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RSS feed for Figshare Profile David KetchesonPyClaw: Accurate, Scalable Solution of Hyperbolic PDEs in Python
https://figshare.com/articles/poster/PyClaw_Accurate_Scalable_Solution_of_Hyperbolic_PDEs_in_Python/1424952
This poster describes PyClaw (see www.clawpack.org), a Python package for solving hyperbolic PDEs. It was presented at the 2015 SIAM CSE conference.Numerical Analysis2015-05-26 09:27:03Nonlinear waves in periodic media
https://figshare.com/articles/poster/Nonlinear_waves_in_periodic_media/1284689
This poster advertises several recent theoretical developments the computational modeling of nonlinear waves in periodic materials, by the Numerical Mathematics Group at KAUST. The papers referenced in the poster are linked to below.Computational Physics, Numerical Analysis2015-01-05 19:46:36Advances in time integration of PDEs
https://figshare.com/articles/poster/Advances_in_time_integration_of_PDEs/1284690
This poster advertises several recent advances in numerical time integration for partial differential equations, including the development of one-step methods optimized for the strong stability preserving property and for linear stability properties, as well as analysis of optimal-order stability polynomials and an application to spectral differencing CFD.Numerical Analysis2015-01-05 19:32:01Simulation of a shock wave collision with low-density bubble
https://figshare.com/articles/media/Simulation_of_a_shock_wave_collision_with_low_density_bubble/1279431
This is an animation of a fluid dynamics simulation appearing in http://dx.doi.org/10.1137/110856976. The compressible Euler equations are solved using weighted essentially non-oscillatory methods and a Roe Riemann solver, all implemented in PyClaw. A shock wave enters from the left and collides with a low-density bubble. The simulation is reduced from 2 to 3 dimensions by assuming cylindrical symmetry.Computational Physics, Numerical Analysis2014-12-26 18:23:25Dispersion in layered periodic media
https://figshare.com/articles/figure/Dispersion_in_layered_periodic_media/1179200
From Two-dimensional wave propagation in layered periodic media
by Manuel Quezada de Luna and David I. Ketcheson
What happens when waves pass through a composite made of alternating horizontal layers of two materials? The four possible kinds of behaviour are shown here. Each quadrant shows an initially symmetric perturbation near (x,y)=(0,0) expanding in a medium with different properties. The inset shows the layered structure of the materials. The coloured plots and solid red lines are the result of numerical simulation. The dashed lines are theoretical predictions.
The top left shows a wave in a homogeneous medium for reference. If the two materials are different, the behaviour depends on their relative impedances and sound speeds.
If the impedances differ (bottom left), then waves propagating normal to the layers are dispersed (by reflections) -- note the trailing ripples in the red and black trace plot (along x=0) to the left. Meanwhile, waves traveling along the layers exhibit no such dispersion.
On the other hand, if the sound speeds differ (top right), waves propagating along the layers are dispersed (by diffraction) while waves moving normal to the layers are not. This effective dispersion is a new discovery and the main subject of the manuscript.
If both the sound speed and the impedance differ (bottom right), then waves in both directions are dispersed.See http://arxiv.org/abs/1309.6666.
Applied Physics, Computational Physics2014-09-24 06:27:45Diffractons reproducibility repository
https://figshare.com/articles/software/Diffractons_reproducibility_repository/963087
Reproducibility repository for paper on diffractons: see http://arxiv.org/abs/1312.4122.Applied Physics, Computational Physics, Solid Mechanics, Numerical Analysis2014-03-17 12:09:16RK-Opt 0.2 User Manual
https://figshare.com/articles/journal_contribution/RK_Opt_0_2_User_Manual/691021
This is the user manual for version 0.2 of RK-Opt, a package for the design of Runge-Kutta methods.Computational Physics2013-04-25 17:41:24Positive Numerical Solution of Differential Equations
https://figshare.com/articles/journal_contribution/Positive_Numerical_Solution_of_Differential_Equations/639184
A successful 3-year, 4-institution proposal submitted to KAUST's first round of faculty-initiated collaborations (FIC). The proposal aims to develop high order numerical methods for initial value problems that provably maintain positivity of the solution.Computational Physics2013-02-25 16:18:14High Performance Computing and High-Level Programming Concepts for Hyperbolic PDE Codes
https://figshare.com/articles/journal_contribution/High_Performance_Computing_and_High_Level_Programming_Concepts_for_Hyperbolic_PDE_Codes/639183
Successful proposal requesting funding from KAUST for the second [HPC]^3 meeting, which was held in early 2012.Applied Computer Science, Computational Physics2013-02-25 16:09:21Wave Propagation for Next-Generation Supercomputers
https://figshare.com/articles/journal_contribution/Wave_Propagation_for_Next_Generation_Supercomputers/639182
A successful proposal for 15M core-hours on the Shaheen BG/P supercomputer at KAUST, for simulations of solitary waves in periodic media using the PyClaw software based on Clawpack.Applied Computer Science, Computational Physics2013-02-25 16:03:11Riemann invariants of a stegoton wave train
https://figshare.com/articles/figure/Riemann_invariants_of_a_stegoton_wave_train/94019
Riemann invariants of a stegoton wave train, plotted in phase space.Applied Physics2012-08-02 21:52:02