5 ms·

Broadly speaking, the field is Computational Science and Engineering (CS&E). It occupies the space between applied mathematics, engineering, physics, and softwa

Broadly speaking, the field is Computational Science and Engineering (CS&E). It occupies the space between applied mathematics, engineering, physics, and software (high and low level). CS&E picks up around where physicists write the equations they would like to solve and handles aspects like discretization, solvers, optimization, and uncertainty quantification. Software is needed for each of these steps, and it usually needs to be high performance, scale on diverse parallel architectures, and be extensible to accommodate new problems. Something that I find especially interesting is adjusting the discretization so that it is better suited to the hardware that is available (e.g. reducing memory bandwidth requirements in exchange for more flops which are relatively cheaper) while maintaining scalability and robustness. Looking at the plenary talks [1] for the upcoming ICIAM meeting might provide some perspective on the field (perhaps slightly biased towards applied mathematics). Part of the difficulty in finding qualified people is that there are few universities with courses aimed at the core of CS&E. Instead, each discipline teaches a subset as viewed from their own corner. The whole is definitely greater than the sum of the parts. The status quo curriculum is a recognized problem that will hopefully be resolved in the next few years. [1] http://www.iciam2011.com/index.php?option=com_content&view=article&id=12&Itemid=26 http://www.iciam2011.com/index.php?option=com_content&vi...

Plimsoll 15y ago
You got me interested. I'm personally studying theoretical physics and have studied all computational courses they give at my university. Seeing these computational tasks from other angle would certainly be pleasant experience. Can you recommend any comprehensive book about CS&E or link to some university's course listing (assuming such list has recommended readings for those courses)
- jedbrown 15y ago
  Hmm, I can't think of a single general book that could be considered general CS&E. There are many great books in, e.g. numerical linear algebra, domain decomposition methods, finite element or finite volume methods, etc. While these are quite valuable, I never felt like they really changed my perspective on the field. So instead, here are some less conventional starting points. Any talk by David Keyes. This one is mostly directed towards a physics audience (it's not specifically about ice sheets). http://www.columbia.edu/~kd2112/IceSheets09.pdf http://www.columbia.edu/~kd2112/IceSheets09.pdf This one is directed at a computing audience http://www.cespr.fsu.edu/lighthill/keyes_publiclecture.pdf http://www.cespr.fsu.edu/lighthill/keyes_publiclecture.pdf (http://www.youtube.com/watch?v=RYxNVX9SYtk http://www.youtube.com/watch?v=RYxNVX9SYtk (skip ahead a few minutes to skip the introduction)). This review paper has more background from an implicit solvers perspective and lots of citations for more background. http://www.cs.odu.edu/~keyes/papers/jfnk.pdf http://www.cs.odu.edu/~keyes/papers/jfnk.pdf An open source library. I learned a lot from experimenting with methods and reading PETSc source code. (And soon started developing the library too.) http://mcs.anl.gov/petsc http://mcs.anl.gov/petsc Algorithms like multigrid, fast multipole, and WENO that are unreasonably better than naive alternatives (for appropriate problems). Note: CS&E is significantly bigger than partial differential equations, but PDEs are still a very central component.
rfrey 15y ago
Thanks, a concise and extremely informative answer.

Plimsoll 15y ago

You got me interested. I'm personally studying theoretical physics and have studied all computational courses they give at my university. Seeing these computational tasks from other angle would certainly be pleasant experience. Can you recommend any comprehensive book about CS&E or link to some university's course listing (assuming such list has recommended readings for those courses)

jedbrown 15y ago
Hmm, I can't think of a single general book that could be considered general CS&E. There are many great books in, e.g. numerical linear algebra, domain decomposition methods, finite element or finite volume methods, etc. While these are quite valuable, I never felt like they really changed my perspective on the field. So instead, here are some less conventional starting points. Any talk by David Keyes. This one is mostly directed towards a physics audience (it's not specifically about ice sheets). http://www.columbia.edu/~kd2112/IceSheets09.pdf http://www.columbia.edu/~kd2112/IceSheets09.pdf This one is directed at a computing audience http://www.cespr.fsu.edu/lighthill/keyes_publiclecture.pdf http://www.cespr.fsu.edu/lighthill/keyes_publiclecture.pdf (http://www.youtube.com/watch?v=RYxNVX9SYtk http://www.youtube.com/watch?v=RYxNVX9SYtk (skip ahead a few minutes to skip the introduction)). This review paper has more background from an implicit solvers perspective and lots of citations for more background. http://www.cs.odu.edu/~keyes/papers/jfnk.pdf http://www.cs.odu.edu/~keyes/papers/jfnk.pdf An open source library. I learned a lot from experimenting with methods and reading PETSc source code. (And soon started developing the library too.) http://mcs.anl.gov/petsc http://mcs.anl.gov/petsc Algorithms like multigrid, fast multipole, and WENO that are unreasonably better than naive alternatives (for appropriate problems). Note: CS&E is significantly bigger than partial differential equations, but PDEs are still a very central component.

rfrey 15y ago

Thanks, a concise and extremely informative answer.