Jobs for masters in Computational Science

[Poopsilon]

So I have the opportunity to spend two years getting a masters in computational science at the university I got my bachelors at. Its through the math dept. and my undergrad degree was in math so it shouldn't be a problem getting in. If I do it I intend to do my interdisciplinary concentration in physics (fluid dynamics, mechanics, heat transfer etc.).

Thus it will be a lot of courses in stuff like:
-PDE's
-Non linear waves
-Scientific modeling
-Scientific computing
-Classical mechanics
-Electromagnetism
-Computational physics
etc.

Keep in mind this will be on top of a very strong bachelor's degree in math (big focus on analysis and continuous mathematics in general).

Thus I would be looking for careers in mathematical modeling (I'm assuming!), I'm not sure what the difference is between that and computational science. Can someone let me know how I could expect to fare on the job market with this type of background? I've searched comp. science/physics on various job search sites and it seems like everything that comes up is for stuff associated with universities and they all want Phds.

The reason I like this degree is because I'm hoping it will allow me to explore other areas of science and allow me to apply my math expertise to them in creative ways. But can I break into this field with just a masters?

 

[Astronuc]

Mathematical modeling could be done analytically as well as numerically, but often it is mathematical or computational science, e.g., computational physics, which can be done on various scales, e.g., quantum (either subatomic or atomic), molecular, mesoscale, or continuum/engineering scales.

 

[Poopsilon]

Hi Astronuc, after seeing your name come up in some of my searches for similar posts I was hoping you would respond to this thread. Could you explain what you mean by analytically? Also do you have any information you could impart to me with regard to some of my other questions in my original post?

 

[Astronuc]

Analytic (some folks like me say analytical) solutions implies that the problem (usually stated by a differential equation with initial and/or boundary values) solved by an exact solution that describes the behavior (physics) of what is being modeled.

In physics and engineering the usual terminology is "analytical solution", a solution found by evaluating functions and solving equations; systems too complex for analytical solutions can often be analysed by mathematical modelling and computer simulation.

http://en.wikipedia.org/wiki/Closed-form_expression
http://www.myphysicslab.com/numerical_vs_analytic.html
http://mathworld.wolfram.com/Analytic.html
http://mathworld.wolfram.com/ExactSolution.html
http://tutorial.math.lamar.edu/Classes/DE/Exact.aspx
http://farside.ph.utexas.edu/teaching/329/lectures/node48.html
http://home.comcast.net/~cmdaven/burgers.htm

Simple ODEs and PDEs may be solved with analytical solutions, especially if they have constant coefficients or good functions.
http://ejde.math.txstate.edu/Volumes/2003/79/adibi.pdf

Numerical solutions are usually necessary for many applications in compuational physics, particularly for non-linear and/or systems of coupled differential equations.

http://www.math.chalmers.se/cm/education/courses/0405/ala-b/tex/diffequation.pdf

Most of the applications/problems in computational physics (mechanics (structural mechanics), fluid dynamics, chemistry, material science, . . . . ) are highly non-linear and one cannot develop an analytic solution, except for some highly idealized cases. This is particularly the case where coefficients of the differential equations are subject to change, which means they are functions of the dependent variables in addition to the independent variables (position, time).

An example is the heat conduction equation where the thermal conductivity is a function of temperature, particularly when it is a nonlinear function, with path-dependencies (trajectory in state space). Other examples include turbulent flow, cracking in solid materials, chemical reactions (e.g., corrosion) in a fluid or solid, lattice damage in a material, . . . . .

Some of the most challenging problems include dynamic/impact analysis, or plasma simulation (particularly instability simulation), computational astrophysics (e.g., modeling CMEs, . . . ), . . . .

http://www.mathworks.com/mathematical-modeling/technicalliterature.html


It's important to 'know' the underlying theory in computational science rather than simply entering input and processing output, although the latter is important with respect to understand the problem.

Perhaps this might be of interest - Mathematics Handbook for Science and Engineering by Råde and Westergren
http://www.studentlitteratur.se/o.o.i.s/?id=1488&artnr=2505-05&what=toc&csid=66&mp=4918

 

[Poopsilon]

Ah ok, that's what I suspected it might be.

 

[Astronuc]

I recently attended a presentation of MOOSE by INL staff. There is growing interest in this computational system.
http://www.inl.gov/research/moose/

Multiphysics Object-Oriented Simulation Environment, or MOOSE
www.inl.gov/technicalpublications/Documents/4336141.pdf

http://users.ices.utexas.edu/~vikram/research_files/Adjoints/report.pdf

http://ocw.mit.edu/courses/mathemat...erential-equations-spring-2009/lecture-notes/