Andrew M. Bradley Postdoctoral Scholar, Geophysics; CEES Numerical Analyst My principal research interest is developing mathematical software in support of science and engineering. Currently I am a postdoc in Prof. Paul Segall's group. I'm also a Numerical Analyst (25% time) with Stanford's Center for Computational Earth & Environmental Science (CEES).

CEES Numerical Analyst:

As the Numerical Analyst for CEES, I'm happy to help School of Earth Sciences researchers with any of a large range of computational math problems. Examples: numerical formulations of mathematical problems, solving equations, speeding up code through software or algorithm changes, programming issues (including bugs), floating point issues, parallelization, error analysis.

I'm also happy to give tutorials at research group meetings. Example topics: using sparse matrices effectively, solving (non)linear least squares problems efficiently, constrained optimization, efficient computation of boundary element methods, the adjoint method, checkpointing, parallelization, solving linear equations.

Email me to set up one-on-one consulting. We can discuss your ideas, look at your code, or (for larger problems) discuss a collaboration.

Software:

hmmvp0.16, a package to construct an H-matrix and compute matrix-vector products of the form B*x, B(rs,:)*x, and B(rs,cs)*x(cs). [Coming soonish: a pure-C++ version (with Matlab bindings).]

kfgs0.2, a Matlab package to compute the gradient of the log likelihood function from a Kalman filter.

Some individual files. Highlights: pointers in Matlab, a nice peak finder, a mop.

Tutorials:

A tutorial on the adjoint method.

A code-based tutorial on some numerical linear algebra operations in Matlab.

A code-based tutorial (with solutions) on elementary, but important, concepts concerning the stability and order of accuracy of ODE integration methods. This is appropriate for a one-session review in a science class, for example.

Publications:

K. M. Johnson, D. R. Shelly, and A. M. Bradley (2013), Simulations of tremor-related creep reveal a weak crustal root of the San Andreas Fault, Geophys. Res. Lett., doi:10.1002/grl.50216, in press. [link]

P. Segall and A. M. Bradley. "Slow-slip evolves into megathrust earthquakes in 2D numerical simulations," Geophys. Res. Lett., 39(18), doi:10.1029/2012GL052811, 2012. [pdf]

P. Segall and A. M. Bradley. "The role of thermal pressurization and dilatancy in controlling the rate of fault slip," J. of Applied Mechanics, 79(3), doi:10.1115/1.4005896, 2012. [pdf]

N. M. Bartlow, S. Miyazaki, A. M. Bradley, and P. Segall, "Space-time correlation of slip and tremor during the 2009 Cascadia slow slip event," Geophys. Res. Lett. (2011), doi:10.1029/2011GL048714. [pdf]

P. Segall, A. M. Rubin, A. M. Bradley, and J. R. Rice, "Dilatant strengthening as a mechanism for slow slip events," J. Geophys. Res., 115 (2010), B12305, doi:10.1029/2010JB007449. [pdf]

A. M. Bradley and L. Wein, "Space debris: Assessing risk and responsibility," Adv. in Space Res. 43 (2009). [pdf; code to run model. Figs. 3a,b have label errors: in 3a, Intact-Intact should be switched with Cat. Intact-Fragment; in 3b, Noncat. should be switched with Cat.. Fig. 5 erroneously shows (solid line) steady-state, rather than maximum, lifetime risk; these differ only for compliance rate near 1: see this version for details.]

Reports:

A. M. Bradley, "H-Matrix and Block Error Tolerances". [arXiv]

A. M. Bradley and W. Murray, "Matrix-Free Approximate Equilibration". [arXiv]

Posters:

AGU 2012 poster.

AGU 2011 poster.

Thesis:

Algorithms for the Equilibration of Matrices and Their Application to Limited-Memory Quasi-Newton Methods, Ph.D. Thesis, Stanford ICME, May 2010. [pdf; ssbin and snbin from Chapter 2 (with improvements)]