AJOU_SPARSE_2011.TEX
Sparse Grids for Stochastic Integrals

I gave a talk on 24 September 2011, at Ajou University in Suwon, Korea, to the Workshop on Numerical Methods for Stochastic PDE's. My host was Professor Hyung-Chun Lee of the Mathematics Department. The talk was titled:

Sparse Grids for Stochastic Integrals.

An abstract for the talk is available in ../../ajou_sparse_2011_abstract.txt.

A PDF version is available as ../../presentations/ajou_sparse_2011.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,
   bgw_ijnam_2007.pdf.
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,
   webster_thesis.pdf.

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

• ajou_sparse_2011.tex, the main LaTeX file;
• 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_sports_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.
• multimedia.sty, a LaTeX style file;
• 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.