sparse_2011_ajou

sparse_2011_ajou, "Sparse Grids for Stochastic Integrals", a talk at Ajou University in Suwon, Korea, to the Workshop on Numerical Methods for Stochastic PDE's, on 24 September 2011.

My host was Professor Hyung-Chun Lee of the Mathematics Department.

An abstract for the talk is available in sparse_2011_ajou.txt.

• sparse_2011_ajou.tex
• sparse_2011_ajou.pdf

Some information on the sparse grid research I participated in is included in these references:

1. John Burkardt, Max Gunzburger, Clayton Webster,
   Reduced Order Modeling of Some Nonlinear Stochastic Partial Differential Equations,
   International Journal of Numerical Analysis and Modeling,
   Volume 4, Number 3-4, 2007, pages 368-391
2. Clayton Webster,
   Sparse Grid Stochastic Collocation Techniques for the Numerical Solution of Partial Differential Equations with Random Input Data,
   PhD Dissertation,
   Mathematics Department,
   Florida State University, May 2007

The following files constitute the LaTeX file used to create the slides:

• boxes_level0.png, a diagram in "level space" of the components of the level 0 sparse grid in 2D.
• boxes_level1.png, a diagram in "level space" of the components of the level 1 sparse grid in 2D.
• boxes_level2.png, a diagram in "level space" of the components of the level 2 sparse grid in 2D.
• boxes_level3.png, a diagram in "level space" of the components of the level 3 sparse grid in 2D.
• boxes_level4.png, a diagram in "level space" of the components of the level 4 sparse grid in 2D.
• cc_d2_o17x17.png, a PNG image of a 2D product grid made from two order 17 Clenshaw Curtis rules.
• cc_d2_o9x5.png, a PNG image of a 2D product grid made from order 9 and order 5 Clenshaw Curtis rules.
• cc_d3_level5.png, a view of a 3D Clenshaw-Curtis sparse grid, level 5.
• cc_sequence.png, a sequence of Clenshaw-Curtis rules.
• cc_sparse_2d.png, a Clenshaw-Curtis sparse grid of level 4.
• fsu_logo.pdf, a logo.
• gl_sequence.png, a sequence of Gauss-Legendre rules.
• level4_o1x17.png, a 1x17 product grid.
• level4_o3x9.png, a 3x9 product grid.
• level4_o5x5.png, a 5x5 product grid.
• level4_o9x3.png, a 9x3 product grid.
• level4_o17x1.png, a 17x1 product grid.
• levels.png, a diagram of the levels whose product rules combine to form a particular sparse grid.
• nco_sequence.png, a sequence of Newton-Cotes Open rules.
• pipeline.png, a corroded pipeline.
• sergey_smolyak.png, Sergey Smolyak.
• sm_gl_mc_p28_d6.png, error decay for Smolyak, Legendre and Monte Carlo on problem 28, dimension 6.
• sm_gl_mc_p28_d10.png, error decay for Smolyak, Legendre and Monte Carlo on problem 28, dimension 10.
• smgw1.m, a skeleton MATLAB program for using sparse grid software.
• smgw2.m, a skeleton MATLAB program for using sparse grid software.
• smolyak_p28.png, error decay for a Smolyak sparse grid on problem 28.
• stochastic_mc.pdf, Monte Carlo performance on a stochastic PDE.
• stochastic_mc_and_sm.pdf, Monte Carlo verse Smolyak performance on a stochastic PDE.
• weathervane.png, a weathervane.