Top new questions this week:
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[UPDATING] Here is a solution based on the answer proposed by professor Bangerth down below. To describe what I am trying to do, first rewrite the question into $$\max_X\|(I-\alpha X)^{-1}X\circ AE\|…
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In any FEM problem involving mechanics, we try to solve the differential equation for the displacement field, $u$ given the force vector in the nodes, $F$. In industry, we often see our automobiles …
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I am dealing with a non-trivial Riemannian metric $H$ defined on a particular subset of Euclidean space ($E \subset \mathbb{R}^n$). I was able to show the Riemannian manifold $(E,H)$ is geodesically …
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Consider the following nonlinear diffusion problem, $$ \frac{\partial u}{\partial t} = x^{-2}\frac{\partial}{\partial x}\left(x^2 u^4 \frac{\partial u}{\partial x}\right), \quad 0 < x < 1 $$ We …
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I’m attempting to solve a strange differential equation problem. My goal is to know if there are kinds of ODE solver packages to solve this kind of problem. I’m solving a 1D Partial Differential …
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I have lots of difficulties trying to make a phase plot for the motion of the particle trapped in Lennard-Jones potential: $$V(q)=\epsilon\left[\left(\frac{q_\mathrm{min}}{q}\right)^{12}-2\left(\frac{…
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A recent question in Astronomy SE Numerical Programming using odeint takes more than 17 minutes got me interested in looking closer at SciPy’s odeint. The problem is a modified orbital mechanical …
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Greatest hits from previous weeks:
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I know that the Nitsche’s method is a very attractive methods since it allows to take into account Dirichlet type boundary conditions or contact with friction boundary conditions in a weak way without …
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Does anyone have recommendations on a usable, fast C++ matrix library? What I mean by usable is the following: Matrix objects have an intuitive interface (ex.: I can use rows and columns while …
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What is counterpoise correction exactly ? Can you explain when it is needed and why ?
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$A$ and $B$ are $n \times n$ matrices and $v$ is a vector with $n$ elements. $Av$ has $\approx 2n^2$ flops and $A+B$ has $n^2$ flops. Following this logic, $(A+B)v$ should be faster than $Av+Bv$. Yet,…
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I am doing a molecular dynamics simulation. I need to assign initial velocities to the atoms. I want to assign the initial velocities which follow the Maxwell-Boltzmann distribution. How do I …
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This might be a question better suited for the Software Recommendations side of S.E., however I do believe that people who frequent this part of S.E. are more likely to be able to answer this question….
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Related question: State of the Mac OS in Scientific Computing and HPC A significant number of software packages in computational science are written in Fortran, and Fortran isn’t going away. A …
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Can you answer these questions?
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I’m quite new to the smoothed particle hydrodynamics method, so I’m trying to find Matlab or Python code to help me understand it. Specifically, I want to know how to solve the one-dimensional …
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I am trying to calculate classical trajectories for a single positive ion and a single electron inside an RF trap. Therefore, I am dealing with a two-body system that possesses: Coulomb potential …
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