Thanks for all the helpful perspectives everyone.
I actually heard back about a week ago that I was accepted at ANL! I seem to have been matched pretty well with my mentor. I have a couple more days to decide whether or not to accept, but I just had a question on what the policy is about...
I'm a senior and will be graduating this year with degrees in mechanical engineering and computational math. I kind of applied last minute, having heard of it before but not giving it much thought until a couple of weeks before the deadline.
Anyway, I feel that overall I'm a very strong...
Yup. I've still got an error in my code in the transformation part, so I'm going to take a look at it and re-edit the question :/ sorry for the confusion
Let F_{K}: \hat{K} \to K be defined as follows:
F_{K}(\hat{x},\hat{y}) = B_{K}\left[\begin{array}{c}
\hat{x}\\
\hat{y}\\
\end{array}\right] + b_{K}
i.e. F_{K} maps from (\hat{x},\hat{y}) to (x,y). In a more concrete sense, for this example take the following:
B_{K} =...
Hi all,
The context of this problem is as follows: I'm trying to implement a discontinuous finite element method and the formulation calls for the computation of line integrals over the edges of the mesh.
Anyway, more generally, I need to evaluate \int_{e}f(x,y)ds, where e is a line segment...
I'm trying to solve the equation
$$
\frac{\partial u}{\partial t} + \frac{\partial}{\partial x}\left(Cu\right) - \frac{\partial}{\partial x}\left(D\frac{\partial u}{\partial x}\right) = f(x,t)
$$
where C and D allow for linearity. I'm using a discontinuous Galerkin method in space and...
Preface: just want to start by saying that I'm 99% sure I'm having a stability issue here in the way I'm implementing the time step since if I set \Delta t \ge 1 then for any stopping time > 1, the algorithm works as it should. For time steps smaller than 1, as the time step gets smaller and...
Say we have a = \sup \{ a_{1}, a_{2}, a_{3}, ... \}. Then does this mean we can find some a_{n} \in \{ a_{1}, a_{2}, ... \} such that
|a - a_{n}| < \varepsilon
? My reasoning is that since a (the supremum) is the least upper bound of the set, we have to be able to find some member of the set...
Yes, but I'm not entirely seeing how that initial supposition will help. Is it okay to suppose there exists an i_{0} \in N such that z_{Ni_{0}} = 0 and that for all i \ne i_{0} z_{Ni} > 0? Like I said, I thought the point of the proof was to show that z_{N} \ge 0 is not a strong enough condition...
This was on my homework this week. I already turned it in but the professor hasn't posted the solutions yet so I'm genuinely curious what the answer is.
Homework Statement
The LP:
http://i48.tinypic.com/25svp6u.png
The problem:
http://i50.tinypic.com/nnnm2w.pngHomework Equations
c^{T}d =...
Need a good real analysis book for undergrad "intro" course
I'm a computational math major (double majoring with MechE) and basically I'm required to take an "intro" (400 level) real analysis sequence with the comp. math department. This course is shaping up to be an incredibly nasty surprise...