burgers_2012_ornl
burgers_2012_ornl,
"Parallel Collocation for Uncertainty Quantification on High Performance Systems",
a talk at Oak Ridge National Laboratory on 2 May 2012,
part of the SAMSI workshop "Uncertainty Quantification
for High-Performance Computing".
The following files were used:
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burgers_base.png,
the "base" solution of the steady Burgers equation.
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burgers_convergence.png,
study of the approximation of the quantity of interest, Q=U(X=0,T=3),
for the time dependent Burgers equation, using sparse grids and
the Monte Carlo method, for three values of viscosity.
-
burgers_grid.png,
a schematic of the time and space grid for Burgers equation with
an initial condition and periodic boundaries.
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burgers_ic.png,
a plot suggestion how an initial condition for the time dependent
Burgers equation could be defined by 9 data values and a spline.
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burgers_ic_perturb.png,
a plot showing how the solution profile at time = 3 of the
Burgers equation would be affected by changing any one of the
9 data values that define the initial condition.
-
burgers_shock.png,
a 3D plot showing how the inviscid Burgers equation can develop
a shock, causing the solution process to break down.
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burgers_time2.png,
the "base" solution of the time dependent Burgers equation, at T = 2.
-
burgers_time3.png,
the "base" solution of the time dependent Burgers equation, at T = 3.
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cc_3d.png,
images of the first 6 sparse grids in 3D, based on the Clenshaw Curtis points.
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fsu_logo.pdf,
a logo for FSU.
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sensitivity_a.png,
a rough exploration of the sensitivity of the "base" solution of
the steady Burgers equation with respect to the location of the
left boundary condition.
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sensitivity_alpha.png,
a rough exploration of the sensitivity of the "base" solution of
the steady Burgers equation
with respect to the value of the left boundary condition.
-
sensitivity_nu.png,
a rough exploration of the sensitivity of the "base" solution of the steady Burgers equation
with respect to the viscosity.
-
tanh_plot.png,
a plot of the hyperbolic tangent function, which is essentially the solution
to our simple steady Burgers equation.
-
x0_alpha.png,
a plot of the location where the solution to the steady Burgers equation
changes sign, as a function of the value of alpha, the value specified
at the left boundary.
Last revised on 02 February 2024.