Top new questions this week:
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Consider the following 1D problem \begin{align*} \begin{cases} \displaystyle -\frac{d^2u}{dx^2} = f(x), \hspace{0.5cm} x\in (a,b) \\[4mm] u(a) = u_{a}, \ \ u(b) = u_{b} \end{cases} \end{align*} I …
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I was looking at the matlab function pinv.m for the compuation of the pseudoinverse. The code uses the singular values decomposition. $$ A = U D V $$ When looking for non-zero diagonal elements it …
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I have coded a simple program for a root finding problem using Halley’s method. Here is the code: …
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What are some reasons for approximating a (e.g. parabolic) PDE using the space-time method, with continous finite elements in time, vs discontinuous finite elements in time? Are there e.g. significant …
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I want to run a block Lanczos block-tridiagonalization on a hermitian, sparse matrix (of relatively small size $\sim 10^2 \times 10^2$). However the matrix typically has many eigenvalues that are …
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Let a function $u \in H^1_0(\Omega)$ defined by its values at the mesh nodes. Can we compute its Laplacian using the matrix resulting from the finite elements discretization of Laplace’s equation? I …
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I want to numerically solve integrals of the form, $$ I = \int_a^b x^k f(x) dx $$ where $k$ is a given integer, and $f(x)$ is a cubic polynomial, expressed as, $$ f(x) = c_0 + c_1 (x – a) + \frac{c_2}{…
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Greatest hits from previous weeks:
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I need to write some data from a computation, that will be read later by Paraview (.vtu or vtk file). When it comes to file size , should I go for the ASCII format or the Binary format ?
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I work in computational science, and as a result, I spend a non-trivial amount of my time trying to increase the scientific throughput of many codes, as well as understanding the efficiency of these …
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Fortran has a special place in numerical programming. You can certainly make good and fast software in other languages, but Fortran keeps performing very well despite its age. Moreover, it’s easier to …
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I just started studying FEM in a more structured basis compared to what I used to do during my undergraduate courses. I am doing this because, despite the fact that I can use the “FEM” in commercial (…
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How to find all roots of an equation in Matlab? I tried and it gave me just one of the roots. For example: my equation is $F(x)=0$ where …
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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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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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Can you answer these questions?
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Consider system of ordinary differential equations $$ \begin{align} \frac{dx}{dt}&=\sigma(y-x)\\ \frac{dy}{dt}&=\rho x-y-xz\\ \frac{dz}{dt}&=xy-\beta z \end{align} $$ with $\sigma=10$, $\…
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Let’s define scaling, as how linear the speedup of using more than one GPU or CPU is. For example, having 2 GPUs gives you 2x faster execution time. I have noticed that in many software (e.g. …
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I am currently coding a solution to the following PDE: $\frac{\partial T }{\partial t} =\frac{\partial}{\partial \theta}(A(\theta ,\phi )\frac{\partial T }{\partial \theta}) +\frac{\partial }{\partial …
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