# All Questions

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### Strong vs. weak solutions of PDEs

The strong form of a PDE requires that the unknown solution belongs in $H^2$. But the weak form requires only that the unknown solution belongs in $H^1$. How do you reconcile this?
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### Prove that the set of maximizers are independent of parameter in the objective function

A maximization problem reads as $$J(y) = \sum_{k=1}^{K} \sigma_k^q(y) \mathop{\rightarrow}^{y} max$$ where $q \in [1,\infty]$ is a user-defined parameter and functions $\sigma_k, k=\{1,\dots,K\}$ ...
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I would like to plot the points contained in this file with Paraview, but can't seem to figure out how to do so. Each column in this file corresponds to a set of 2048 points on a 64x32 grid. Each ...
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### Necessary information that a toplogical optimisation solver needs to collecte from a pre-processed CAD model

I am developing a solver that gets a CAD model as entry and does the topological optimisation calculation on it. My solver is inspired by the open source codes presented in literature. Since it is ...
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### Find index for submatrix with maximum sum

Given an N-dimensional matrix A, I want to find an M<N dimensional index array I such ...
81 views

### Custom exponents for Lennard Jones in LAMMPS

I am trying to run an MD simulation using this generalized version of Lennard Jones. $$U(r) = \left(\frac{r_0}{r}\right)^A -\frac{A}{B}\left( \frac{r_0}{r} \right)^B$$ However, I do not know how ...
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### Complex differentiation of linear solvers

I have a linear system $$Ax=b$$ which I'm solving approximately, and I need to take the frechet derivative of x with respect to z. Were I solving the problem exactly (either analytically or to machine ...
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### Recommendation for a fixed-step ODE solver?

My problem involves the solution of a second-order ODE with a fixed-step (input and output). Specifically, this ODE is the radial part of Dirac and Schrödinger equation for a spherical symmetric ...
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### What guidelines should I follow for simulation software projects?

I am not sure whether this question belongs here, but I would like to give it a try and benefit from the experience of the people at scicomp.SE. From my experience, the software quality in ...
92 views

### fastest way to compute many small dot products

I have two n-by-3 blocks contiguous in memory ("n vectors of length 3") and I'd like to compute the dot product between each of the rows as fast as possible. In numpy, using ...
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### Does the k-th approximate solution of a stationary iteration belong to the k-th Krylov subspace?

For an stationary iteration method solving $Ax=b$ as follows: $$Mx_k = Nx_{k-1}+b,$$ I have known that when $M = I$, i.e., the Richardson iteration, the k-th solution $x_k = x_{k-1}+r_{k-1}$ is in ...
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### What is the standard, extrapolation, and modified version of Richardson iteration method?

I have been studying the iterative methods recently. For classical iterative methods solving $Ax=b$, I have seen that the most simplest iteration method is the so-called "Richardson iteration". But I ...
295 views