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1500 questions
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Why performance is given in Gflop/s rather than actual time in seconds

While reading many research-papers comparing parallel implementations of algorithms on different machines/architectures, I have noticed that the performance comparison is always listed in terms of GFlop/s and not the actual wall-clock time for the…
gdawg
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Proving convergence of adaptive finite elements - min res FEM?

There's a body of work out there dealing with the discrete convergence of adaptive finite element methods using error estimators. Most deal with proving the property $\|u-u_{k+1}\|_U \leq (1-\alpha) \|u-u_{k}\|_U, \quad 0<\alpha < 1$ by relying on…
Jesse Chan
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A simple function for generating a nonuniform mesh in 1D with fixed minimum spacing

I am solving an advection-diffusion problem where the solution variable is mostly flat apart from a small region near the centre of the domain where there are shape gradients. I would like to generate mesh faces for 1D finite volume cells (see…
boyfarrell
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What algorithms are known for computing exact eigenvalues for rational matrices?

Let $M$ be a matrix which has the following properties: 1) $M$ is Hermitian 2) $M$ has only rational entries 3) $M$ is known to have rational eigenvalues What algorithms are there for exactly computing the eigenvalues of $M$? Mathematica seems to be…
dan8394
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linear independence constraint qualification: what to do when they don't hold?

I want to solve a general nonlinear constrained optimization problem $$\min_q\ f(q)\quad \textrm{s.t.}\quad g_i(q) = 0,\ h_j(q) \geq 0.$$ The problem is that while the equality constraints $g_i(q)$ are individually smooth and have non-vanishing…
user168715
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Python scripting in Paraview

I've been using the basic visualization features of Paraview. Now, I want to go further by writing python macros to handle some specific tasks. My question for the advanced users: Are there any known guides to get a proper start ? Already…
SAAD
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Unknown domain in optimization problem

I have a similar question compared to this post. I am trying to maximize a function, which is a black-box to me. I have tools of gradient-free methods; in fact, this problem is reasonably smooth that I can even use the numerical approximation of…
Shawn Wang
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Continuation procedure to solve for a 2D curve that satisfies f(x,y) = 0

I have some function of $R^2$, that must be numerically computed. For instance, I might be interested in a real-valued contour integral that begins from (x,y) = 0. $$ f(x,y) = \Re\left[\int_0^{x + iy} t^3 + t^5 \, dt \right] $$ where $\Re$ is for…
TSGM
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Significance of p-convergence studies

Consider a method (e.g., FEM) with variable approximation order $p$. Now, we know that the optimal order of convergence is given by $$e = C h^{p+1},$$ where $h$ denotes the mesh size and a constant $C$ that does not depend on $h$. As a result, we…
bigge
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Computing $\sin(\pi/2)$ numerically

I'm trying to understand the types of numerical errors, to do this I want to calculate $\sin(\pi/2)=1$ numerically. To do this I use the Taylor series of $\sin(x)$ in 0: $$\sin(x)=x-\frac{x^3}{6}+\frac{x^5}{120}-\frac{x^7}{5040}+ \ldots$$ To make…
Msegade
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Measures of parsimony for numerical models?

There are hundreds of different types of performance measures for numerical models, many of which are applicable to many different types of models. But a good model doesn't just perform well, it performs well while being as simple as possible, and…
naught101
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Hashing algorithms/implementations for Monte Carlo simulation

To summarise this question in advance, I'm looking for a good hash function that is suitable for generating pseudo-random numbers in Monte Carlo simulations. This means it should be reasonably fast (so something like md5 is ruled out) but have…
N. Virgo
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Local inversion of small matrices on GPUs?

I don't know much about GPU computing at the moment, so please pardon the simple question. Can one invert local matrices in parallel on the GPU? CUBLAS doesn't seem to support factorization, and most of the LU/QR/Chol libraries I've found for GPUs…
Jesse Chan
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What computational methods would allow me to rank 2D surfaces (with examples)

I have a program which compares the similarity of two images for different positions, so my surface consists of points which correspond to X and Y translations each with a value (mutual information). Here is an example of a surface I want to be…
Luka Milic
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Finite elements for Stokes with traction boundary conditions

Suppose we are given the Stokes equations with Neumann conditions on part of the boundary: $-\nabla\cdot\boldsymbol{\sigma} = \mathbf{f}, \quad \text{and} \quad \nabla\cdot \mathbf{u} = 0 \quad \text{in} \quad \Omega$ Here $\boldsymbol{\sigma}…
Christian Waluga
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