22 14 16 2 2 14 22 14 8 28 20 20 20 28 4 4 4 4 28 20 8 4 4 4 28 20 8 24 24 24 24 0 0 24 0 0 24 12 12 24 0 0 24 12 12 12 0 0 12 0 0 12 0 0 12 12 0 12 0 0 12 12 0 8 4 4 16 8 8 8 4 4 8 10 2 8 4 4 8 10 2 12 12 12 12 12 12 12 12 12 12 0 12 12 12 12 12 0 12 1 C C C C C C C C C C C C C C C A Table 5: Kets for the three-dimensional projection of the FCHC model, corresponding to the choice of bras in Table4 . The rst four columns are the hydrodynamic kets, and the last 14 are the kinetic kets.... ..."

Cited by 2

### Table 1 Smooth solution: Errors and convergence rates in (u; p).

in Mixed Finite Element Approximation of Incompressible MHD Problems Based on Weighted Regularization

2004

"... In PAGE 28: ... The number of elements in the mesh Ti is proportional to 22i; the mesh-size hi of Ti is thus proportional to 2 i. If ei denotes the error in some component of the approximation on cycle i (in a suitable norm), the corresponding numerical rate of convergence is given by ri = log(ei=ei 1) log(hi=hi 1): In Table1 and Table 2, we show the errors in the indicated norms for the hydrodynamic variables (u; p) and the magnetic eld b, respectively, obtained with exponents = 0, = 0:5, and = 1. We also list the number of degrees of freedom (dofs) for each of the solution components.... ..."

### Table 2 Smooth solution: Errors and convergence rates in b.

in Mixed Finite Element Approximation of Incompressible MHD Problems Based on Weighted Regularization

2004

"... In PAGE 28: ... The number of elements in the mesh Ti is proportional to 22i; the mesh-size hi of Ti is thus proportional to 2 i. If ei denotes the error in some component of the approximation on cycle i (in a suitable norm), the corresponding numerical rate of convergence is given by ri = log(ei=ei 1) log(hi=hi 1): In Table 1 and Table2 , we show the errors in the indicated norms for the hydrodynamic variables (u; p) and the magnetic eld b, respectively, obtained with exponents = 0, = 0:5, and = 1. We also list the number of degrees of freedom (dofs) for each of the solution components.... ..."

### Table 12: Software packages on ship theory and hydrodynamics

2000

"... In PAGE 56: ... A list of the major commercial CAD / CAE packages for shipbuilding, available in the market today is listed in Table 11 below. Hydrodynamics and ship theory software is listed in Table12 while class / rules related software is listed in Table 13. Apart from the specific SW packages listed here there is a number of general pur- pose CAD / CAE packages are used in shipbuilding.... ..."