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1500 questions
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Universities known for computational physics
I am very interested in computational physics and it is great lot of fun studying these topics. Since I am planning to go one semester abroad, I was wondering what universities are known for computational physics? Especially in regard to…
ftiaronsem
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Illustrative examples of mimetic finite difference methods
As much as I try to find a concise explanation on the internet, I can't seem to grasp the concept of a mimetic finite difference, or how it even relates to standard finite differences. It would be really helpful to see some simple examples of how…
Paul
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Implicit finite difference schemes for advection equation
There are numerous FD schemes for the advection equation $\frac{\partial T}{\partial t}+u\frac{\partial T}{\partial x}=0$ discuss in the web. For instance here:
http://farside.ph.utexas.edu/teaching/329/lectures/node89.html
But I haven't seen anyone…
tiam
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How is B3LYP implemented in Gaussin 0*, GAMESS-US, Molpro, ... etc?
Specifically I want to extend work involving B3LYP started with Gaussian 03 but continued with GAMESS-US. The energies provided by the default B3LYP methods are not the same. There is a discussion about this in the GAMESS-US manual (Further…
Yann
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SciComp Modeling Jobs
The meta seemed to suggest that career advice is ok . . . so here goes.
I have a couple of close friends in the ML and mathematical modeling fields just finishing PhD's and starting out on the job hunt. While both are quite qualified and talented,…
meawoppl
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What is the purpose of the test function in Finite Element Analysis?
In the wave equation:
$$c^2 \nabla \cdot \nabla u(x,t) - \frac{\partial^2 u(x,t)}{\partial t^2} = f(x,t)$$
Why do we first multiply by a test function $v(x,t)$ before integrating?
Andy
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Should I rent computing resources, or buy my own computers
Since this question is related to computation, I decided to post here. Hopefully it will be seen as appropriate.
I've just started running atmospheric and oceanic models, and I realize that I need more cores, memory, and disk space than my current…
user4624937
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What is the fastest algorithm for computing the inverse matrix and its determinant for positive definite symmetric matrices?
Given a positive definite symmetric matrix, what is the fastest algorithm for computing the inverse matrix and its determinant? For problems I am interested in, the matrix dimension is 30 or less.
High accuracy and speed is really necessary.…
Orders
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Are direct solvers affected by the condition number of a matrix?
If I were to solve a relatively small problem, that is, a problem that can be handled by a direct method like LU, then does the condition number of the linear operator affect the accuracy of the solution?
One of the research problems I am working on…
Justin
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I/O Strategies for computational problems with large data sets?
My research group focuses on molecular dynamics, which obviously can generate gigabytes of data as part of a single trajectory which must then be analyzed.
Several of the problems we're concerned with involve correlations in the data set, which…
aeismail
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Why isn't my Matrix-Vector Multiplication Scaling?
Sorry for the long post but I wanted to include everything that I thought was relevant in the first go.
What I want
I am implementing a parallel version of Krylov Subspace Methods for Dense Matrices. Mainly GMRES, QMR and CG. I realized (after…
Inquest
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Puzzling remark about stability region of fifth-order Runge-Kutta method
I came across a puzzling remark in the paper
P. J. van der Houwen, The development of Runge-Kutta methods for partial differential equations, Appl. Num. Math. 20:261, 1996
On lines 8ff on page 264, van der Houwen writes:
"For the Taylor polynomials…
Brian Zatapatique
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The Remez Algorithm
The Remez algorithm is a well-known iterative routine to approximate a function by a polynomial in the minimax norm. But, as Nick Trefethen [1] says about it:
Most of these [implementations] go back many years and in fact, most of them do not…
Hans W.
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How to avoid catastrophic cancellation in python function?
I am having trouble implementing a function numerically. It suffers from the fact that at large input values the result is a very large number times a very small number. I am not sure if catastrophic cancellation is the correct term so please…
Dipole
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Are there any open source inverse-based multilevel ILU implementations?
I am very impressed with the serial performance of multilevel inverse-based ILU preconditioners, particularly for heterogeneous Helmholtz, but I am surprised to not be able to find any open source implementations. In particular, ILUPACK makes…
Jack Poulson
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